Book of Abstracts - GAMM 2012 - Technische Universität Darmstadt

83rd Annual Scientific Conference of the International
Association of Applied Mathematics and Mechanics
Book of Abstracts
Version for use on a standalone computer
Technische Universität Darmstadt
March 26 – 30, 2012
Hans-Dieter Alber Cameron Tropea
Unter Mitwirkung von
Anke Böttcher, Dieter Bothe, Petra Fuhrmann, Peter Hagedorn, Christiane Herdler,
Carsten Juretzka, Natalia Kraynyukova, Richard Markert, Anke Meier-Dörnberg,
Birgit Neuthe, Martin Oberlack, Stefan Ulbrich, Nicole Wagner

Prandtl Lecture 3
Prandtl Lecture
Ludwig-Prandtl-Gedächtnisvorlesung Mon, 13:30–14:30
Chair: Cameron Tropea dmstm–spectrum, plenary lectures
Aero-Struktur-Dynamik großer Flugzeugtragflügel in schallnaher Strömung
Josef Ballmann (RWTH Aachen) Schedule
Das Strömungsfeld über den Tragflügeln großer Passagierflugzeuge, die mit der Machzahl Ma=0,8
bis 0,85, d. h. mit 80 bis 85 % der Geschwindigkeit des Schalls in der umgebenden Luft, fliegen,
ist durch lokale Überschallgebiete gekennzeichnet, die stromab durch Verdichtungsstöße abgeschlossen
sind. Diese Stöße beschleunigen große Luftmengen, die sich bei Windstille ursprünglich
in Ruhe befanden, in Flugrichtung und verursachen den sogenannten Wellenwiderstand, der den
neben der Reibung in den Strömungsgrenzschichten der Luft an der Flugzeugoberfläche den wichtigsten
Anteil des Gesamtwiderstandes und damit des Brennstoffverbrauchs im Reiseflug bildet.
In dem Bestreben, diesen Widerstandsanteil durch Verminderung der Stärke der am Ende eines
Überschallgebietes unvermeidlichen Stöße zu minimieren, wurden sogenannte überkritische
Profile der Tragflächen entwickelt, die auf der Oberseite einen großen Bereich mit nur schwacher
konvexer Krümmung aufweisen und sehr dünn sind. Je schlanker aber die Profile und je größer die
Spannweiten der Flügel sind, desto wichtiger wird es aus Sicherheitsgründen und zur Erzielung
eines wirklichkeitsnahen aerodynamischen Optimums, die Verformungen der Tragflügel im Flug
schon in den aerodynamischen Entwurf einzubeziehen. Gleichzeitig gilt es, zeitabhängige dynamische
Wechselwirkungen zwischen Strömungs- und Strukturkräften, etwa durch Böeneinwirkung
oder Strukturschwingungen, im katastrophalen Fall Flattern oder, stark das Material ermüdend,
Grenzzyklusschwingungen, schon in der Entwurfsvorhersage zu beherrschen und auszuschließen,
sodass die Sicherheit und der Reisekomfort der Passagiere über eine lange Lebensdauer des Flugzeugs
jederzeit gewährleistet bleiben.
Die außer der Machzahl für experimentelle und rechnerische Vorhersagen wichtigste Strömungskennzahl
ist die Reynoldszahl, die als Quotient aus dem Produkt der Fluggeschwindigkeit
mit einer charakteristischen Abmessung des Flugzeugs dividiert durch die dynamische Viskosität
des Strömungsmediums definiert ist und bei Großraumflugzeugen Werte von bis zu Re = 80 · 106
erreicht. In Windkanälen für Modelle im verkleinerten Maßstab, etwa 1:30 bei „großen“ Modellen,
ist das Erreichen solcher Werte nur möglich, indem man die dynamische Zähigkeit des Gases
entsprechend herabsetzt. Das gelingt mit Stickstoff als Testgas durch Herunterkühlen auf minus
150 o C und Erhöhen des Drucks im Windkanal auf 4 bar. Das sind auch für Versuchsmodelle sehr
unwirtliche Bedingungen. Auf der Welt existieren seit jetzt etwa 20 Jahren zwei Windkanäle, in
denen diese Bedingungen möglich sind, der „European Transonic Windtunnel“ (ETW) in Europa
und der NTF („National Transonic Facility“) in den USA. Im Vortrag werden die Entwicklungen
der theoretisch-numerischen und experimentellen Methoden der Aeroelastik seit Prandtl bis heute
kurz gestreift. Vertiefter eingegangen wird auf die an der RWTH Aachen in den letzten Jahren
vorangetriebenen Methodenentwicklungen für die numerische Lösung aero-struktur-dynamischer
Probleme der Luftfahrt mithilfe algebraisch gekoppelter Finite-Volumen-Verfahren für das Strömungsfeld
und Finite-Elemente-Methoden für die umströmte Struktur sowie die Anstrengungen
zur Gewinnung aero-struktur-dynamischer Windkanaldaten im ETW bei realen Mach- und
Reynoldszahlen, die zu einem Teil inzwischen zur weltweiten Nutzung für die Überprüfung numerischer
Methoden für die schallnahe Aero-Struktur-Dynamik bereit gestellt wurden. In einer
nach dem Vorbild der Reihe „Drag Prediction Workshop“ (DPW) unter dem Dach des AIAA neu
gegründeten Reihe mit dem Titel „Aero-elastic Prediction Workshop“ (AePW) gehören sie zu den
wichtigsten ersten Testfällen.

4 Plenary Lectures
Plenary Lectures
Plenary Lecture 1 Mon, 14:30–15:30
Chair: Christian Wieners dmstm–spectrum, plenary lectures
Preconditioning for PDE-constrained optimization
Andy Wathen (University of Oxford) Schedule
Many control problems for PDEs can be expressed as Optimization problems with the relevant
PDEs acting as constraints. As is being discovered in other areas such as multi-physics, there
seem to be distinct advantages to tackling such constrained Optimization problems ‘all-at-once’
or with a ‘one-shot’ method. That is, decoupling of the overall problem in some loosely coupled
iterative fashion appears to be a rather poorer approach than to compute on the fully coupled
problem.
The use of iterative methods for the relevant linear algebra is crucial here since the overall
dimensions (including the Optimization and PDE) are usually very large, but matrix vector
products as required in Krylov subspace methods such as MINRES are still readily computed.
The work to ensure rapid convergence is in preconditioning and it is this topic that we will mostly
focus on in this lecture.
We will describe our general approach via block preconditioning and demonstrate its use for
the control of Poisson and Stokes problems and also for the fully time-dependent heat equations.
This is joint work with Tyrone Rees, Martin Stoll, Sue Thorne and John Pearson.
Plenary Lecture 2 Tue, 08:30–09:30
Chair: Peter Hagedorn dmstm–spectrum, plenary lectures
From direct to inverse analysis in flexible multibody dynamics
Olivier Brüls (University of Liège) Schedule
Today, state-of-the-art simulation packages in flexible multibody dynamics allow the high-fidelity
analysis of industrial mechanisms and machines in many application fields including robotics,
automotive systems, aeronautics, deployable structures or wind turbines. The dynamic response
of a given system can thus be evaluated in the time-domain for given load cases and given initial
values. However, in many practical cases, the engineer does not have a precise knowledge of the
mechanical design, the loading conditions and the initial state. This situation occurs for example
in structural optimization, optimal control, experimental identification and health monitoring
problems. The complexity of simulation codes and the computational cost of high-fidelity models
are still important obstacles for the development of efficient resolution methods for these inverse
problems. A current challenge is thus to elaborate simplified and more efficient modelling strategies
in flexible multibody dynamics in order to enable the development of inverse analysis methods.
The talk is divided into three parts. The first part provides an overview of available simulation
techniques for flexible mechanisms with a particular emphasis on finite element-based approaches
and time integration methods. Some illustrations are presented in the fields of deployable structures,
vehicle dynamics and wind turbines. In the second part, optimization problems in flexible
multibody dynamics are addressed and solved using gradient-based methods. Efficient methods
for sensitivity analysis are discussed and special problems are treated such as the structural optimization
of mechanical components or the numerical solution of inverse dynamics problems.
The third part discusses a recently-developed Lie group approach which allows the formulation of
the equations of motion of a multibody system in a parameterization-free setting. Based on this

Plenary Lectures 5
general formalism, which is characterized by an increased modularity and a reduced complexity,
a large variety of Lie group solvers are foreseen not only for time integration but also for model
reduction, sensitivity analysis and optimization.
Plenary Lecture 3 Wed, 08:30–09:30
Chair: Richard Markert S1|01–A1
Physics of Sports
Christoph Clanet (École Polytechnique Paris) Schedule
Physics consists in identifying repeatable sequences in our environment and finding the simplest
underlying laws. In these lecture, the environment is Sport. We will walk in the footprints of
modern precursors, JB Keller and B.Benjamin and show that Sports do entangle a large number
of physical concepts. The main domains will be football, badminton and ski jump, in which we
will discuss fluid mechanics, elasticity and some statistical physics.
Plenary Lecture 4 Thu, 08:30–09:30
Chair: Martin Oberlack S1|01–A1
Multi-Scale Model Development for LES of Practical Combustion Applications
Heinz Pitsch (RWTH Aachen) Schedule
Modeling combustion in technical combustion devices is challenging, because of the multi-scale
character, complex geometry, flow and mixing, and the multitude of different interacting processes,
including turbulence, chemistry, spray formation, spray dynamics and evaporation, radiation,
and pollutant formation. Here, using the example of aircraft engine combustors, the interaction
of these effects in practical combustion devices will be assessed. Direct numerical simulations and
large-eddy simulations will be used to demonstrate the subtle effects of liquid fuel evaporation on
small-scale flame structure and large-scale combustion behavior. Based on the knowledge from
these studies, suitable combustion models have been developed. The application of the combustion
models in predictions of soot and nitrogen oxide emissions from aircraft engines will be discussed.
Plenary Lecture 5 Thu, 09:30–10:30
Chair: Dieter Bothe S1|01–A1
Infinite-dimensional port-Hamiltonian systems
Birgit Jacob (Universität Wuppertal) Schedule
Modeling of dynamical systems with a spatial component leads to lumped parameter systems,
when the spatial component may be denied, and to distributed parameter systems otherwise.
The mathematical model of distributed parameter systems will be a partial differential equation.
Examples of dynamical sytems with a spatial component are, among others, temperature
distribution of metal slabs or plates, and the vibration of aircraft wings.
In this talk we will study distributed parameter port-Hamiltonian systems. This class contains
the above mentioned examples. The norm of such a system is given by the energy (Hamiltonian)
of the system. This fact enables us to show relatively easy the existence and stability of solutions.
Further, it is possible to determine which boundary variables are suitable as inputs and outputs,
and how the system can be stabilized via the boundary.

6 Plenary Lectures
Plenary Lecture 6 Thu, 11:00–12:00
Chair: Klaus Hackl S1|01–A1
The critical nature of plastic flow
Lev Truskinovsky (École Polytechnique Paris) Schedule
Steady state plastic flows have been compared to developed turbulence because the two phenomena
share the inherent complexity of particle trajectories, the scale free spatial patterns and the
power law statistics of fluctuations. The origin of the apparently chaotic and at the same time
highly correlated microscopic response in plasticity remains hidden behind conventional engineering
theories which are based on fitting functions and therefore fail to capture intermittency. To
regain access to fluctuations, we study a minimal mesoscopic model whose goal is to elucidate the
origin of scale free behavior in plasticity. We limit our description to fcc type crystals and leave
out both temperature and rate effects. We argue that the origin of complexity in rate independent
athermal plastic flows with highly mobile dislocations is marginal stability of the underlying elastic
system. Our conclusions are based on a reduction of an over-damped visco-elasticity problem
for a system with a rugged elastic energy landscape to an integer valued automaton. We show
that already two dimensional models are adequate for describing power law statistics of avalanches
and fractal character of dislocation patterning. Most remarkably, in addition to realistic values
of critical exponents, a minimal 2D model generates shape functions in scaling laws which are in
agreement with observations.
Plenary Lecture 7 Fri, 08:30–09:30
Chair: Hans-Dieter Alber S1|01–A1
Looking for the hot spot: homogenization and localization of a convection-diffusion
equation in a bounded domain.
Gregoire Allaire (École Polytechnique Paris) Schedule
This is a joint work with I. Pankratova and A. Piatnitski. Motivated by upscaling of transport phenomena
in porous media, we consider the homogenization of a non-stationary convection-diffusion
equation posed in a bounded domain with periodically oscillating coefficients and homogeneous
Dirichlet boundary conditions. Assuming that the convection term is large, we give the asymptotic
profile of the solution and determine its rate of decay. In particular, it allows us to characterize
the “hot spot”, i.e., the precise asymptotic location of the solution maximum which lies close to
the domain boundary and is also the point of concentration. Due to the competition between
convection and diffusion the position of the “hot spot” is not always intuitive as exemplified in
some numerical tests.
Plenary Lecture 8 Fri, 09:30–10:30
Chair: Volker Mehrmann S1|01–A1
Optimal Control of High-Throughput-Screening (HTS) Systems in a Dioid Algebra
Jörg Raisch (TU Berlin) Schedule
High-Throughput-Screening (HTS) has become an important technology to rapidly test thousands
of biochemical substances. HTS plants are fully automated systems containing a fixed set
of resources performing, e.g., liquid handling, storage, reading, plate handling and incubation
steps. All operations which have to be conducted to analyse one set of substances are combined
in a so-called batch. In order to compare screening results, the single batch time scheme, i.e., the

Plenary Lectures 7
sequence and timing of activities for one batch, is usually required to be identical for all batches.
In previous work, we proposed a method to determine a globally optimal (in the sense of achieving
maximal throughput) solution for the resulting scheduling problem. However, this optimal
schedule is generated off-line and can therefore not react appropriately to unforeseen disturbances
and delays. To handle these in a systematic manner, we have investigated methods to enhance a
given off-line schedule by appropriate feedback. It turns out that the resulting feedback synthesis
problem is (non-benevolently) nonlinear when considered in the standard algebra. However, formulating
the problem in a suitable dioid algebra provides a linear representation. A dioid is an
idempotent semiring, with the so-called (max,+) algebra being the most well-known example. We
will discuss why a different dioid, commonly referred to as M ax
in [γ, δ ], is particularly suitable to
model HTS problems. We will also discuss how to analytically determine a feedback control law
which will start all activities as late as possible without violating the overall aim of throughput
maximisation and will therefore implement a closed-loop just-in-time policy.
This is the joint work with Tom Brunsch and Laurent Hardouin.
Plenary Lecture 9 Fri, 11:00–12:00
Chair: Ulrich Langer S1|01–A1
Exponential integrators
Marlis Hochbruck (KIT) Schedule
In this talk we will give an overview on the construction, analysis, implementation and application
of various exponential integrators. Exponential integrators are time integration schemes, which
involve the evaluation or approximation of the exponential (or related) function of a suitable
matrix (e.g. the Jacobian of the differential equation). Such methods have been proposed about
50 years ago but for a long time have been regarded as not practical. Significant advances on the
approximation of the product of a matrix function with a vector during the last decade including
multiple time stepping approaches have renewed the interest in these integrators. By now it has
been shown that such integrators are competitive or even outperform state of the art standard
methods in certain applications.
We will discuss basic ideas to construct such integrators for different applications and we
will explain some convergence results for abstract partial differential equations. Moreover, we
consider the approximation of matrix functions and show how these methods can be implemented
in problems arising in optics and photonics.
Plenary Lecture 10 Fri, 12:00–13:00
Chair: Sergio Conti S1|01–A1
Microstructure and effective behavior of materials
Georg Dolzmann (Universität Regensburg) Schedule
The importance of fine structures in solids on their elastic and plastic behavior has been recognized
for a long time. Their explicit resolution, for example in numerical simulations, is a challenging
problem and has inspired the search for macroscopic models which predict the overall behavior
of the material without resolving all the fine scales explicitly.
From the mathematical point of view, this question is usually addressed by seeking effective
models in the framework of nonlinear elasticity theory based on modern methods in the calculus
of variations. The scope of this presentation is to give an overview of the appropriate methods
and to illustrate them for two specific model systems, namely for the elastic response of nematic

8 Plenary Lectures
elastomers and the elasto-plastic behavior of single crystals.

Minisymposia MA1 – MA3 9
Minisymposia MA1 – MA3
Mini-MA1: Preconditioning in optimization with PDE constraints
Organizers: Martin Stoll (MPI Magdeburg) Mon, 16:00–18:00
Walter Zulehner (Johannes Kepler Universität Linz) dmstm–dynamicum 0.04
On the preconditioning of PDE constrained shape optimization problems
Volker Schulz (Universität Trier), Stephan Schmidt (Imperial College), Roland Stoffel (Universität
Trier) Schedule
Shape optimization is an aspect of optimization which is rich of applications but also requires
special techniques, since global parameterizations are only viable in very restricted cases. In this
talk preconditioning in two aspects will be considered: on the level of the shape Hessian as well as
on the PDE level. Recent approaches are discussed and their efficacy is demonstrated for practical
industrial applications.
Fast Iterative Solvers for Time-Dependent PDE-Constrained Optimization Problems
John Pearson (Oxford University), Martin Stoll (MPI Magdeburg), Andy Wathen (Oxford University)
Schedule
An area of much recent attention in applied mathematics and numerical analysis is the numerical
solution of optimal control problems. In this talk, we consider in particular iterative methods for
solving matrix systems resulting from time-dependent PDE-constrained optimization problems.
We motivate and derive the preconditioners used, crucial to the development of which are saddle
point theory, mass matrix approximation, and good approximation of the Schur complements of
the matrix systems we are solving. We present numerical results to demonstrate that our preconditioners
yield convergence of the appropriate iterative method in few iterations for a number
of problems, while only requiring the storage of matrices which are small in comparison to the
matrix systems being solved.
On the Preconditioning of Linear Systems Arising in Trust-Region Methods
Roland Herzog, Susann Mach (TU Chemnitz) Schedule
Trust-region methods are widely used for the numerical solution of nonlinear constrained and unconstrained
optimization problems. Similar as line-search methods, they take turns in minimizing
local models of the objective. In contrast to line-search methods, however, trust-region approaches
do not require nor promote the positive definiteness of the local Hessian approximations.
In this presentation, we address issues arising in the context of the preconditioned approximate
solution of these local models. The talk will highlight connections between algorithmic
optimization and linear algebra.
A multigrid framework applied to an elliptic optimal control problem with reduced
regularity
Stefan Takacs, Walter Zulehner (Universität Linz) Schedule
In this talk we consider the convergence theory for all-at-once multigrid methods for solving
saddle point problems, like the optimality system of a PDE-constrained optimization problem. For
general linear systems we identify four sufficient conditions for convergence. The analysis follows
classical lines. The result may be an essential help if a parameter-dependent problem is considered,
because the fact that the four sufficient conditions are satisfied with constants independent of the

10 Minisymposia MA1 – MA3
parameters implies that also the bounds for the convergence rates are parameter-independent.
We apply this theory to an elliptic optimal control model problem of tracking type. The new
approach allows to extend previously known convergence results based on full elliptic regularity
to problems with reduced regularity.
Indefinite Preconditioners for PDE-constrained optimization problems
Valeria Simoncini (Universita’ di Bologna) Schedule
Symmetric indefinite preconditioners are being more and more employed for the efficient solution
of saddle point algebraic linear systems in PDE-constrained optimization problems. In this talk
we review some recent numerical and theoretical aspects that make indefinite preconditioners
appealing over symmetric positive definite acceleration strategies.
Preconditioning for PDE-constrained optimization using proper orthogonal decomposition
Ekkehard W. Sachs, Xuancan Ye (Universität Trier) Schedule
The main effort of solving a PDE constrained optimization problem is devoted to solving the
corresponding large scale linear system, which is usually sparse and ill conditioned. As a result,
a suitable Krylov subspace solver is favourable, if a proper preconditioner is embedded. Other
than the commonly used block preconditioners, we exploit knowledge of proper orthogonal decomposition
(POD) for preconditioning and achieve some interesting features. Numerical results
on nonlinear test problems are presented.
Mini-MA2: High-performance linear algebra on GPUs
Organizers: Paolo Bientinesi (RWTH Aachen) Mon, 16:00–18:00
Enrique S. Quintana-Orti (University Jaume I) dmstm–germanium2 3.02/03
The implications of GPUs for parallel numerical simulation
Jan-Philipp Weiss (KIT) Schedule
Fast and accurate numerical simulation based on linear algebra operations relies on both efficient
parallel schemes and platform-optimized parallel implementations. Due to the paradigm shift towards
manycore technologies, as exemplified by GPUs, both aspects have become more intricate.
Parallelism needs to be increasingly more fine-grained and has to be expressed across several system
levels. Moreover, exploitation of data locality in hierarchically organized memory subsystems
as well as data layout and memory access patterns are performance-critical factors.
This talk details the configuration of modern GPU hardware and points out how specific capabilities
of GPUs can be expressed in the application mapping procedure by related programming
models. We investigate the implications of hardware-aware computing on the design and adaptation
of parallel numerical methods. Furthermore, we describe an approach that takes the burden
of explicit hardware knowledge from the application programmer and allows writing generic, portable
and high-performance numerical solvers.
Preconditioned Block-Iterative Methods on GPUs
Maxim Naumov (NVIDIA) Schedule
In this presentation we focus on parallel algorithms that are building blocks for the incomplete-LU
preconditioned block-iterative methods on Graphics Processing Units (GPUs). In particular, we
focus on the techniques and the associated tradeoffs used to implement sparse matrix-vector multiplication
with multiple vectors and sparse triangular solve with multiple right-hand-sides using

Minisymposia MA1 – MA3 11
the CUDA parallel programming model. Finally, numerical experiments comparing the GPU and
CPU implementations are also presented.
Parallel Preconditioners for GPU-Multigrid Solvers
Robert Strzodka (NVIDIA) Schedule
GPUs perform best on regular, independent work-loads while effective preconditioners ask for
complex, serially coupled computations. The extreme cases of best hardware performance on
slowly converging numerical schemes or quickly converging schemes with slow serial execution are
poor choices. The talk discusses how to find the middle ground by challenging the hardware with
more complex data dependencies and at the same time relaxing purely serial dependencies with
parallel variants. For structured matrices, we can now solve very ill-conditioned linear equation
systems that were intractable with GPU hardware before.
The nonequispaced FFT on graphics processing units
Susanne Kunis (Universität Osnabrück) Schedule
Without doubt, the fast Fourier transform (FFT) belongs to the algorithms with large impact
on science and engineering. By appropriate approximations, this scheme has been generalized for
arbitrary spatial sampling points. This so called nonequispaced FFT is the core of the sequential
NFFT3 library and we discuss which its computational costs in detail. On the other hand, programmable
graphic processor units have evolved into highly parallel, multithreaded, manycore
processors with enormous computational capacity and very high memory bandwith. By means of
the so called Compute Unified Device Architecture (CUDA), we parallelized the nonequispaced
FFT using the CUDA FFT library and a dedicated parallelization of the approximation scheme.
Mini-MA3: Crystals and defects
Organizers: Patrick Dondl (Durham University) Mon, 16:00–18:00
Bernd Schmidt (Universität Augsburg) dmstm–helium2 3.08/09
Ginzburg Landau energies for dislocations
Marcello Ponsiglione (La Sapienza, Roma) Schedule
In this talk I will present some variational approaches to dislocations. The purpose is to derive
macroscopic Ginzburg Landau energies starting from basic discrete (or microscopic) dislocation
models.
Twinned martensite configurations arising as ground states of a two-well discrete
Hamiltonian
Georgy Kitavtsev (MPI Leipzig), Stephan Luckhaus (Universität Leipzig) Schedule
In this talk we construct and analyze a two-well Hamiltonian on 2D atomic lattice considered
with nonconvex interactions. Two wells of the Hamiltonian are given by two rank-one connected
martensitic twins, respectively. Our combined analytical and numerical results show that the
structure of ground states under appropriate boundary conditions is close to the macroscopically
expected twinned configuration plus additional exponential boundary layers localized near the
twinning interface.

12 Minisymposia MA1 – MA3
A Force-based Hybrid Method for Solids: Theory and Numerics
Pingbing Ming (Institute of Computational Mathematics and Scientific/Engineering, AMSS, Chinese
Academy of Sciences), Jianfeng Lu (Courant Institute New York), Zhijian Yang (Wuhan
University) Schedule
We study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity
model. We show the proposed scheme converges to the solution of the atomistic model with second
order accuracy, as the ratio between lattice parameter and the characteristic length scale of the
deformation tends to zero. Convergence is established for general finite range atomistic potential
and simple lattices in three dimension. The proof is based on consistency and stability analysis.
General tools for stability analysis are developed in the framework of pseudo-difference operators.
Some numerical examples will also be reported.
Line-tension model as the Γ-limit of a nonlinear dislocation energy
Caterina Ida Zeppieri (Universität Bonn), Lucia Scardia (TU Eindhoven) Schedule
The motion of dislocations is regarded as the main cause of plastic deformations, therefore a
large literature is focused on the problem of deriving plasticity models from more fundamental
dislocation models. The starting point of our derivation is a semi-discrete dislocation model. The
main novelty of our approach is that we consider a nonlinear dislocation energy, whereas most
mathematical and engineering models are based on quadratic energies. Our choice of a nonlinear
stress-strain relation guarantees that the dislocation strain energy is well defined also in the
vicinity of the dislocations, eliminating the need of introducing a fictitious cut-off radius that is
typical of the linear theories. The Γ-limit of our nonlinear dislocation energy as the length of the
Burgers vector tends to zero is a strain-gradient model for plasticity and has the same form as
the limit energy obtained by starting from a quadratic dislocation energy. Our result, however, is
obtained by starting from a more reliable physical model.

Minisymposia ME1 – ME3 13
Minisymposia ME1 – ME3
Mini-ME1: Homogenization from submicro to micro scales
Organizers: Franz Rammerstorfer (TU Wien) Mon, 16:00–18:00
Bob Svendsen (RWTH Aachen) dmstm–platinum2 2.07/08
Variational Homogenization of Microstructures for Gradient-Extended Dissipative
Materials with Length Scales
Christian Miehe, Dominic Zäh (Universität Stuttgart) Schedule
The homogenization-based scale bridging is the key ingredient of modern multiscale modeling
techniques. When bridging submicro to micro scales, non-standard modeling techniques must be
taken into account which account for discrete length scales. At a homogenized level, these length
scales can often be modeled by gradient-extended dissipative continua. Typical examples are
theories of strain gradient plasticity, gradient damage, phase field models of fracture and phase
transformations, as well as electric polarization and magnetization in functional materials. A generic
theoretical and computational approach to these problems can be constructed in an elegant
format based on rate-type variational principles. This lecture provides an overview of the formulation
and computational exploitation of canonical variational principles for the homogenization
of gradient-extended dissipative solids. It develops rate-type and incremental minimization and
saddle point principles for a class of materials which incorporate order parameter fields, whose
gradients enter the energy storage and dissipation functions. In contrast to classical local continuum
approaches based on locally evolving internal variables, these global parameter fields are
governed by additional balance-type partial differential equations including boundary conditions.
We outline a unified framework for the homogenization of first-order gradient-type standard dissipative
solids. Particular emphasis is put on mixed multi-field representations, where both the
order parameter fields itself as well as their dual driving force are present. These mixed variational
settings are suitable for models with threshold- or yield-functions formulated in the space
of driving forces. It is shown that the coupled field equations follow in a natural way as the Euler
equations of minimization and saddle point principles, which are based on properly defined
rate-type and incremental potentials. The unified character of the computational framework is
demonstrated by a spectrum of model problems, which covers computational homogenization of
submicro models of plasticity, damage mechanics as well as phase field models of electric and
magnetic domain evolution.
Multiscale Modelling of Continua with Energetic Surfaces at the Microscale
A. McBride, A. Javili, P. Steinmann (Universität Erlangen-Nürnberg) Schedule
The objective of this presentation is to detail an application of the computational micro-to-macro
transition framework that involves the surface energy theory of Gurtin and Murdoch. For this
application, the microstructure contains voids with additional surface energy. The response of
the associated macrostructure is approximated using classical elasticity theory. Homogenisation
provides a consistent methodology to link the macroscopic and microscopic scales.
The motivation for endowing the surface of the voids at the microscale with their own structure
is to capture the well-documented effect whereby the surface plays an ever-increasing role in
the overall macroscopic response as the size of the voids decrease. Our key contribution is the
numerical determination of the effective macroscopic material properties as a function of both the
microscopic void size and the coupling between the microscopic bulk and surface free energies. At
the microscopic scale we have a continuum with a surface structure and the constitutive laws are

14 Minisymposia ME1 – ME3
presumed known. At the macroscopic scale the constitutive relations are not explicitly known;
they are replaced by the results of the computations on the microscopic scale using numerical
homogenisation.
Key features of the application are demonstrated via a series of numerical computations using
the finite element method. An interesting outcome of endowing the microstructure with one or
more energetic surfaces is that the response of one microstructure relative to another is dependent
on the ratio of the area of the energetic surfaces to the volume of the bulk. Thus, the microscopic
response is inherently scale dependent.
From Nano to Micro - Perspectives for Homogenization in Crystalline Solids
J. Schröder, B. Eidel, D. Balzani, D. Brands (Universität Duisburg-Essen) Schedule
For the direct incorporation of micromechanical information into macroscopic boundary value
problems, the FE 2 -method provides a suitable numerical framework. Here, an additional microscopic
boundary value problem, based on evaluations of representative volume elements (RVEs),
is attached to the quadrature points of the discretized macrostructure. However, relevant macroscopic
problems can only be simulated if simplified microstructures are used. One approach is to
construct statistically similar RVEs by minimizing least-square functionals that take into account
statistical measures describing the microstructure. An application of this concept for the scale
transition from nano to micro is different from micro-macro transitions, since atomistics differs
from continuum mechanics in various physical aspects. Atomistic models reflect the discreteness of
matter, atomic interactions are nonlocal and they are concepts of energies and forces. Continuum
mechanics, in contrast, considers matter as a continuum, constitutive models are typically local
theories and they are a very concept of stress. Moreover, an adequate RVE for nanostructures
must account for inelastic defects like dislocations, stacking faults, voids etc. in fully atomistic
resolution along with highly accurate interatomic potentials. In continuum mechanics however,
suchlike defects and their evolution are modelled by internal variables based on rate equations.
The talk adresses perspectives for the computational homogenization of heterogeneities at submicron
to micron length scales and discusses aspects to consolidate the differences in atomistics
and continuum mechanics.
Theoretical Aspects of a Continuum Dislocation Microplasticity Theory and Numerical
Examples
Thomas Böhlke, Stephan Wulfinghoff (KIT) Schedule
Modern continuum approaches for microplasticity applications try to fill the gap between sizeindependent,
phenomenological plasticity models for macroscopic simulations and microplasticity
models based on discrete objects like ab-initio methods or Discrete Dislocation Dynamics. Besides
phenomenological strain gradient plasticity models several dislocation density-based theories have
emerged that account explicitly for dislocation transport and production. The kinematical theory
of Hochrainer et al. [1], numerically implemented by Sandfeld et al. [2], averages the collective
motion of three-dimensional discrete, connected and curved dislocation lines. The theory can be
considered as a generalization of Nye’s work [4]. Besides Geometrically Necessary Dislocations
it contains additional detailed information on the dislocation microstructure. As the theory is
numerically expensive in three-dimensional multislip applications, a simplified version (see e.g.
Sandfeld et al. [3]) of the kinematical continuum mechanical dislocation-density framework is
considered in the presentation based on two evolution equations for the dislocation density ρt
and the average dislocation curvature ¯ k. The dislocation velocity ν couples the dislocation field
problem to the elasto-visco-plastic crystal plasticity framework via Orowan’s equation ˙γ = ρtbν,

Minisymposia ME1 – ME3 15
where γ is the plastic slip. Furthermore, the kinetic coupling based on hardening approaches like
the Taylor-relation τY ∼ √ ρt as well as boundary conditions are discussed. Three-dimensional
model problems highlight the advantages of the dislocation based approach.
[1] T. Hochrainer, M. Zaiser and P. Gumbsch, A three-dimensional continuum theory of dislocations:
kinematics and mean field formulation. Philosophical Magazine 87 (2007), 1261–1282.
[2] S. Sandfeld, T. Hochrainer, M. Zaiser and P. Gumbsch, Numerical implementation of a 3D
continuum theory of dislocation dynamics and application to micro-bending, Philosophical
Magazine 90 (2010), 3697–3728.
[3] S. Sandfeld, T. Hochrainer, M. Zaiser and P. Gumbsch, Continuum modeling of dislocation
plasticity: Theory, numerical implementation, and validation by discrete dislocation
simulations. J. Mater. Res. 26 (2011), 623–632.
[4] J. F. Nye, Some geometrical relations in dislocated crystals. Acta Metallurgica 1 (1953),
153–162.
On non-local and semi-discrete generalizations of continuum dislocation field theory
Bob Svendsen (RWTH Aachen) Schedule
Like standard continuum plasticity theory, the Volterra or continuum theory of dislocations based
on linear elasticity theory is devoid of any material lengthscale or regard for the atomic structure
of the material. In particular, it is well-known (e.g., [1]) that the model breaks down near the
dislocation core, something which can also be related to the fact that the model has no material
lengthscale. Among other things, this has led a number of workers to propose generalizations of
this approach in which different types of lengthscales play a role. In particular, these include (i)
couple-stress elasticity, (ii) non-local elasticity, and (iii) semi-discrete approaches, e.g., the Peierls-
Nabarro model. Whereas the first two are, like the Volterra model itself, purely phenomenological
in nature, semi-discrete methods like the Peierls-Nabarro model offer the chance of scale-bridging
with atomistic models for dislocations. Besides a comparison of the core regularization offered by
these approaches, the purpose of the current work is to show in detail how the Volterra model
represents the asymptotic limit of the Peierls-Nabarro model as the core size is allowed to vanish.
In addition, the connection of the Peierls-Nabarro model with lattice models such as Frenkel-
Kontorova will be examined.
[1] J. P. Hirth, J. Lothe, Theory of Dislocations, 2 nd edition (1982), Wiley.
Mini-ME2: Micro- and nanofluidics
Organizers: Stephan Gekle (TU München) Mon, 16:00–18:00
Steffen Hardt (TU Darmstadt) dmstm–spectrum
Nanoscale pumping of water by AC electric fields
Klaus Rinne (FU Berlin), Stephan Gekle, Douwe Jan Bonthuis (TU München), Roland Netz (FU
Berlin) Schedule
Using molecular dynamics simulations we present a novel mechanism for pumping of water through
a carbon nanotube by time-dependent electric fields. The fields are generated by electrodes with
oscillating charges in a broad GHz frequency range which are attached laterally to the tube.

16 Minisymposia ME1 – ME3
The key ingredient is a phase shift between the electrodes to break the spatio-temporal symmetry.
A microscopic theory based on a polarization-dragging mechanism accounts quantitatively for
our numerical findings.
Blood Flow through Microchannels: From Single Cells to Blood Rheology
Gerhard Gompper (Forschungszentrum Jülich) Schedule
The flow behavior of vesicles and blood cells is important in many applications in biology and medicine.
For example, the flow properties of blood in micro-vessels is determined by the mechanical
properties of red blood cells (RBCs). Blood flow is therefore strongly affected by diseases such
as malaria or diabetes, where RBC deformability is strongly reduced. Furthermore, microfluidic
devices nowadays allow the manipulation of small amounts of suspensions of particles or cells.
Of fundamental interest is here the relation between the flow behavior and the deformability
of the blood cells, their long-range hydrodynamic interactions in microchannels, and thermal
membrane undulations. We study these mechanisms in a model, which combines particle-based
mesoscale simulation techniques [1] for the fluid hydrodynamics with a triangulated-surface model
[2] for the membrane. The essential control parameters are the volume fraction of RBCs (tube
hematocrit) and the flow velocity.
In narrow channels, single RBCs in capillary flow show a transition from biconcave-disk to
parachute shape with increasing flow velocity [3]. At higher volume fractions, hydrodynamic interactions
are responsible for a strong deformation-mediated clustering tendency at low hematocrits,
as well as several distinct flow phases at higher hematocrits [4]. For larger channels, blood behaves
like a continuum fluid. As a function of shear rate, a strong shear-thinning behavior is
found, which is predicted from RBC deformability and cell-cell attraction [5]. Recent progress in
simulation techniques now also allows to study more complex systems, such as mixtures of RBCs
and white blood cells (WBCs). WBCs may accumulate near the vessel walls, a process called
margination. Flow conditions for WBC margination are predicted and discussed [6].
[1] G. Gompper, T. Ihle, D.M. Kroll and R.G. Winkler, Adv. Polymer Sci. 221, 1–87 (2009).
[2] G. Gompper and D.M. Kroll, in Statistical Mechanics of Membranes and Surfaces (2nd
edition), p.359–426, edited by D. R. Nelson, T. Piran and S. Weinberg (World Scientific,
Singapore, 2004).
[3] H. Noguchi and G. Gompper, Proc. Natl. Acad. Sci. USA 102, 14159 (2005).
[4] J.L. McWhirter, H. Noguchi, and G. Gompper, Proc. Natl. Acad. Sci. USA 106, 6039 (2009).
[5] D.A. Fedosov, W. Pan, B. Caswell, G. Gompper, and G.E. Karniadakis, Proc. Natl. Acad.
Sci. USA 108, 11772–11777 (2011).
[6] D.A. Fedosov, J. Fornleitner, and G. Gompper, Phys. Rev. Lett., to appear (2012).
Influence of the electric double layer on charged anisotropic particles of colloidal size
Florian Keller, Willy Dörfler, Hermann Nirschl (KIT) Schedule
Colloidal particles, i.e. particles with a size below 1 m, play an important role in chemical,
biological and environmental engineering. Since particles in aqueous solutions normally carry a
non-zero surface charge, an electric double layer around the particles develops. Due to an ambient
fluid flow this double layer gets distorted and exerts an additional electrostatic force and torque on

Minisymposia ME1 – ME3 17
the particle. Because of the large surface to volume ratio of colloids these forces and torques alter
the particle motion and cannot be neglected. In this talk we will especially consider the influence
of the electric double layer on anisotropic particles. As a model system we therefore use prolate
spheroids. However the majority of the theoretical work available in the literature considers only
spherical particles, while for spheroidal particles most works suffer from severe restrictions on
the ion concentrations, Peclet numbers but also on the geometry. In the latter case, it is thereby
often assumed the thickness of the spheroidal particle is small compared to its length. However
in practical applications one often has to deal with non-spherical particles with moderate aspect
ratios. In this talk we use direct numerical simulation to investigate the effects of the electric
double layer on charged spheroidal particles with moderate aspect ratios in uniform flow fields
as well as in shear flow. It is shown that the influence of the particle charge behaves in analogy
to the case of charged spheres, while the influence of the double layer thickness largely deviates
from these results and depends on the orientation of the spheroids. In a linear shear flow, we
will further show that the motion of the spheroids can be compared to the motion of uncharged
spheroids.
Microjet formation in a capillary by laser-induced cavitation
Ivo R. Peters, Yoshiyuki Tagawa, Nikolai Oudalov, Chao Sun, Devaraj van der Meer, Detlef Lohse
(University of Twente) Schedule
A vapor bubble is created by focusing a laser pulse inside a capillary that is partially filled with
water. Upon creation of the bubble, a shock wave travels through the capillary. When this shock
wave meets the meniscus of the air-water interface, a very thin jet is created that can reach
speeds exceeding the speed of sound. A crucial ingredient is the shape of the meniscus, which is
responsible for focusing the energy provided by the shock wave into a jet.
We examine the formation of this jet numerically using a boundary integral method, where we
prepare an initial interface at rest inside a tube with a diameter ranging from 50 to 500 µm. We
apply a strong pressure pulse on the bubble with a typical duration of 50 ns, after which the jet
forms. We investigate the influence of the contact angle, tube radius, distance of the bubble from
the meniscus, and pressure amplitude on the jet formation. The jet shape and velocity obtained
by the simulation compare well with experimental data, and provides good insight in the origin
of the jet.
Using potential flow theory we develop an approximate expression that accurately reproduces
the dependencies on the above mentioned parameters. In particular, we show that the jet speed
is proportional to the pressure amplitude, and the inverse of the distance between the bubble and
the free surface. The model agrees well with experiment and simulation.
Propulsion of Leidenfrost solids on structured and unstructured surfaces
Tobias Baier, Stefan Herbert (TU Darmstadt), Guillaume Dupeux, David Quere (Ecole Polytechnique),
Steffen Hardt (TU Darmstadt) Schedule
Since the publication of the first work on self propelling Leidenfrost drops on ratchets by Linke
et al. in 2007 [1] the mechanism for their propulsion has been debated. A number of reasons
have been proposed, including viscous shear, net pressure forces due to the drop surface following
the ratchets contour, thermocapillary flows, gradients in Laplace pressure, coupling of surface
waves and droplet oscillations to the motion, recoil pressure or thermal creep flow. All or some of
these mechanisms may play a role for the net propulsion; however, the complexity of the problem
including the liquid motion makes it hard to make quantitative predictions about the relative
importance of the terms.
A new spin was given to the field in [2] where the movement of platelets of dry ice levitating

18 Minisymposia ME1 – ME3
over a hot structured surface was studied. Being a solid where internal degrees of freedom can
be neglected, this system excludes many of the above mechanisms making it more amenable to
analysis. We propose a mathematical model for the the propulsion of such Leidenfrost solids. We
identify the sublimation rate by solving the energy equation between the ratchet and the ice coupled
to a solution of the Navier-Stokes equation for the gas flow. We pursue this model at various
states of rigor, from a numerical calculation using finite volume discretisation to a lubrication
approximation. In particular, we make predictions about the scaling of the net propulsive force
with the geometric parameters of the structured surface and the size of the platelet.
Additionally, a novel mode of propulsion of Leidenfrost solids is proposed on non-structured
surfaces. Evidently, a homogeneous cylindrical disc of dry ice in the Leidenfrost state on a flat
surface will levitate without a net lateral force due to symmetry. However, breaking the symmetry
by an inhomogeneous mass distribution must be compensated by a non-symmetric pressure
distribution in the gas layer below the platelet, resulting in a slight tipping. This in turn results
in a net lateral pressure force which together with the viscous forces leads to a net propulsion of
the platelet. We investigate this mechanism in our lubrication model.
[1] H Linke, BJ Aleman, LD Melling, MJ Taormina, MJ Francis, CC Dow-Hygelund, V Narayanan,
RP Taylor, and A Stout. Self-propelled Leidenfrost droplets. Phys.Rev.Lett. 96 (15),
2006.
[2] G Lagubeau, M Le Merrer, C Clanet, and D Quere. Leidenfrost on a ratchet. Nature Physics
7 (5):395398, 2011.
Analysis of thin liquid bilayers
Dirk Peschka, Sebastian Jachalski, Robert Huth (WIAS Berlin), Barbara Wagner (TU Berlin),
Andreas Münch (University of Oxford) Schedule
This talk is about mathematical analysis of stationary states of liquid-liquid systems with negative
spreading coefficient. Stationary solutions for the lubrication equation with precursor are
studied using Γ-convergence. For the latter a simple proof of existence and uniqueness of energy
minimizers is given for suitable boundary conditions. We use these results to compare the different
PDE formulations of the problem.
Mini-ME3: Modelling of phase transformations in solids
Organizers: Klaus Hackl (Ruhr-Universität Bochum) Mon, 16:00–18:00
Christian Miehe (Universität Stuttgart) dmstm–vanadium2 2.02/03
Martensitic transformation vs. plastic deformation in superelastic deformation of
NiTi
Petr Šittner, Jan Pilch (Academy of Sciences of the Czech Republic, Prague), Caroline Curfs
(ESRF Grenoble), Remi Delville (University of Antwerps) Schedule
Simultaneous martensitic transformation and plastic deformation taking place during cyclic superelastic
deformation of thin NiTi wires in tension will be discussed based on the recent experimental
evidence obtained by in-situ synchrotron X-ray diffraction, electrical resistivity and ex-situ transmission
electron microscopy studies of microstructures in deformed wires. The obtained results
serve as a basis for dedicated simulations of NiTi superelasticity in a wide temperature range
by micromechanics model of SMA polycrystal. It is found that, beyond the basic characteristics
of the martensitic transformations involved and plastic yield stress of the alloy, the shape and

Minisymposia ME1 – ME3 19
stability of superelastic stress-stress curves depends critically on the grain interactions i.e. on the
partitioning of stress, strain and phase fractions among particularly oriented polycrystal grains.
This partitioning depends significantly on the parent austenite texture of the wire and develops
during superelastic cycling in case of simultaneous transformation and plasticity. As an ultimate
outcome of this research, it is suggested how combination of microstructure control by the cold
work/annealing, fine precipitate strengthening and texture control can be used to achieve optimized
stable superelasticity of NiTi wires in tension.
Variational Phase Field Modeling of Laminate Microstructure at Large Strains
F. Hildebrand, C. Miehe (Universität Stuttgart) Schedule
The macroscopic mechanical behavior of many materials crucially depends on the formation
and evolution of their microstructure. Many materials develop laminate-type microstructure as
a consequence of phase transformations. In this work, we outline theoretical and computational
modeling concepts for such microstructures based on phase field approaches.
Focussing on the regularization of kinematically compatible sharp interfaces, we present a new
variational phase field approach to the coupled problem of mechanical deformation and dissipative
phase transformation in martensitic CuAlNi. We demonstrate the capability of our formulation
to predict the formation and dissipative evolution of laminate microstructure.
Starting point for our approach is the discussion of the link between the sharp interface
formulation and its phase field regularization which is connected to the notion of Γ-convergence.
Based on these considerations, we derive a physically motivated coherence-dependent interface
energy enforcing kinematical compatibility, an energetically concise bulk energy and a dissipation
potential accounting for the dissipative phase boundary propagation. The results are exploited for
the formulation of a regularized phase field model for elastic materials undergoing large strains and
dissipative phase transformations. Finally, a suitable gradient-extended rate-type and incremental
variational framework is constructed.
To demonstrate the modeling capabilities and numerical solution techniques, we carry out
simulations of the formation and evolution of laminate microstructure in two-phasic martensitic
CuAlNi. We then increase the complexity of our framework towards the inclusion of phase transitions
with envolving three or more phase variants. Finally, we outline the conceptual extension
to the formation and evolution of laminate deformation microstructure in crystal plasticity.
On the interrelation between dissipation and chemical energies in modeling shape
memory alloys
Philipp Junker, Klaus Hackl (Ruhr-Universität Bochum) Schedule
Material modeling can be carried out in many different ways. We choose the principle of maximum
dissipation to derive a thermo-mechanically coupled material model for shape memory
alloys. The application of this modeling method requires approaches for both Helmholtz free
energy and dissipation. Although there exist different ways to define an appropriate energy, all
material parameters occurring here are well defined. These are elastic constants, heat capacity or
entropy and enthalpy differences, for instance.
A general framework how to define dissipation is well known, too, which has to be adopted depending
on the expected material reaction. However, for this purpose material parameters have
to be set which can hardly be measured. We present for the simulation of shape memory alloys an
approach to derive this additional dissipation parameter just from the previously mentioned, well
known energetic parameters. This approach allows to display exactly the experimentally observed
material reaction for a purely thermal loading. An outlook to the application of this ansatz to
mechanical problems is given as well as comparison to experiments.

20 Minisymposia ME1 – ME3
Modeling phase transformations during mechanical loading
Alexander Hartmaier, Christoph Begau, Aenne Köster, Anxin Ma (Ruhr-Universität Bochum)
Schedule
Different mechanisms can contribute to the plastic deformation of materials. In this work we
focus our attention on plastic deformation by dislocation slip and phase transformations. These
mechanisms are often alternative and competing for different materials under different loading
conditions described by stress state, strain rate and temperature. Two illustrative examples for
competing mechanisms of dislocation-based plasticity and austenite-martensite transformationinduced
plastic deformation will be given:
(i) Atomistic models for shape memory alloys (SMA) are used to study the competition between
dislocation-based deformation of the austenitic phase and the austenite-martensite transformation
that is the origin of the shape memory effect. Due to the fundamental nature of the
atomistic models the competition of both mechanisms can be studied without any ad hoc assumptions.
Different loading scenarios reveal that dislocation-based deformation occurs preferentially
for deformation along certain crystallographic axes. However, it is also observed that dislocations
can stabilize the martensite due to their eigenstress field once all external loads are removed.
(ii) A continuum model for transformation induced plasticity (TRIP) steels based on the wellknown
work of Olson and Cohen [1] is modified in the following aspect: a dislocation mechanism
based crystal plasticity approach describes local stress and plastic shear in each slip system of face
centered cubic (FCC) austenite. Thus, we estimate the shear band intersections and calculate the
resulting martensite nucleation probability. To calculate the macroscopic material properties we
make use of a micromechanical approach, by setting up a representative volume element (RVE),
in which all phases are represented according to given volume concentrations and morphologies.
Consequently, the properties of the RVE can be homogenized to yield the macroscopic mechanical
properties that result from the given microstructure.
By comparing both studies a way will be sketched, how continuum transformation models will
be based on the results of fundamental atomistic simulations in future work.
[1] G.B. Olson and M. Cohen, Kinetics of strain induced martensite nucleation, METALLUR-
GICAL AND MATERIALS TRANSACTIONS A 6 (1975) 791-795.
Analytical and numerical comparison of two phase field models for phase interfaces
in solids
Hans-Dieter Alber (TU Darmstadt), Bernd Markert (Universität Stuttgart) Schedule
The propagation speed of phase interfaces in phase field models can be determined by higher
order asymptotic expansions with respect to a parameter determining the width of the interface
even if the width is not small. Such higher order expansions have been developed for phase field
models for interfaces in solids, which consist of either one of the evolution equations
or
ϕt = −f(−∂ϕψ(ε, ϕ) − ν∆xϕ)
ϕt = −f(−∂ϕψ(ε, ϕ) − ν∆xϕ)|∇xϕ|
for the order parameter ϕ coupled to the equations of linear elasticity. We discuss these expansions
and present numerical results, by which coefficients in these expansions have been determined,
which cannot be computed analytically.
The model which consists of the second one of these evolution equations coupled to the equations
of nonlinear elasticity is studied by Hildebrandt and Miehe and will be discussed in another
talk of this minisymposium.

Minisymposia YR-MA1 – MA3 21
Minisymposia YR-MA1 – MA3
Mini-YR-MA1: Stochastic partial differential equations (SPDEs) and applications
Organizers: Alexander Litvinenko (TU Braunschweig) Tue, 10:00–12:00
Claudia Schillings (Universität Trier) dmstm–dynamicum 0.04
Numerical treatment of uncertainties in aerodynamic shape optimization
Claudia Schillings, Volker Schulz (Universität Trier) Schedule
The proper treatment of uncertainties in the context of aerodynamic shape optimization is a
very important challenge to ensure a robust performance of the optimized airfoil under real life
conditions. This talk will propose a general framework to identify, quantize and include stochastic
distributed, aleatory uncertainties in the overall optimization procedure. Appropriate robust
formulations of the underlying deterministic problem and uncertainty quantification techniques
in combination with adaptive discretization approaches are investigated in order to measure the
effects of the uncertainties in the input data on quantities of interest in the output. Finally, algorithmic
approaches based on multiple-setpoint ideas in combination with one-shot methods as
well as numerical results are presented.
Uncertainty Quantification in numerical Aerodynamic via low-rank Response Surface
Alexander Litvinenko, Hermann G. Matthies (TU Braunschweig) Schedule
On the example from numerical aerodynamic we illustrate how uncertainties in the input data:
parameters and computational domain propagate into the solution [1,3]. The mathematical model
is described via a Navier-Stokes system of equations with a k-w turbulence model. The computing
domain is the RAE-2822 airfoil. To reduce storage requirement and computing time, we demonstrate
the rSVD based algorithm, which computes a low-rank approximation of the whole set of
realisations of the random solution [1,3]. This approximation allows us to compute a low-rank
approximation of the response surface and then perform postprocessing (e.g. compute the mean
value, variance, etc) with a linear complexity and with drastically reduced memory requirements.
In [2] we offer numerical algorithms, based on the canonical tensor format, to handle uncertainties
in high-dimensional spaces.
[1] A. Litvinenko, H. G. Matthies, Uncertainty Quantification in numerical Aerodynamic via
low-rank Response Surface, accepted in Special Issue of the Communications in Statistics
Journal devoted to SMTDA2010, (2010).
[2] M. Espig, W. Hackbusch, A. Litvinenko, H. G. Matthies, and E. Zander, Efficient Analysis
of High Dimensional Data in Tensor Formats, submitted in 2011 to Springer Lecture Note
series for Computational Science and Engineering.
[3] A. Litvinenko, H. G. Matthies, Sparse data formats and efficient numerical methods for uncertainties
quantification in numerical aerodynamics,
Proceedings of ECCM-2010, www.eccm2010.org/complet/fullpaper_1036.pdf, pp. 1-15, Paris,
(2010).
Efficient Global Response Surfaces for Aerodynamic Functions
Benjamin Rosenbaum, Volker Schulz (Universität Trier) Schedule
We want to approximate aerodynamic functions coming from CFD solvers like the TAU code.
The solver is regarded as a black-box and we only measure relations between vector valued input

22 Minisymposia YR-MA1 – MA3
and scalar output parameters (response). For these input-output relations we want to generate
a surrogate model which is fast to evaluate, using only few computationally expensive CFD
evaluations. The aerodynamic functions like lift or drag for an airfoil depending on inputs like
the Mach number and the angle of attack α behave highly nonlinear, so that traditional response
surface methods like regression models perform poorly.
The statistical interpolation method called Kriging has been widely used in geostatistics since
the fifities, it was introduced for computer experiments in the eighties and is nowadays applied
to CFD simulation and optimization. It is a very flexible method, allowing the use of different
correlation models and even the incorporation of secondary information: e.g. Cokriging makes use
of the cross-correlation with a secondary variable for increasing the approximation quality, while
in Gradient Enhanced Kriging derivatives of the response y(x) are additionally used. This aspect
is especially significant in the CFD context, where gradient information can be relatively cheaply
accessed by adjoint solvers.
Since CFD evaluations consume an enormous amount of computation time, the need for an
appropriate design of experiment arises. Simple space filling designs like the Latin hypercube
design cannot capture critical regions of the input parameter space, while many expensive CFD
evaluations are wasted on redundant samples. We investigate sequential adaptive sampling strategies,
where at every stage a surrogate model is generated and assessed to find suitable locations
for new samples.
In order to further reduce the number of required samples, we introduce the new concept of
generic surrogate models. Response surfaces of a mutual problem class (like lift depending on
(Ma, α) for different airfoil geometries) share mutual characteristics which we want to exploit for
new testcases. Previously generated surrogate models for different airfoil geometries are stored in
a sample function database and a principal component analysis is performed. For a new testcase’s
sample data, a generic surrogate model is generated by fitting a linear combination of the
most important components. Then the sample data is interpolated by a variable fidelity method,
a Kriging-type interpolation which uses the generic surrogate model as a global trend. With this
framework, the approximation error can be reduced compared to normal Kriging and globally
valid surrogates can be generated from small sample sizes.
A stochastic variational inequality approach to elastoplastic problem described by
uncertain parameters
Bojana V. Rosic, Hermann G. Matthies (TU Braunschweig) Schedule
Following the principles of the theory of stochastic variational inequalities of second kind, we
derive the abstract mixed variational formulation of the quasi-static elastoplasticity described by
uncertain parameters, such as bulk and shear modulus, yield stress and hardening. By applying
standard results of convex analysis we show the existence, uniqueness, and convergence of the
solution by extending the results obtained for the corresponding deterministic formulation. Since
the problem reduces to the minimisation of convex functional, we numerically solve it via stochastic
closest point projection algorithm in “white noise analysis “ manner. In other words, we
apply intrusive stochastic Galerkin method fundamentally based on polynomial chaos algebra. As
it does not rely on sampling, the method is shown to be very robust and accurate. Finally, the
method is validated on simple numerical examples in plane strain conditions by comparison with
the direct integration techniques.
Numerical methods for shape optimization under uncertainty
Martin Pach, Rüdiger Schultz (Universität Duisburg-Essen) Schedule
We investigate the impact of uncertainty in shape optimization problems. In particular, we consi-

Minisymposia YR-MA1 – MA3 23
der elastic structures under random forces. Therefor a formulation for shape optimization models
with risk functions will be presented. The required numerical methods, these are level set methods
and a grid generation algorithm, are discussed.
Efficient approximation of the stochastic Galerkin matrix in the canonical tensor
format
Philipp Wähnert, Mike Espig, Wolfgang Hackbusch (MPI Leipzig), Hermann G. Matthies (TU
Braunschweig) Schedule
In this talk we consider the stochastic diffusion problem −∇ · (exp γ∇u) = f with zero boundary
conditions where γ denotes a Gaussian random field with zero mean and given covariance
function. The Stochastic Galerkin discretization permits to calculate deterministically a random
field solving this partial differential equation with uncertainties. However this approach usually
leads to stiffness matrices K whose size grows exponentially with the degree of freedom used
by the discretization. Various attempts were made to attenuate this curse of dimensionality by
using different iterative solvers which take advantage of the special block structure of the stiffness
matrix and parallelization techniques for further optimizations.
Our approach is to approximate the stiffness matrix K in a data sparse tensor format. This
allows to perform matrix vector multiplication effectively in order to apply iterative solving techniques
in high dimensions. Regarding the special structure of the truncated Karhunen-Loève
expansion of exp γ and the polynomial chaos expansion of the resulting random variables it is
possible to construct an approximation in the canonical tensor format. Under additional assumptions
on γ we are able to proof that the rank of this approximation does not depend exponentially
on the number of degrees of freedom in the stochastic discretization.
Mini-YR-MA2: Differential algebraic equations: theory, numerics and applications
Organizers: Stephan Trenn (TU Kaiserslautern) Tue, 10:00–12:00
Matthias Voigt (MPI Magdeburg) dmstm–germanium2 3.02/03
On perturbations in the leading coefficient matrix of time-varying index-1 DAEs
Thomas Berger (TU Ilmenau) Schedule
Time-varying index-1 DAEs and the effects of perturbations in the leading coefficient matrix are
investigated. A reasonable class of allowable perturbations is introduced. Robustness results in
terms of the Bohl exponent and perturbation operator are presented. Finally, a new stability
radius involving these perturbations is introduced and investigated. In particular, a lower bound
for the stability radius is derived. The results are presented by means of illustrative examples.
A converse Lyapunov theorem for switched DAEs
Stephan Trenn, Fabian Wirth (Universität Würzburg) Schedule
For switched ordinary differential equations (ODEs) it is well known that exponential stability under
arbitrary switching yields the existence of a common Lyapunov function. The result is known
as an “converse Lyapunov Theorem”. For switched differential algebraic equations (DAEs) such a
result is not known yet in general. Recently, it was shown that a certain commutativity condition
yields a quadratic Lyapunov function similar as for the switched ODE case. Since the solution of
switched DAEs might exhibit jumps the generalization of the converse Lyapunov Theorem is not
trivial. The talk will aim to present a solution to this problem.
Coupled systems as Abstract Differential-Algebraic Equations
Michael Matthes (Universität zu Köln) Schedule

24 Minisymposia YR-MA1 – MA3
We study so called Abstract Differential-Algebraic Equations (ADAEs) which are Differential-
Algebraic Equations (DAEs) with operators acting on infinite dimensional Hilbert or Banach
spaces. In applications these equations arise when coupling DAEs and partial differential equations
(PDEs). Information is shared between these two systems by certain coupling operators. For
example specific models in circuit simulation were already studied in the literature in the context
of ADAEs or PDAEs.
While theory and numerics of DAEs and PDEs were well developed in the last 20 years there
are just a few results for coupled DAE-PDE systems concerning solvability and convergence. We
study a general prototype class of a coupled system where the infinite dimensional part of the
system is governed by a monotone operator. Investigating especially the coupling terms we give an
existence and uniqueness result of this prototype system. Also the Galerkin approach is discussed
as it is important for numerical applications.
Numerical Methods for PDAE Constraint Optimal Control
Jan Heiland, Volker Mehrmann (TU Berlin) Schedule
The basis for the numerical analysis of optimal control problems governed by partial differential
equations with algebraic constraints is the linear time varying differential-algebraic equation system.
This is due to the fact that sooner or later a numerical solution procedure approximates the
PDAE by a linearization and a space discretization.
Therefore the work presented concentrates on time-varying descriptor systems and quadratic
cost functionals. The associated Euler-Lagrange equations that provide necessary and sometimes
sufficient conditions are given by a boundary value problem. This boundary value problem is
always a differential-algebraic equation system. Thus a solution may not exist because of inconsistency,
lacking smoothness of the data or singularity of the cost functional.
We give conditions on the state equations and the cost functional for the existence of a
solution to the Euler-Lagrange equations if one employs a Riccati ansatz. A special focus lies on
semi-explicit DAEs of differentiation index 2 that may be used to formulate spatially discretized
Navier-Stokes equations.
We further discuss numerical approaches to the approximate solution of the so obtained differential
algebraic Riccati matrix equations and the application to flow control problems.
H∞-Norm Computation for Large Sparse Descriptor Systems
Matthias Voigt, Peter Benner (MPI Magdeburg) Schedule
In this talk we discuss an iterative algorithm for the computation of the H∞-norm of continuoustime
linear-time invariant descriptor systems
E ˙x(t) = Ax(t) + Bu(t), y(t) = Cx(t),
with transfer function G(s) := C(sE − A) −1 B. Hereby we focus on the case where E and A are
large and sparse matrices, so direct methods as described in [1] cannot be applied.
Our algorithm is based on the computation of the complex structured stability radius of the
matrix pencil λE − A, defined by
rC(E, A, B, C) := inf {�∆� 2 : Λf(E, A + B∆C) ∩ iR �= ∅} ,
and the relation
1
�G� = H∞ rC(E, A, B, C) .
To obtain rC we compute a sequence of complex structured pseudospectral abscissae
αε(E, A, B, C) := max {Re z : z ∈ Λε(E, A, B, C)}

Minisymposia YR-MA1 – MA3 25
with the complex structured pseudospectrum
Λε(E, A, B, C) := � z ∈ C : z ∈ Λ(E, A + B∆C) for a ∆ ∈ C m×p with �∆� 2 < ε � .
Then, αrC (E, A, B, C) = 0. To compute αε(E, A, B, C) for given ε we adapt an existing iterative
scheme for the computation of the unstructured stability radius of a matrix [2] to our problem.
[1] P. Benner, M. Voigt: L∞-norm computation for continuous-time descriptor systems using
structured matrix pencils, IEEE Trans. Automat. Control, 2011, accepted.
[2] N. Guglielmi, M. L. Overton: Fast algorithms for the approximation of the pseudospectral
abscissa and pseudospectral radius of a matrix, 2011, submitted.
Mini-YR-MA3: Trends in model predictive control
Organizers: Timm Faulwasser (Universität Magdeburg) Tue, 10:00–12:00
Karl Worthmann (Universität Bayreuth) dmstm–helium2 3.08/09
Introduction to Model Predictive Control
Karl Worthmann (Universität Bayreuth), Timm Faulwasser (Universität Magdeburg) Schedule
In recent years model predictive control (MPC) has become a very active field of research in
systems and control theory. The scientific interest in MPC is fostered by the increasing needs to
run industrial systems and processes both safely and efficiently. The possibility to consider nonlinear
models with state and input constraints as well as the online optimization of the process
performance are key features which lead to application related interest in MPC. Although many
successful applications of nonlinear MPC are reported, there are still numerous open theoretical
questions regarding MPC schemes with guaranteed stability and robustness properties. Furthermore,
the extension to advanced control tasks is subject of ongoing research, e.g. schemes suitably
designed for trajectory tracking, direct cost optimizing control, or the control of time-varying systems.
In addition, the development of efficient optimization strategies, which allow for fast online
solutions of the underlying optimal control problems, is of vital interest for the application of
nonlinear MPC.
The focus of the minisymposium lies upon system theoretic as well as on algorithmic and
numerical aspects of theoretically sound MPC schemes. This introductory talk presents the basic
methodology of MPC and indicates some concepts for ensuring stability of the MPC closed loop.
An active set solver for robust receding horizon control
Johannes Buerger, Mark Cannon, Basil Kouvaritakis (University of Oxford) Schedule
An efficient optimization procedure is proposed for computing a receding horizon control law for
linear systems with additive disturbances. The algorithm uses an active set method based on
Riccati recursions to solve the underlying dynamic programming problem associated with the
min-max optimization of an H-infinity performance index. The active set at the solution is determined
at each sampling instant as a function of the current system state using the first-order
necessary conditions for optimality. The resulting algorithm has complexity per iteration which
grows only linearly with prediction horizon length. The talk summarizes previous work (which
focussed on the input constrained case) and gives extensions to the general setting including linear
state constraints. This allows to ensure recursive feasibility through the use of suitable polyhedral

26 Minisymposia YR-MA1 – MA3
backwards reachable sets guaranteeing that the state predictions enter a robust positive invariant
terminal set. In the presence of state constraints the optimal value of the cost can be discontinuous,
leading to degenerate subproblems at such points a key challenge which will be addressed
in the talk.
Improving the NMPC Algorithm via Sensitivity Analysis
Jürgen Pannek (Universität der Bundeswehr München) Schedule
Typically, model predictive control (MPC) algorithms consist of three steps: estimation of the
initial state, solution of an optimal control problem over a finite horizon, and implementation of
the first element of the optimal control sequence. Although the state estimation problem can be
quite challenging, the usual bottleneck of MPC is the solution of the optimal control problem.
In particular, long prediction horizons and high dimensional systems may easily render the MPC
algorithm to be unapplicable in real time. One way to deal with this issue is to use a forward
prediction of the estimated initial state which allows for larger computing times but may be troubling
in terms of robustness. Different from that, an analytically precomputed continuous feedback
could be used as a tracking input. While the required prediction horizon for such an approach is
typically short, the continuous feedback may be hard to obtain. Here, we follow the idea of using
sensitivity analysis to combine the basic ideas of these two approaches: In a slow outer loop, the
standard MPC algorithm is used to compute a feedback sequence and the corresponding sensitivity
data. Then, in (one or more) inner loops, based on the sensitivity information a feedback is
generated which utilizes the outer loop control as a feed forward for tracking. For this setting, we
present stability results and suboptimality estimates of the proposed method with respect to the
infinite horizon optimal control.
Unconstrained Model Predictive Control and Suboptimality Estimates for Nonlinear
Systems
Marcus Reble (Universität Stuttgart) Schedule
In this talk, we present a continuous-time version of recent results on unconstrained nonlinear
model predictive control schemes. In order to guarantee asymptotic stability, we derive explicit
conditions on the prediction horizon based on a controllability assumption of the system and two
corresponding äbstractïnfinite-dimensional linear programs. The particular structures of both linear
programs allow solutions involving only a single integration of a scalar variable. Furthermore,
the setup allows to give guaranteed bounds on the performance compared to an infinite horizon
optimal controller.
Periodic Model Predictive Control
Ravi Gondhalekar (Osaka University) Schedule
Model predictive control (MPC) has proven highly effective for control of systems subject to
constraints, but is usually considered in a time-invariant setting. On the other hand, periodic
control has been considered for many decades, but usually in an unconstrained setting. In this
talk recent advances in linear-periodic MPC are presented. The presented methods are extensions
of the well-known methods for MPC of linear time-invariant (LTI) systems, both in the sense that
the MPC concepts are extended from the LTI to the periodic setting, but importantly also in
that when the periodic system has a period length of unity (i.e., LTI system) they reduce to the
well-known LTI-MPC methods. There are three reasons why periodic MPC is useful. First, systems
with periodic dynamics exist in practice, for example turbines, engines and walking robots.
Second, systems with time-invariant dynamics may lead to periodic control problems, because the
factors affecting the system are periodic. An example of this is building climate control. Third,

Minisymposia YR-MA1 – MA3 27
periodic systems are convenient models of systems that may be time-invariant, but are subject
to asynchronous timing constraints on the inputs. The talk highlights the final reason.
Model Predictive Control for Constrained Trajectory Tracking
Timm Faulwasser, Rolf Findeisen (Universität Magdeburg) Schedule
For set-point stabilization using model predictive control approaches many solutions exist. For
application relevant problems beyond set-point stabilization – like trajectory tracking and path
following– only a few results with explicit stability guarantees exist.
We discuss a model predictive control approach to trajectory tracking problems of constrained
continuous time systems, where the reference trajectory is apriori known. To handle the timevarying
nature of the tracking problem we advocate the use of time-varying level sets of Lyapunov
functions as terminal regions. We present necessary and sufcient conditions for positive invariance
of these sets. We show how these sets can be efficiently computed via an infinite dimensional linear
programm, if a quadratic Lyapunov function is available. The applicability of the method is shown
considering a nonlinear CSTR.

28 Minisymposia YR ME1 – ME3
Minisymposia YR ME1 – ME3
Mini-YR-ME1: Structural optimization in view of robustness and sensitivity
Organizers: Martin Liebscher (DYNAmore GmbH) Tue, 10:00–12:00
Uwe Reuter (TU Dresden) dmstm–platinum2 2.07/08
Uncertainty in structural dynamics and aeroelasticity: modelling, propagation and
identification
Hamed Haddad Khodaparast (The University of Liverpool) Schedule
Knowledge in the field of modelling and predicting the dynamic responses of aerostructures is
constantly developing. Modelling of uncertainty is considered as one of the tools that increases
confidence by providing extra information. This information may then be useful in planning physical
tests. The complexity of structures together with uncertainty-based methods leads inevitably
to increased computation; therefore deterministic approaches are preferred by industry and a safety
factor is incorporated to account for uncertainties. However, the selection of a proper safety
factor relies on engineering insight. Hence, there has been much interest in developing efficient
uncertainty-based methods with a good degree of accuracy.
In this lecture we first briefly introduce the methods for modelling uncertainty in the parameters
of structural model. Then methods for propagation of structural uncertainty through dynamic
systems are explained. Although the propagation method may be used directly for quantification
of dynamic responses but an issue of very practical significance is the initial estimation of the
parameter uncertainty to be propagated particularly when the uncertain parameters cannot be
measured, such as damping and stiffness terms in mechanical joints or material-property variability.
What can be measured is the variability in dynamic behaviour as represented by natural
frequencies, mode shapes, or frequency response functions. The inverse problem then becomes
one of inferring the parameter uncertainty from statistical measured data. These approaches are
referred to as uncertainty identification or stochastic model updating. Two uncertain identification
methods which have been already developed by the author are explained in this lecture.
A combined approach of considering uncertainty in optimization tasks to efficiently
identify robust designs
Marco Götz, Stephan Pannier, Wolfgang Graf, Michael Kaliske (TU Dresden) Schedule
The aim of almost all design tasks is to determine a robust design. In order to assess the robustness,
the uncertainty of input parameters has to be taken into account. The incorporation of
uncertain parameters in an optimization task may succeed in an active or passive manner. In an
active approach, also denoted as here-and-now strategy, the uncertainty for a respective design
is known and the robustness can be assessed directly. Thereby, the numerical effort to determine
a robust optimum can be tremendous. In a passive approach, also denoted as wait-and-see
strategy, the optimal design is determined without a distinct knowledge about the uncertainty of
this design. A first good shot about an optimal robust design can be determined efficiently, but
a quantification of the robustness is hindered.
In this contribution, the theoretical bases of active and of passive optimization strategies are
introduced. Both approaches are evaluated in detail and on the basis of the obtained results a
combined approach is elaborated. In a combined approach the advantages should be intensified
while the disadvantages should be reduced. Hence, a robust design can be identified in a numerically
efficient way. The applicability of the presented approach is demonstrated by means of
examples.

Minisymposia YR ME1 – ME3 29
Advanced analysis of sensitivities in parameter-free shape optimisation
Nikolai Gerzen, Franz-Joseph Barthold (TU Dortmund) Schedule
This contribution deals with sensitivity analysis in parameter-free shape optimisation. Sensitivity
analysis is one of the most important parts of a structural optimisation algorithm. The efficiency
of the algorithm mainly depends on the obtained sensitivity information. The pseudo load and
sensitivity matrices which appear in sensitivity analysis are commonly used to derive and to calculate
the gradients and the Hessian matrices of objective functions and of constraints. The aim
of this contribution is to show that these matrices contain additional useful information which is
not used in structural optimisation until now. We demonstrate the opportunities and capabilities
of the new information which are obtained by singular value decomposition (SVD) of the pseudo
load and sensitivity matrices and by eigenvalue decomposition of the Hessian matrix. We present
some structural optimization algorithms which are based on the made observations. Furthermore,
we avoid jagged boundaries in parameter-free shape optimisation by applying a density filtering
technique well-known in topology optimization and obtain consistently filtered first and second
order sensitivities. Numerical examples illustrate the advocated theoretical concept.
Global sensitivity analysis for the efficient solution of optimization problem in design
process
Uwe Reuter, Zeeshan Mehmood (TU Dresden), Martin Liebscher (DYNAmore GmbH) Schedule
Optimization of a structural design is a computationally extensive process. Complexity of structural
optimization problems can be reduced if the relationship between the design parameters
and the model response is effectively identified. This relationship is captured by the methods of
sensitivity analysis. Sensitivity analysis helps in identifying the most significant model parameters
affecting a specific model response. In this contribution properties of certain meta-models or
approximation techniques (e.g. neural networks, support vector machines) are evaluated for extracting
sensitivity information directly from these models. These methods capture the non-linear
relationships of the underlying input parameters to the design response. Sensitivity analysis with
meta-models or approximation techniques is likely to be less computationally expensive and can
be easily applied to the relevant industry problems.
Assessment of robustness and sensitivity with solution spaces
Markus Zimmermann, Lavinia Graff, Johannes Fender (BMW, Department of Vehicle Safety)
Schedule
Classical optimization methods seek a minimum or a maximum in the design space in order to
find the best solution. Often, however, this solution is not best, e.g. when it is not robust or
it is in conflict with other design goals. Therefore, more advanced methods like robust design
optimization or multidisciplinary optimization are applied. Unfortunately, they have other disadvantages:
they are computationally expensive, information on how to improve a non-robust
solution is limited and for a multi-disciplinary optimization, a model that comprises all relevant
disciplines must be provided, e.g. a model for a simultaneous vehicle crash and vibration analysis,
which is typically not available. The alternative method proposed here identifies a solution space
of a design problem in one discipline like crash analysis. The computed solution space is such
that it guarantees a supercritical or subcritical output with a defined probability for all enclosed
designs. For simplicity, the solution space is expressed as corridors for each input parameter. The
corridors may be used to assess robustness and sensitivity or they may be combined with corridors
of other disciplines their cross sections are global solution spaces. The underlying method
relies on the Monte Carlo sampling technique built into an iterative scheme. Problems may be
non-linear, high-dimensional and noisy. Practical applications to crash analysis are presented.

30 Minisymposia YR ME1 – ME3
Topology synthesis of large-displacement, compliant mechanisms possessing optimized
flexure hinges
Frank Dirksen (Universität der Bundeswehr Hamburg, University of California, Berkeley), Tarek
Zohdi (University of California, Berkeley), Rolf Lammering (Universität der Bundeswehr Hamburg)
Schedule
This paper presents the synthesis of large-displacement, path-following compliant mechanisms
(CM) possessing optimized flexure hinges. A non-intuitive topology optimization algorithm based
on a continuum design domain is described and applied to maximize the motion of the design
CM on a user-specified output direction. Non-linear geometric effects are taken into account to
ensure proper modelling of large displacements occurring in CM. A robust and efficient staggered
optimization scheme, based on optimality criteria method (OC) and globally convergent method
of moving asymptotes (GCMMA), is implemented to solve the optimization problem. The obtained
final topology of the CM is able to follow the specified direction within the given precision
limit.
As in many current topology optimization methods, this procedure yields final topologies of
CM that include the positions of artificial (flexure) hinges but not their optimal shape leaving
doubts on the physical meaning as well as an uncertainty in the manufacturing process. To overcome
this drawback of optimized compliant mechanisms’ topologies, artificial hinges are replaced by
real flexure hinges meeting the performance specifications given by the CM’s kinematics and/or
by the intended application.
Different flexure hinges were investigated beforehand in terms of relevant performance criteria
such as maximum deflection range, bending stiffness, natural frequency and, most importantly,
fatigue life. Explicit analytical expressions are derived and are validated by experimental data
(cf. [1]). Solving these explicit expressions inversely enables to select or to design optimal flexure
hinges meeting the desired performance specifications of each individual flexure hinge prior to
any modeling or manufacturing efforts. Embedding the appropriately selected or designed flexure
hinges results in final CM that are ready to manufacture. Thus, the synthesis and manufacturing
process of compliant mechanisms can be accelerated significantly.
[1] F. Dirksen, R. Lammering, On mechanical properties of planar flexure hinges of compliant
mechanisms, Mechanical Sciences – Future directions of compliant mechanisms 2 (2011), 1
– 109-117.
Mini-YR-ME2: Advanced material modeling strategies at different scales with
application to production processes
Organizers: Benjamin Klusemann (RWTH Aachen) Tue, 10:00–12:00
Ivaylo Vladimirov (RWTH Aachen) dmstm–spectrum
A meshfree quasicontinuum formulation for scale-bridging material models based on
interatomic potentials
Dennis M. Kochmann, Malena I. Espanol, Michael Ortiz (Caltech) Schedule
Modeling the mechanical behavior of solids at the micro- and nanometer scale is challenging as the
discrete nature of the crystal becomes apparent: simulations using molecular dynamics provide
the required accuracy but come with prohibitively high computational expenses severely limiting
the simulation capabilities. Continuum models are much more attracting yet not suitable at those

Minisymposia YR ME1 – ME3 31
scales where the continuum hypothesis breaks down. Hence, multiscale techniques are needed to
bridge the scales from atomistics to the continuum.
The quasicontinuum (QC) method was introduced to overcome the practical limitations of
classical atomistic modeling in terms of simulation time and space. The QC methodology employs
a combination of full atomistic resolution in regions of high variations and an approximate
continuum model in the major part of the simulation domain away from those regions. As the
continuum description is based on discrete lattice statics with atomic positions constrained by an
interpolation scheme, the model can be solely based on atomistic potentials without the need for
phenomenological continuum models.
Here, we present a novel quasicontinuum formulation that is based on a meshfree interpolation
scheme (making use of local maximum-entropy shape functions) and new summation rules that
involve representative atoms and additional quadrature-point sampling to result in high accuracy.
In addition, we present a proof of convergence and demonstrate sample applications of deformation
processes in crystalline solids.
Deformation patterning and grain boundary modeling through strain gradient crystal
plasticity
Tuncay Yalcinkaya (European Commission - Joint Research Centre, Institute for Energy and
Transport) Schedule
A rate dependent strain gradient crystal plasticity framework is presented where the displacement
and the plastic slip fields are considered as primary variables. These coupled fields are determined
on a global level by solving simultaneously the linear momentum balance and the slip evolution
equation, which is derived in a thermodynamically consistent manner. The slip law differs from
classical ones in the sense that it includes a non-convex free energy term, which enables patterning
of the deformation field. The formulation of the computational framework is at least partially
dual to a Ginzburg-Landau type of phase field modelling approach. The framework is enriched by
incorporating a non-dissipative dislocation-grain boundary interaction potential in terms of grain
boundary Burgers tensor. For the treatment of grain boundaries within the solution algorithm,
an interface element is formulated. The proposed formulation is capable of capturing the effect of
misorientation of neighbouring grains and the orientation of the grain boundaries on slip evolution
in a natural way. The numerical examples illustrate the patterning of deformation field in grains
and plastic slip accumulation at the grain boundaries.
Application of non-convex gradient plasticity to the modeling of stress relaxation
and microstructure evolution
Benjamin Klusemann, Bob Svendsen (RWTH Aachen) Schedule
During loading of real (i.e., materially heterogeneous) metallic materials, local microscopic stress
concentration activates individual microscopic defects (e.g., dislocations) in the material, resulting
in a spatially heterogeneous plastic strain. During this process most metals form cellular
dislocation structures, e.g. dislocation cells and dislocation walls. In general, this will take place
in the material llong“before the macroscopic activation or yield threshold is reached.
Only when a sufficient criticalnnumber of such defects are activated, do they collectively
breakthrough to the macroscopic level, resulting, e.g., in macroscopic yield and macroscopic stress
relaxation. As is well-known, one way to model such emergent behavior in many physical systems
and contexts is with the help of phase-field methods and non-convexity. Several sources
of non-convexity are known in material science, e.g., dislocation-lattice interaction, glide-system
interaction or large deformation. As very simple non-convex energy forms we examine polynomialbased
Landau-Devonshire type forms, as well as periodic forms such as the Frenkel form.

32 Minisymposia YR ME1 – ME3
The purpose of this work is the modeling of the microstructure behavior of metals with gradient
plasticity via energetic non-convexity. For this a model formulation based on continuum
thermodynamics and rate-variational methods is presented. An exemplary metal which we are
trying to model are TWIP steels. TWIP steels show different stages of deformation which can be
related to the microstructural deformation mode. First the deformation is mainly slip dominated
with pronounced strain hardening. Afterwards a non-pronounced serrated flow can be observed
in the stress-strain curve which is related to the onset of deformation twinning. Finally the stressstrain
curve shows serrated flow which is related to heavy twinning and twins intersection at the
microstructural level. First numerical results of these effects will be given.
Efficient simulation of non-linear micro-heterogeneous structures using an orderreduction
approach
Felix Fritzen, Thomas Böhlke (KIT), Samuel Forest (Ecole des Mines) Schedule
The homogenization of physically nonlinear materials with microstructure is a challenging procedure.
This is due to the path dependency of the local constitutive variables and the geometrical
complexity on the small scale. In the past decade the nonuniform transformation field analysis
(NTFA) has proven to give accurate predictions of the effective nonlinear response of such microheterogeneous
materials in the presence of elasto-plasticity. The method belongs to the class of
order-reduction algorithms and uses an approximation of the space-time dependent plastic strain
field via a finite-dimensional basis of spatially nonuniform basis functions determined in numerical
experiments. These fields can account for the geometry and the physical properties of the
examined materials. The evolution of the new internal variables determines the local and, thus,
global stress response. Notably not only the effective stress but also the phase averages can be
replicated with good accuracy even if anisotropic morphologies are considered.
A concise review of previous order-reduction based homogenization schemes is presented and
the capabilities of these method are outlined with respect to numerical savings and computational
accuracy. Further, a novel order-reduction based homogenization scheme for visco-elastic
composite materials is developed. Such materials occur in many engineering applications, e.g., in
terms of fibre-reinforced polymers. The new method does not require a phenomenological evolution
equation for the set of reduced internal variables representing the microscopic fields, which is
a drawback in previous NTFA related works. A set of tools for the efficient analysis of the effective
material behavior of visco-elastic composites is developed based on the presented formulation.
Numerical results outline the capabilities of an order-reduction based approach to homogenization
for the considered class of materials.
A rate independent polycrystal model and a specific application for asymmetrically
rolled aluminum sheets
Ricardo Alves de Sousa (University of Aveiro) Schedule
The asymmetric rolling process differs from conventional rolling through the use of different
roll circumferential velocities or diameters. Using proper parameters, asymmetric rolling imposes
intense shear deformations across the sheet thickness, leading not only to the occurrence of shear
texture, but also to grain refinement. In fact, some shear texture components are known to improve
plastic strain ratio values, and thus formability.
In this work, the rate-independent polycrystal model of Gambin [2] was efficiently implemented
and applied to predict texture on asymmetrical rolling. For FCC materials, this polycrystal
plasticity model avoids the uniqueness issue related to the choice of the set of active slip systems

Minisymposia YR ME1 – ME3 33
by applying a regularized Schmid Law. Consequently, it generates yield surfaces with smooth
corners where the normal vector is always uniquely defined. Also, it doesn’t require the arbitrarily
defined reference strain rate commonly used in the viscous-approximation of rate-dependent
models.
For validation purposes, a 1050-O sheet was asymmetrically rolled and annealed. Shear texture
was obtained, as opposed to typical gamma-fiber texture obtained on sheets rolled through the
conventional process. Moreover, shear texture was found to be retained after annealing. Shear
tests were used to evaluate strength and formability, and the obtained experimental results were
compared with numerical simulations. In the end, the accuracy of simulation results as well as
the advantages of the asymmetric rolling process, when compared to conventional rolling are the
main topics of discussion.
[1] K. -H. Kim and D. N. Lee (2001), Analysis of deformation textures of asymmetrically rolled
aluminum sheets, Acta Materialia 49, pp2583-2595.
[2] Gambin, W. (2000), Plasticity and Textures, Kluwer Academic Press.
[3] F.J.P. Simões, R.J. Alves de Sousa, J.J. Grácio, F. Barlat, J.-W. Yoon, Mechanical behavior
of an asymmetrically rolled and annealed 1050-O sheet, International Journal of Mechanical
Sciences 50:1372-1380, 2008
Production simulation by means of a structure tensor-based framework of anisotropic
plasticity - numerical aspects and experimental validation
I. N. Vladimirov, S. Reese (RWTH Aachen) Schedule
Advanced finite element simulations of sheet metal forming operations are essential nowadays for
the design of tools and processes. One of the decisive factors influencing the simulation result
is the material model being used. Sheet metal parts are subjected to stretching, bending and
straightening during forming, and an accurate prediction of e.g. the blank springback requires the
use of appropriate modelling approaches capable of describing the cyclic hardening behaviour of
metals. In addition, due to the inherent anisotropy of sheet metals, the material model should
be able to describe initial and deformation-induced anisotropy. Sheet metals exhibit anisotropic
plastic behavior due to their textured or generally orientation-dependent microstructure. Many
problems in sheet metal forming arise due to the inherent sheet anisotropy. During the rolling
process of the sheet, large plastic deformations take place which may induce texture and are
responsible for the initial anisotropy.
In this work, we discuss a finite strain continuum mechanical model combining both nonlinear
isotropic hardening and nonlinear kinematic hardening. The kinematic hardening component,
which is the significant factor in simulating springback, represents a continuum extension of the
classical rheological model of Armstrong-Frederick kinematic hardening. The evolution of elastic
anisotropy is represented by defining the Helmholtz free energy as a function of a family of
evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the
yield surface on the plastic deformation and on the same family of structure tensors. Exploiting
the dissipation inequality leads to the interesting result that all tensor-valued internal variables
are symmetric. Thus, the integration of the evolution equations can be efficiently performed by
means of a form of the exponential map algorithm based on an implicit time integration scheme.
It automatically satisfies plastic incompressibility in every time step, and in addition, has the
advantage of preserving the symmetry of the internal variables.

34 Minisymposia YR ME1 – ME3
Mini-YR-ME3: Non-standard discretization methods for multi-physics
Organizers: Dirk Hartmann (Siemens AG) Tue, 10:00–12:00
Thomas Richter (Universität Heidelberg) dmstm–vanadium2 2.02/03
Computational Challenges in Multi-Physics Problems
Dirk Hartmann (Siemens AG, Corporate Technology) Schedule
Computational modelling of continuum mechanical phenomena plays an important role in many
engineering disciplines as well as in many industrial developmental processes. Setting up corresponding
computational studies in existing computational tools is rather complex involving four
major steps: simplification of CAD geometries, generating appropriate meshes, solution of the
underlying physical models, and visualization of the results. Considering problems involving different
physical models the process of setting up simulations is even more complex since typically
several different computational algorithms have to be coupled.
In this talk, we will address two of the major challenges: an efficient handling of complex
domains and the corresponding CAD and mesh generation process as well as a simplification of
current computational tool chains. Furthermore, we will outline a meshless particle based method
for continuum mechanics, being a candidate to solve the two challenges. The presented Lagrangian
particle method can efficiently realize also Dirichlet boundary conditions via appropriate
interpolation schemes and thus allows an elegant formulation of multiphysics problems, e.g. fluid
structure interaction problems as well as multiscale problems like crack growth. Using Multi -
GPGPU architectures the method can be efficiently parallelized and thus allowing a simulation of
rather complex setups on Desktop PCs. The presented method is therefore a candidate to resolve
two of the major challenges in computational engineering and industrial developmental processes.
The Unfitted Discontinuous Galerkin method as a Multi-Physics framework
Christian Engwer (Universtät Münster) Schedule
We are facing an increasing complexity in the models of scientific computing. Multi-physics applications,
highly non-linear processes and domains exhibiting a complex shape are only some
examples of such complexity. These changes pose a big challenge to the development of scientific
software. On the one hand the requirements on the software are growing, e.g. broader feature sets,
demand for easy parallelism. On the other hand the turn over times are getting shorter, which
requires shorter development times.
To handle these requirements, DUNE provides a flexible framework for grid based methods for
the solution of PDEs. We present an extensions of the DUNE framework to handle multi-physics
and multi-domain applications. It is based on the Unfitted Discontinous Galerkin method, which
provides higher order cut-cell methods based on a Discontinuous Galerkin discretization. The
module allows flexible computations while still allowing an efficient, i.e. rapid, implementation of
new simulations. Domain boundaries are given as a level-set function, which allows computations
on time-depended domains. Suitable coupling conditions are imposed along the interface.
We introduce the new framework and show some brief example applications.
A multiscale mesh-free modeling of particles in suspension
Xin Bian, Marco Ellero, Nikolaus A. Adams (TU München) Schedule
We apply the smoothed dissipative particle dynamics (SDPD)[1] method to model hard particles
in suspension. SDPD is a Lagrangian mesh-free method, which is based on smoothed particle
hydrodynamics (SPH) discretization of the Navier-Stokes equations and further incorporates

Minisymposia YR ME1 – ME3 35
thermal fluctuations on the hydrodynamic variables in a thermodynamically consistent way. The
resultant SDPD algorithm has similar formulation as another popular mesoscopic method, namely
dissipative particle dynamics (DPD). Therefore SDPD is considered as a multiscale framework
linking SPH to DPD[2] and it can be used as a simulation tool for fluid problems ranging from
granular flow down to colloidal suspension.
Rigid structures (e.g., grain, colloid, micro-channel) are modeled by frozen SDPD particles
(boundary particles) and no-slip boundary condition on the interface is improved by velocity
interpolation during viscous and stochastic force calculations[3]. After pairwise forces between
SDPD particles are calculated, the total force and torque on the rigid structure are obtained
by accumulating forces and torques exerted by surrounding solvent particles on the boundary
particles. Then the dynamics of the rigid body is decoupled from the solvent by integrating a
separate Newtonian equation of motion. As numerical results, dynamics of both one and multiple
solid particles are simulated and compared with references.
[1] P. Español and M. Revenga, Smoothed dissipative particle dynamics, Phys. Rev. E, 67(2):,
026705, 2003.
[2] A. Vázquez-Quesada, M. Ellero, and P. Español, Consistent scaling of thermal fluctuations
in smoothed dissipative particle dynamics, J. Chem. Phys., 130(3): 034901, 2009.
[3] X. Bian, S. Litvinov, R. Qian, M. Ellero, and N. A. Adams, Multiscale modeling of particle
in suspension with smoothed dissipative particle dynamics, Phys. Fluids, accepted, 2012.
Numerical Simulations of Chemotaxis-Driven PDEs
Andriy Sokolov, Stefan Turek, Robert Strehl (TU Dortmund) Schedule
In the last twenty years one can observe a rapid and consistent growth of interest for biomathematical
applications. Among them are modeling of tumor invasion and metastasis (Chaplain
et al.), modeling of vascular network assembly (Preziosi et al.), pattern formations due to
the Turing-type instability (Murray et al.) or chemotaxis-driven processes (Horstmann et al.),
protein-protein interaction on the membrane (Goryachev, Bastiaens) and others. These mathematical
models, presented as systems of advection-reaction-diffusion equations, can take into consideration
various biological processes (e.g. transport, random walk, reaction, chemotaxis, growth
and decay, etc.). In order to get an accurate numerical solution in a reasonably finite time one has
to construct an efficient, fast and robust numerical scheme for a sufficiently large class of partial
differential equations.
In our recent research we combine the system of the generalized Keller-Segel model for multispecies
with reaction-diffusion equations on (evolving in time) surfaces, which can be mathema-

36 Minisymposia YR ME1 – ME3
tically written in the following form
∂ui
∂t =
+
random walk/diffusion
� �� �
D u i ∆ui + ∇ ·
⎡ species-species interaction species-agents interaction⎤
�� �� �
⎢ n�
� �� �� �
m�
�
⎥
⎢
⎥
⎢ κi,kui∇uk − χi,kui∇ck ⎥
⎣
⎦ +
k=1,k�=i
kinetics
� �� �
fi(c, ρ), in Ω, (1)
∂cj
∂t = Dc decay production
� �� � � �� �
m�
n�
j∆cj − αk,jck + βk,juk +gj(u, ρ), in Ω (2)
∂ρl
∂t =
k=1
diffusion on surface
� �� �
D ρ
l ∆Γρl
source
k=1
� �� �
+ sl(u, c), on Γ (3)
where ui(, t) (i = 1, n) and cj(, t) (j = 1, m) are some solutions (for example, species and chemical
agents) defined in a domain Ω ⊂ d (d = 1, 2, 3), and ρl (l = 1, p) are solutions defined on a
surface Γ(t) ⊂ Ω. By ∆Γ· we denote the Laplace-Beltrami operator on Γ. Corresponding initial
and boundary conditions are prescribed.
Equations (3) describe the change of concentrations or substances on a (time dependent) surface.
These equations have a variety of applications in computational physics, scientific visualization,
image analysis and computer graphics. For example, from the molecular biology it is known that
many important and scientifically interesting processes in a cell occur on a membrane. The form
of which can vary in time as a response to these processes (for example protein-protein interaction
in works of Goryachev and Bastiaens). The presence of the equations (3) helps to keep track on
solutions, which react on the membrane. To find both numerical solutions of the system of PDEs
on a surface and the modification of a shape of the evolving in time surface is a very nontrivial
task. It requires a profound research and a sufficient amount of time for the algorithmic realization
and programming implementation.
On the other hand, the generalized Keller-Segel system for multi-species (1)–(2) is very interesting
from both a mathematical and a modeling point of view, since it describes a wide range of patternforming
and aggregating behavior, blow-up phenomena and stability effects. Moreover, numerical
challenges require the construction of a positivity-preserving and non-oscillatory scheme, since
straightforward FEM simulation of the system (1)–(2) is not possible. Also, efficient solvers
for coupled nonlinear systems should be taken into account. Here, we present a new symmetric
flux-corrected transport (FCT) algorithm applied to the generalized Keller-Segel model (1)–(2).
Corresponding numerical simulations demonstrate a realistic behavior for chemotaxis-driven problems.
We believe that the construction of a fast, efficient and robust numerical scheme for the system
(1)–(3) will serve as a basis for a reliable software tool to be used as a ’virtual biomathematical
laboratory’ for different hierarchies of models and parameter settings in various applications
of biology and medicine.
A dynamic load-balancing MPI-PThreads hybrid implementation of the Optimal
Transportation Meshfree (OTM) method
Bo Li, Mark Stalzer, Michael Ortiz (Caltech) Schedule
We present a parallel computational implementation of the Optimal Transportation Meshfree
(OTM) method of Li et al. [1] and the parallel seizing contact and variational material point
failure algorithms for simulating general fluid and solid flows. The OTM method of Li et al.
k=1

Minisymposia YR ME1 – ME3 37
combines elements of Optimal Transportation theory with local MaxEnt meshfree interpolation
of the fields and material point sampling. The OTM method enforces mass transport and
essential boundary conditions exactly as well as exact conservation of linear and angular momentum.
The parallel implementation of the OTM method uses a multilevel distributed memory and
shared memory scheme. Domain decomposition algorithms based on graph theory or geometric
techniques are employed to distribute material points to separate processors. A shadow scheme
is proposed to define the shared information among partitions which is synchronized by using
the de facto standard message passing interfaces (MPI). To this end, the collection of material
points on each processor is further partitioned based on a dynamic computational cost function
as a second level parallelization with the utilization of the POSIX Threads library. The parallel
approach has been applied to predict the high energy density dynamic response of materials on
departmental class systems. Excellent speedup to O(10 5 ) threads is achieved in our large scale
three-dimensional OTM simulations of ballistic/hypervelocity impact. We also find ideal weak
scaling in our applications of concurrent multiscale computing.
[1] B. Li, F. Habbal, M. Ortiz, Optimal transportation meshfree approximation schemes for fluid
and plastic flows, Int. J. Numer. Meth. Engng 83(2010), 1541–1579.
Fluid Structure Interaction in Fully Eulerian Coordinates
Thomas Richter (Universität Heidelberg) Schedule
In this contribution we present a formulation for fluid-structure interaction problems which is
given in Eulerian coordinates for both sub-problems, fluid and solid. By this setting it is possible
to derive a novel monolithic formulation of the coupled problem.
In contract to the well-established Arbitrary Lagrangian Eulerian (ALE) coordinates - a very
common basis for monolithic modeling of fluid-structure interactions - the Eulerian formulation
goes without the introduction of an artificial coordinate system and artificial domain mappings.
In ALE coordinates this mapping of the fluid domain often gives rise to problems when dealing
with large deformation, free movement of the structure or even contact of the structure with
parts of the boundary (topology change). While the Eulerian formulation in principal allows for
such problems it brings along new difficulties connected to the Eulerian coordinate system used
to describe the structural problem.
We will describe the basic idea of modeling fluid-structure interactions in Eulerian coordinates
and present a finite element scheme for its discretization. Further, for verification of this
novel formulation, we analyze benchmark-problems in comparison to classical approaches like
the Arbitrary Lagrangian Eulerian coordinates. Finally, we point out capabilities offered by this
formulation which cannot be considered in classical monolithic approaches.

38 Section 1: Multi-body dynamics
Section 1: Multi-body dynamics
Organizers: Peter Betsch (Universität Siegen), Bernd Simeon (TU Kaiserslautern)
S1.1: Optimization of MBS Tue, 13:30–15:30
Chair: Peter Betsch S2|02–C110
Planned contacts and collision avoidance on optimal control problems
Sigrid Leyendecker (Universität Erlangen-Nürnberg), Gwen Johnson, Michael Ortiz (Caltech)
Schedule
When simulating the dynamics of three-dimensional multibody systems, the treatment of contact
always imposes a challenge. One simple solution is to formulate a smooth problem where the
bodies are allowed to overlap by a certain amount, which is penalized via a penalty potential. Of
course, the drawbacks going along with this approach of inadmissible configurations and inexact
contact forces are obvious. Non-smooth formulations require the specification of a contact force
that (for elastic collisions) reflects the momentum normal to a contact surface at a given time and
configuration. In the context of a structure preserving time integration method (being consistent
in the evolution of energy and momentum maps) that uses a predefined equidistant time grid,
there is no other known procedure except for resolving the collisions in the sense that each contact
time (which is likely between the nodes), configuration, and force are exactly computed, see [1].
This work will show how the described alternatives for the treatment of collisions can be
included in the context of optimal control problems. In the smooth formulation with a penalty
potential, there arises some difficulty for the optimiser to distinguish between a contact and a
control force, since both might point into the same direction. For the nonsmooth treatment, the
optimal control problem formulation gives more freedom than the forward dynamics problem,
since periodic boundary conditions or leaving the exact placement of time nodes (within certain
bounds) to the optimiser leaves the freedom to assume that contact takes place at a certain
time node without loss of generality, i.e. without fixing its physical time. A further challenge
is the detection of contact for non-convex three-dimensional bodies where a new strategy based
on a supporting separating hyperplane linear programming approach is used [2]. Reconfiguration
and docking manoeuvres with collision avoidance and with planned collisions are considered as
examples.
[1] R.C. Fetecau, J.E. Marsden, M. Ortiz, and M. West. Nonsmooth Lagrangian mechanics and
variational collision integrators. Siam J. applied dynamical systems, 2, 381-416, 2003.
[2] G. Johnson, M. Ortiz, and S. Leyendecker. A linear programming-based algorithm for the
signed separation of (non-smooth) convex bodies. Submitted for publication, 2011.
Topology Optimization of Members of Elastic Multibody Systems
Alexander Held, Robert Seifried (Universität Stuttgart) Schedule
Lightweight techniques are applied increasingly often for modern machine designs in order to reduce
the moving masses and therewith the energy consumption. However, as a result the stiffness
of the system decreases causing undesired elastic deformations and therewith end-effector deviations.
In this talk a topology optimization procedure for elastic multibody systems is presented
to lower end-effector tracking errors.
To capture both the large nonlinear working motion and the deformation of the bodies the
system has to be modeled as elastic multibody system. In case the deformations are compara-

Section 1: Multi-body dynamics 39
tively small the floating frame of reference formulation is often the most efficient approach. In
this formulation the global nonlinear motion is described by a reference frame while the elastic
deformations are described with respect to the reference frame using shape functions and elastic
coordinates.
In topology optimization the goal is to distribute a limited amount of mass in a reference
domain such that the compliance of the structure becomes minimal under certain loads. For the
presented topology optimization the Solid Isotropic Material with Penalization (SIMP) approach
is used. However, since the global shape functions are obtained from finite element models by
modal analysis, the SIMP approach is slightly adapted to avoid localized modes. To solve the
large scale optimization problem efficiently the Method of Moving Asymptotes is applied.
The established optimization workflow resembles the equivalent static loads method. Thereby
a series of transient simulations is performed. After each transient simulation a set of equivalent
static loads is derived and an improved design is determined. In doing so the highly expensive
sensitivity analysis of the design variables in the time domain is avoided. To lower tracking errors,
the displacement fields are selected at the time points at which the highest end-effector deviations
occur.
The results show that topology optimization can be successfully employed to optimize the
design of elastic members of elastic multibody systems. More precisely the system is stiffened
with respect to the dynamical loads of a specified motion. Thereby the number of global shape
functions should be selected carefully since they determine the representable displacement fields
and therewith the quality of the optimization results.
Trajectory Planning and Optimization of Mechanisms with Redundant Kinematics
for Manufacturing Processes with Constant Tool Speed
Andreas Scholz, Francisco Geu Flores, Andrés Kecskeméthy (Universität Duisburg-Essen) Schedule
The present paper deals with the optimal path planning for kinematically redundant mechanisms
in manufacturing processes which require constant tool speed along given paths on the workpiece.
A three-stage optimization method is introduced that allows for the computation of the
mechanisms optimal design and its control by discretizing the problem and transforming it into a
nonlinear constrained optimization problem which can be solved using standard SQP algorithms.
The method is presented by means of a planar serial robot with three rotational degrees of freedom
θ ∈ R 3 and an auxiliary mechanism with one rotational degree of freedom ϕ ∈ R about
an axis normal to the robot‘s working plane. The tool is mounted at the end effector, whereas
the workpiece is fixed to the auxiliary mechanism. Since it is required that the tool traverses
a prescribed path S on the workpiece with a given, constant velocity ˙s and angle of attack ψ,
the motion of the system is defined by the motion ϕ(t) of the auxiliary mechanism. The goal is
to compute the optimal control ϕ(t) as well as the optimal initial pose of the mechanism with
respect to the robot‘s inertial coordinate system which allow for a maximal constant tool velocity
˙s subject to the maximally allowed angular displacements, velocities, and accelerations at the
robot‘s actuators. The control ϕ(t) is parameterized by an interpolating quadratic spline with m
spline parameters. The optimal set of parameters and the initial pose of the mechanism relative
to the robot are sought by means of a three step optimization method. The first stage consists
in searching for a feasible initial guess by minimizing the standard deviation of the joint angles
during the motion using only few spline segments and a small value for ˙s. In the second stage,
the number of spline segments is refined while ˙s remains unmodified. The third stage consists of
a sequence of optimization runs with increasing tool speed ˙s at each intermediate step. Hereby, ˙s
is increased in small increments such that the optimizer is always able to find a feasible solution

40 Section 1: Multi-body dynamics
and ˙s approaches asymptotically its maximal value. The three stage optimization method yields
good convergence properties, allowing for the determination of the minimal process cycle time.
A Hamiltonian conserving indirect optimal control method for multibody dynamics
Ralf Siebert, Peter Betsch (Universität Siegen) Schedule
In the past, a lot of effort has gone into the development of structure-preserving time-stepping
schemes for forward dynamic problems. This is due to the superior numerical stability of these
integrators. Guided by previous developments in the design of energy-momentum integrators for
forward dynamic problems, a Hamiltonian conserving indirect optimal control method will be
introduced. For the state equations, a midpoint evaluation or a consistent variant thereof will be
applied. Based on this specific discretization of the state equations, a discretization of the costate
equations will be introduced, which is based on the notion of a discrete derivative and which
leads to the algorithmic conservation of the discrete Hamiltonian. As in the forward dynamic
case, it can be expected, that a Hamiltonian conserving method will yield superior numerical
stability properties. Therefore, the newly developed method will be compared with a previously
introduced direct transcription method. We will test the newly proposed method with some
numerical examples, which are, for example, the optimal control of a 3-link manipulator. Therein,
the control effort, which is necessary for moving the multibody system from one configuration to
another, will be minimized.
About identifying inertia and friction parameters in mechanisms
Johannes Rutzmoser, Markus Roßner, Thomas Thümmel, Heinz Ulbrich (TU München) Schedule
Mechanisms in general are transmissions with speed droop and continuous and non-continuous
motion. They are widely used in processing machines. For identifying the inertia parameters, which
are the crucial parameters for the dynamics of the system, the eigenmotion of the mechanism can
be utilized for contributing to an objective function in an optimization.
This methodology is shown at a crank rocker mechanism test rig, where the inertia parameters
are identified in a first step. The experimentally created pseudo-eigenmotion is compared with
the ideal eigenmotion of the multibody simulation model. With numerical optimization the error
between experiment and simulation is minimized by varying the unknown inertia parameters. In
order to improve accuracy, the sensitivity of the different parameters with respect to the indicator
functions is evaluated and regarded in the optimization.
In a second step the friction parameters of the joints are identified with transient operations
of the machine. Therefore, force- and speed-dependent friction laws are used. Covering noncontinuous
motion of the mechanism components, boundary lubrication regimes are considered
in the speed-dependent model. Further comparisons of different settings in experiment and simulation
show that a speed-dependent friction model describes the observed speed of the test rig
quite well.
S1.2: Analytical Mechanics Tue, 16:00–18:00
Chair: Christian Hesch S2|02–C110
An Approach for Decomposition of Finite Rotations
Clementina Mladenova (Institute of Mechanics, Bulgarian Academy of Sciences) Schedule
The presentation of rigid body displacements is an old mechanical problem but of a great importance
in solving different real tasks. In geometrical and computational mechanics rigid body
kinematics is considered through vectors and matrices approaches. In this aspect the rotation

Section 1: Multi-body dynamics 41
group in three dimensional space may be described combining our knowledge from analytical mechanics,
vector analysis, algebra and differential geometry. Here is the place to mention that the
different parameterizations of the rotation group SO(3) influence on the efficiency of the kinematic
and dynamic models as at one rigid body so in multibody mechanical systems. The analytical
representations of any rotation can be expressed by defining its action on vectors, quaternions
or spinors. On the other hand the parameterizations of the rotations are: Eulerian angles in the
classical 3-1-3 sense and all other combinatons like: 3-2-3, 3-2-1, 1-2-3 and etc., are known as
Bryant angles, Eulerian parameters, Cayley-Klein parameters and etc. To find the resultant axis
and angle of rotation after two, three or more finite partial rotations is a problem very important
in multibody mechanics. But the inverse problem, namely, to decompose a finite rotation into
three partial rotations about prescribed axis is a more difficult one and it is very important in
motion planning in the group of rotations and inverse kinematic problem at a manipulator system
as well. The present paper gives explicit formulae in solving this problem using vector-like
parameterization of rotation group. In the first part the notion vector-parameter is introduced
and its properties are given. After that the above-mentioned problem is solved and exemplified
in concrete settings. The method is realized analytically using the computer algebra system Mathematica.
Cases of Complete Integrability in Transcendental Functions in Dynamics and Certain
Invariant Indices
Maxim V. Shamolin (Institute of Mechanics, Lomonosov Moscow State University) Schedule
The results of this work appeared in the process of studying a certain problem on the rigid body
motion in a medium with resistance, where we needed to deal with first integrals having nonstandard
properties. Precisely, they are not analytic, not smooth, and on certain sets, they can
be even discontinuous. Moreover, they are expressed through a finite combination of elementary
functions. However, the latter circumstances allowed us to carry out a complete analysis of all
phase trajectories and show those their properties which have a roughness and are preserved for
systems of a more general form having certain symmetries of latent type.
This work is the study of the problem of 2D- and 3D- motion of a symmetric rigid body that
interacts with the medium only through a plane part (cavitator) of its exterior surface too. In
constructing the force field, we use the information about the properties of streamline flow around
under quasistationarity conditions, and the medium motion is not studied in this case. In contrast
to the previous works where the dependence of the force moment on the body angular velocity
is neglected, in this work, in accordance with experiment, we take into account the effects of
influence of the rotational derivatives of hydro-aero-dynamical forces in components of the body
angular velocity.
The multiparameter family of system phase portraits on the two- and threedimensional cylinder
wich characterized the invariant indices was obtained.
Vibrations of rotating systems with an infinite number of degrees of freedom.
Artur Wirowski (Technical University of Lodz) Schedule
The subject of the paper is a system an infinite number of electrically charged beams, which
interact each other by electrostatic forces. Each beam is simply supported at the center of gravity
and thus has one degree of freedom, it is possible to its rotation around the fulcrum. All of beams
are arranged one above another thus creating electrostatic forces interconnected system with an
infinite number of degrees of freedom.
Aim of this study is to describe the forced vibration of such a system. In this paper, starting
from a single beam equilibrium equation derived continuous equation of motion of this system. Is

42 Section 1: Multi-body dynamics
considered the impact of additional assumptions on the form of the resulting equations of motion,
such as small angles of rotation plates and their uniform distribution. After taking into account
these simplifications, the equation is obtained analogous to the equation of vibrating string:
where γ, θ are constant, M(x, t) is external moment.
1
γ2 ∂2φ ∂t2 − ∂2φ = θM(x, t) (1)
∂x2 The equation (1) is solved for the sample boundary-initial conditions. The paper presents and
discussed the results. In the summary also shows the possible practical applications of the present
theoretical model and the planned directions of further research the author.
[1] G. Genta, Dynamics of rotating systems, Mechanical Engineering Series,
Springer Science+Buisness, NY USA (2005).
[2] P. Blanchard, R.L. Devaney, G.R. Hall, Differential Equations, Thompson, (2006)
The moons perigee and plumb-in line
Dmitry G. Kiryan (Institute of Problems of Mechanical Engineering, RAS), Georgy V. Kiryan
(The Main Astronomical Observatory, RAS) Schedule
In this paper we have established a functional relationship between deflection of a gravitational
field line and lunar perigee location. Physical nature of the process inducing the Chandler wobble
has been shown. We have proved that the Chandler wobble results from a combination of two
types of motion: additional rotation of the Earth and cyclic motion of the Moon around the Earth.
We suggest here a physical model of the Earths interior structure as a system of two separate
masses: the Core and the Earth. The cause-and-effect relationship between the lunar perigee
coordinates and the Core location within the Earth has been revealed. The results obtained fit
well the presently available data from astronomical and gravimetrical observations.
S1.3: Control of MBS Tue, 16:00–18:00
Chair: Hartmut Bremer S2|07–109
Feedforward Control of Multibody Systems by Rheonomic Constraints
Werner Schiehlen, Robert Seifried, Thomas Gorius, Steffen Raach (Universität Stuttgart) Schedule
Controlling nonlinear multibody systems usually the inverse dynamics approach is used, e.g.
[1-3]. The feedforward control scheme is simply computed from the equations of motion, and
complemented by a linear feedback approach to compensate measurement errors and parameter
variations. From a mechanical point of view the feedforward control can also be introduced using
the prescribed motion as a rheonomic constraint. Then, a kinematically determined multibody
system has to be analysed.
In this paper the constraint forces and torques due to rheonomic constraints for kinematically
determined systems without any degree of freedom are discussed, see also [4]. Matrix methods are
presented for the design of the feedforward control. As an example a assembly device is considered
and simulations of the results achieved are shown.
[1] Blajer, W.; Schiehlen, W.: Walking Without Impacts as a Motion/Force Control Problem.
Journal of Dynamic Systems, Measurement, and Control, Trans. ASME 114, 660 – 665,
1992.

Section 1: Multi-body dynamics 43
[2] Spong, M.W.; Hutchinson, S.; Vidyasagar, M.: Robot Modeling and Control. Wiley, Hoboken,
2006.
[3] Liu Fan; Er Meng Joo: Linear and Nonlinear PD-type Control of Robotic Manipulators for
Trajectory Tracking. Industrial Electronics and Applications, 2009. (ICIEA 2009). 4th IEEE
Conference, 25 – 27 May 2009, 3442 – 3447.
[4] Schiehlen, W.; Eberhard, P.: Technische Dynamik. 3. Auflage, B.G. Teubner, Wiesbaden,
2012.
Modeling and Quasi-Static Trajectory Control of a Self-Balancing Two-Wheeled Vehicle
F. Johannes Kilian, Hubert Gattringer, Hartmut Bremer (Universität Linz) Schedule
This paper deals with the kinematical and dynamical model as well as a quasi-static trajectory
controller of a self-balancing two-wheeled vehicle. This mobile robot is about 50cm tall, autonomous,
unstable and driven by two wheels and therefore used for transport purposes. Due to the
nonholonomic contraints only few modeling techniques are feasible. In this contribution several
modeling methods are compared, followed by the derivation of various control strategies.
A partial feedback linearization in combination with a LQR controller is applied to stabilize
the inclination angle of the robot. The quasi-static trajectory controller, which is based on the
kinematical model, uses a flatness based approach in order to remain along the desired path.
Continous curvature paths, composed by clothoids, are used to demonstrate good performance
results in simulation and experiment.
Recursive Methods in Modeling and Control of Modular Robotic Systems
Bernhard Oberhuber, Hubert Gattringer, Hartmut Bremer (Universität Linz) Schedule
This paper addresses the dynamical modeling and control of reconfigurable modular robots. The
modular actuators (brushless DC motors with Harmonic Drive gears) for the robots under consideration
are connected by rigid links. This way the robot can be assembled in different configurations
by rearranging these components. For dynamical modeling the Projection Equation in
Subsystem representation is used, taking advantage of its modular structure. Due to the lack of
position sensors at the gearbox output shaft, deflections caused by the elasticities in the gears
can not be compensated by the PD motor joint controller. Therefore, a correction of the motor
trajectory is needed, which can be calculated as part of a flatness based feed-forward control using
the exact model of the robot. With the recursive approach proposed in this paper the concept of
reconfigurability is retained. For validation a redundant articulated robot arm with seven joints
is regarded and results are presented.
Natural co-ordinates for control applications
Nicolas Sänger, Peter Betsch (Universität Siegen) Schedule
Natural coordinates have emerged to be well-suited for both rigid and flexible multibody dynamics.
Especially the combination of structural elements and energy-momentum consistent time
stepping schemes leads to superior numerical stability as well as an automatable assembly, resulting
in both excellent run-time behaviour as well as moderate modelling effort (see [1]). Incorporation
of modern methods for finite-element simulations, such as mortar methods for contact or
domain decomposition both for structural elements as well as continuum elements is straightforward
([2]).

44 Section 1: Multi-body dynamics
Augmentation techniques allow a systematic integration of both mechanical and non-mechanical
quantities for simulation (see [3] and [4]), which makes this approach suitable especially for emulation
and simulation of mechatronic systems. We will present an approach for evaluating forward
control strategies with flexible multibody systems.
[1] Sänger, N. ; Betsch, P.: A nonlinear finite element framework for flexible multibody
dynamics: Rotationless formulation and energy-momentum conserving discretization . In:
Bottasso, C.L. (Hrsg.) ; Masarati, P. (Hrsg.); Trainelli, L. (Hrsg.): Proceedings of the
ECCOMAS Thematic Conference on Multibody Dynamics. Politecnico di Milano, Milano,
Italy, 25-28 June 2007
[2] C. Hesch and P. Betsch. A mortar method for energy-momentum conserving schemes in
frictionless dynamic contact problems.Int. J. Numer. Meth. Engng, 77(10):1468–1500, 2009.
[3] Bottasso, C.L. ; Croce, A.: Optimal Control of Multibody Systems Using an Energy
Preserving Direct Transcription Method. In: Multibody System Dynamics 12 (2004), Nr. 1,
S. 17–45
[4] Betsch, P. ; Uhlar, S.: Energy-momentum conserving integration of multibody dynamics.
In: Multibody System Dynamics 17 (2007), Nr. 4, S. 243–289
Comparative study on control concepts of a robot manipulator with multiplelink/joint
flexibilities
Peter Staufer, Hubert Gattringer, Hartmut Bremer (Universität Linz) Schedule
If one is dealing with active vibration suppression on a highly nonlinear flexible system, various
techniques are needed. On the one hand a suitable dynamic model of the system is required.
And on the other hand intelligent model based control concepts are necessary for active vibration
damping. We deal with a basic model, where the flexibilities are approximated with linear springs
and dampers, a so called lumped element model (LEM). For the control design a two degree of
freedom control scheme is suggested for solving the tracking problem, based on the LEM. The
most important benefit using this control concept is that the feedforward part can be designed
independent from the feedback part. Hereby the feedforward control is based on the flatness
approach. For the feedback control several strategies are studied using acceleration- and gyrosensor
measurements. Moreover the basis for the latter one is a linearization along the trajectory, where
a tracking error system is obtained.
The contribution is completed with a validation by measurements with a very fast trajectory on
an articulated robot with two flexible links and three elastic joints.
Application of one-dimensional piezoelectric structure in numerical control of a biomechanical
system
Pawel Olejnik, Jan Awrejcewicz (Technical University of Lodz) Schedule
A biomechanical model of human chest with a sensor attached to the chest’s posterior surface is
subject to an impulsive action of external impact force. The sensor is taken into consideration
as a one-dimensional dynamical system of a piezoelectric energy harvester. Investigations focus
on application of a controlled function of reaction that would minimize deformation of the chest
cave caused by the impact loading. Because of difficulties appeared in measurement of the impact
force exciting in the system it is proposed to measure displacement of the chest’s posterior surface
x5 by means of the piezoelectric energy harvester. The one-dimensional dynamical system of a

Section 1: Multi-body dynamics 45
piezoelectric energy harvester (supplement of the controlled system) produces a measurement
signal used in a scheme of active control.
The system of equations of the biomechanical part of the model is as follows:
˙xi = xi+4 , ˙x4 = x7 + ¯ k −1
23 ¯c23(x2 − x4) , ˙x5 = m1 −1� k12(x2 − x1) � ,
˙x6 = m2 −1� k12(x1 − x2) − k23(x2 − x3) − ¯ k23(x2 − x4) − c23(x6 − x7) � , (1)
˙x7 = m3 −1� k23x2 − (k23 + ks)x3 + c23x6 − (c23 + ¯c23 + cs)x7 + ¯c23x8 − u � ,
where: i = 1 . . . 3, m1 . . . m3 denote the separated point masses of the model, ¯c = [c23, c ′ 23, cs], ¯ k =
[k12, k23, k ′ 23, ks] are the vectors of system stiffness and damping (respectively), ¯xd(t) = [x1 . . . x4]
is the vector of system displacements in each direction, ¯xv(t) = [x5 . . . x8] is the vector of system
velocities, but with regard to the introduced rheological description of the model the massless
point reduces dimension of the system to 7. Thus, object of control (the plant) is described by an
odd-dimension system state vector, means ¯x = [¯xd, x5 . . . x7].
The piezoelectric element has mass mp and is connected to a resistor. Its dynamics is described
by a set of three first-order differential equations constituting basic electromechanical coupling
between y1, v and x5:
˙y1 = y2 , ˙y2 = −kpmt −1 y1 + θv − ˙x5 , ˙v = −θcp −1 y2 − cpR −1 v , (2)
where: kp - effective stiffness, mt - approximate total mass of the piezoelectric system, R - leakage
resistance, y1(t) - distance between the proof mass and the base, θ - electromechanical coupling,
v(t) - voltage through the piezoelement.
Preliminary computations confirm that the additional piezoelectric system generate useful
signal of measurement. Reduction of deformation of the idealised chest has been obtained after
utilisation of active control based on minimization of the performance index of LQR method.
S1.4: New Developments in MBS Methodology Wed, 13:30–15:30
Chair: Bernd Simeon S2|02–C110
Bridging Particle Swarm Optimization and Swarm Robotics from A Multibody Point
of View
Peter Eberhard, Qirong Tang (Universität Stuttgart) Schedule
Particle Swarm Optimization (PSO) originally appears as a typical optimization algorithm and
it has been applied to many areas due to its robustness and simple applicability without the need
for cumbersome derivative calculations. In this study we want to bridge some gaps between PSO
and swarm robotics using a multibody point of view.
On the one hand the particles in PSO are moving independently in the search space exchanging
some information according to their update formulae. This is somehow quite similar to the robots
search scenario. If one particle is replaced by one robot then the PSO search for the minimum
of an objective function can be mapped to a scenario of swarm robots searching targets in an
environment. Of course in this case the particles possible motion is determined not only by the
PSO update, but also by the robots mechanical properties and their drives. Thus, the PSO was
extended to a mechanical PSO in order to consider the feasible dynamics, the inertia, and also
the finite size of the robots to avoid collisions during their search.
On the other hand, although groups of robots can give a super behavior in a swarm compared
to simple individuals, it is still a challenge to guide the whole group of robots to search targets
systematically using conventional methods. This is because a group of robots needs heavily simultaneous
localization and mapping. Therefore, one can bring the mechanical PSO to generate

46 Section 1: Multi-body dynamics
the search trajectory as the main guidance for robots by benefiting from PSO’s powerful search
ability. Then the robots further perform fine tuning for obstacle avoidance and mutual avoidance
locally.
Based on above consideration, some tests were performed with both simulations and experiments
using a group of physical robots (the Festo Robotinos).
A modular and efficient approach to computational modeling and sensitivity analysis
of robot and human motion dynamics
Martin Friedmann, Janis Wojtusch, Oskar von Stryk (TU Darmstadt) Schedule
In this paper a new class library for the computation of the forward multi-body system dynamics
of robots and biomechanical models of human motion is presented. By the developed modular modeling
approach the library can be flexibly extended by specific modeling elements like joints with
specific geometry or different muscle models and thus can be applied efficiently for a number of
dynamic simulation and optimization problems. The library not only provides several methods for
solving the forward dynamics problem (like articulated body or composite rigid body algorithms)
which can transparently be exchanged. Moreover, the numerical solution of optimal control problems,
like in the forward dynamics optimization of human motion, is significantly facilitated by
the computation of the sensitivity matrix with respect to the control variables. Examples are
given to demonstrate the efficiency of the approach.
On the Analysis of Multibody Systems in the Presence of Uncertainties
Nico-Philipp Walz, Michael Hanss (Universität Stuttgart) Schedule
As in other areas of simulation technology, the models of multibody systems (MBS), used to
compute large motions of mechanical systems, are continuously improving. In particular, the application
of elastic multibody systems (EMBS) has gained much attention in recent years, aiming
at a better prediction of the dynamical behavior of mechanisms with significant elasticity, such
as light-weight structures.
However, while models are becoming more detailed and more complex, the identification of
the corresponding model parameters becomes more challenging in equal measure. The identified
parameters may exhibit a high level of uncertainty, and exact values for their quantification
can hardly be provided. This non-determinism in numerical models arises as a consequence of
different sources: natural variability or scatter, which is often referred to as aleatory uncertainties,
as well as so-called epistemic uncertainties, which arise from a lack of information, vagueness in
system definition, or simplification and idealization as it usually appears in modeling procedures
to achieve manageable models. Hence, even apparently well modeled MBS may exhibit inherent
uncertainties due to imprecise data, imperfect knowledge or deficiencies in modeling.
While aleatory uncertainties have successfully been taken into account by the use of probability
theory, the additional modeling of epistemic uncertainties still remains a challenging topic. As
a practical approach to solve this limitation, a novel methodology to an advanced modeling of
MBS is presented, which allows for the inclusion of uncertainties from the very beginning of the
modeling procedure. This approach is based on fuzzy arithmetic, a special field of fuzzy set theory,
where the uncertain values of the model parameters are represented by so-called fuzzy numbers,
reflecting in a quite intuitive and plausible way the blurred range of possible parameter values. As
a result of this advanced modeling technique, more comprehensive system models can be derived
which outperform the conventional, crisp-parameterized models by providing simulation results
that reflect both the system dynamics and the effect of the uncertainties. Additionally, the special
fuzzy arithmetical approach is able to compute measures of influence which quantify the effect
of each individual uncertain model parameter on the overall uncertainty of the system output.

Section 1: Multi-body dynamics 47
Thus, the dynamical behavior of the MBS can be rated with respect to the robustness of the
mechanism with respect to uncertainties in the model parameters.
The methodology is illustrated by an exemplary application which reveals that the presented
well-thought-out inclusion of presumably limiting uncertainties can provide significant additional
benefit.
Hybrid coordinate approach for the modelling and simulation of multibody systems
Christian Becker, Peter Betsch, Marlon Franke, Ralf Siebert (Universität Siegen) Schedule
The underlying parametrization in terms of applicable coordinates for the description of multibody
dynamics influences the structure of the governing equations of motion and the ensuing numerical
evaluation. Up to now, this fact has led to a rotationless formulation based on direction cosines,
representing the foundation for an energy-momentum consistent time stepping scheme. Next to
exhibiting superior numerical stability properties, this scheme has proven itself by providing an
uniform framework for the implementation of multibody systems.
The present work deals with the incorporation of an additional angular coordinate into the
aforementioned formulation in the case of fast spinning rotationally symmetric bodies. The idea of
this approach is to achieve higher precision whenever the preferred axis of rotation coincides with
the axis of symmetry. For this purpose, a distinction has been made between a carried and a bodyfixed
coordinate system, regarding the transition from the initial to the actual body configuration.
Moreover the additional coordinate needs to be enforced by an additional conjugated constraint.
An outstanding characteristic of this approach is to which extent the advantageous structure
of the underlying differential-algebraic equations is being preserved. To investigate further the
numerical properties of this approach, a representative numerical example of a spacecraft, equipped
with reaction wheels, will be dealt with.
S1.5: Contact Problems Wed, 16:00–18:00
Chair: Robert Seifried S2|02–C110
The Maxwell-Contact
Kilian Grundl, Thomas Cebulla, Thorsten Schindler, Heinz Ulbrich (TU München) Schedule
Contact models are used to compute contact forces between bodies in multibody systems (MBS).
There are two alternative approaches. The unilateral constraint contact and the unilateral regularized
contact. Both are decoupled contact models, i.e. the contact forces do not depend on other
contacts of the MBS.
This work introduces a new contact model, i.e. the Maxwell-Contact, to couple multiple contact
points quasi-statically. Maxwell’s reciprocal theorem is the basis to derive the underlying equations.
It assumes a linear elastic body and states that the deformation at a point i is influenced by
a force at a point j in the same way as the deformation at j is influenced by a force at i. This
influence is expressed with influence coefficients.
The contact model uses several contour pairings, i.e. contact points defined by the kinematics
of two contours. These kinematics determine a rigid distance between the two contours. The deformations
of both contours depend on all contact forces of all contour pairings that are part
of the Maxwell-Contact. Regarding all contact points, a linear matrix-vector equation follows. It
expresses the (elastic) distances �g due to the rigid distances �˜g and the contact forces � λ of the
single contour pairings:
�g = �˜g + C � λ (1)
where C is the matrix of the influence coefficients that couples the contour pairings.

48 Section 1: Multi-body dynamics
The (elastic) distance as well as the contact force of each contour pairing is constrained. Both have
to be equal or greater than zero. Furthermore, both have to satisfy a complementarity condition:
a force acts only for distances equal to zero and vice versa the force has to be zero for positive
distances:
�0 ≤ �g ⊥ � λ ≥ �0 (2)
where ≤ and ≥ are used element by element. Equations (1) and (2) build the Maxwell Force Law,
i.e. a linear complementarity problem. The contact forces are its solution. Two solution approaches
are considered. The Lemke algorithm solves the system directly by intelligently testing all possible
solutions. Iterative schemes (e.g. a Newton method) use a reformulated system of nonsmooth
equations for the solution. A combination of both approaches is used to get a robust solution
process.
The contact model is implemented into the multibody simulation framework MBSim. It is used
in an academic example to validate the fundamental properties, i.e. a variable stiffness and a
coupling of the contacts due to the Maxwell-Contact.
Self-excited vibrations of deformable multibody systems due to friction: Explanation
with the help of two point masses and a belt
Christian Maier, Christoph Glocker (ETH Zürich) Schedule
The aim of the present work is the stability analysis of a spatial system with 36 degrees of
freedom done by an eigenvalue analysis. The system consists of a cube and a cuboid [1]. Each of
these blocks is discretised by one finite element. The goal of the work is to examine the conditions
under which self-excitation is possible due to friction. In a first step a simplified planar mechanical
system is investigated, which can be solved analytically. It consists of two point masses on top of
a belt, where the belt is moving at a constant velocity. The calculated results are presented in
this paper. The belt system is characterised by three degrees of freedom. The belt is horizontally
movable and is furthermore coupled by a spring-damper element to the environment. The point
masses are supported like mathematical pendulas with elastic bars, where elasticity is taken into
account by spring-damper elements. The point masses are connected to each other by again
a spring-damper element. One of the point masses is additionally coupled to the environment
by an identical element. The motivation for using the above mentioned coupling elements is to
have the possibility to model visco-elasticity. The contact behaviour between the point masses
and the belt are modelled by Signorini’s law in normal direction and by Coulomb friction in
tangential direction. The friction coefficient is defined to be constant and independent of any
relative velocity of the contact. The normal contacts between the two point masses and the belt
are closed and remain closed. In order to allow self-excited vibrations caused by friction, additional
constraints for the values of the friction coefficient for the belt system are deduced. These results
can be used to explain self-excited vibrations due to friction. Furthermore they are the basis for
additional calculations related to the stability behaviour of the spatial model. Finally the results
are compared to those of the spatial model [1] and in that context used to be verified.
[1] Ch. Maier, Ch. Glocker. Deformable multibody systems with impacts and Coulomb friciton
Multibody Dynamics 2011 ECCOMAS, Bruxelles 2011.
Structure Preserving Simulation of Monopedal Jumping
Michael W. Koch, Sigrid Leyendecker (Universität Erlangen-Nürnberg) Schedule

Section 1: Multi-body dynamics 49
This work considers the structure preserving simulation of three-dimensional multibody dynamics
with contacts. We use a variational integrator, based on a discrete version of the Lagrange-
D’Alembert principle and thus yielding a symplectic-momentum method, for the forward dynamics
simulation. Since one of our main goals is structure preservation and geometric correctness,
we have to solve the non-smooth problem including the computation of the contact configuration,
time and force instead of relying on a smooth approximation of the contact problem via a penalty
potential.
In contrast to technically oriented monopedal jumpers, e.g. actuated by extender wheels, the
model of a three-dimensional monopedal jumper in use here is inspired by the human locomotor
system. The dynamics of the interconnected rigid bodies yields a constrained mechanical systems.
Investigated contact formulations cover the theory of perfectly elastic, partly plastic and perfectly
plastic contacts, where the last one means that the foot of the jumper stays in contact to the
ground for a certain period of time. While the contact stays closed, the discrete equations of
motion include a contact force and constraints, whose function is to avoid penetration. As soon
as this contact force changes its orientation (meaning that it would prevent the foot from lifting
off the ground), the contact constraints are released. Thus, the last contact configuration and the
contact release time are determined to guarantee a realistic dynamical behaviour.
A Comparison of Rolling Contact on Roller-Coaster Rails Between Penalty Methods
and Exact Event-Controlled Impact Detection.
Christian Malessa, Andres Kecskemethy (Universität Duisburg-Essen) Schedule
In this paper, two different formulations for the wheel/rail contact problem including clearance
are investigated. The first method, called here the continuous penalty function method, is the
continuous numerical integration, with contact forces arising from step to step as the wheels
penetrate the rails. The second method, termed here the switching penalty function method,
is to register event objects that monitor the distances between wheels and rails in the freefly
phase as well as the impact phase and to stop the integration at the exact time where a
phase changes occurs by a root solver, after which the integrator is re-started with the phases
switched. In the continuous penalty function method, the penetration is computed, and, when
negative, a corresponding repelling force is established according to a spring model (no damping is
considered). In the switching penalty force method, the penetration is registered as a zero-crossing
function within the integration method (in this case we used Lsodar), and, when the function
features a change of sign between the start and end values of an integration step, a zero-crossing
root finding algorithm is started, which determines the exact time of switch condition. Once the
switching time is determined, the integrator is started with the spring contact model, using as
initial condition the integrator variables at the time of switching. In contact, the penetration
is registered as a zero-crossing function as well its zero is used for switching back from contact
to free-fly phase. It can be shown that the new proposed switching method keeps the energy
almost constant, whereby the continuous method shows energy dissipation. Due to the energy
comparison, friction and damping has been neglected in the simulation model. A comparison of
computational time and energy conservation between the two methods showed that the switching
penalty force method not only is clearly more efficient than the continuous penalty force methods,
but also that it is more accurate, as can be seen from the unrealistic energy loss in the continuous
penalty force method, while the switching penalty force method reproduces correctly conservation
of energy. Further work will consider friction at the contacts as well as rolling wheel effects, from
which an accurate model for the better understanding of vibrations for roller-coaster cars on rails
can be established.

50 Section 1: Multi-body dynamics
S1.6: Numerical Methods Thu, 13:30–15:30
Chair: Peter Betsch S2|02–C110
Spurious oscillations in generalized-α time integration methods
Martin Arnold (Universität Halle-Wittenberg), Olivier Brüls (University of Liège), Alberto Cardona
(Universidad Nacional Litoral - Conicet, Santa Fe, Argentina) Schedule
Classical ODE and DAE time integration methods from system dynamics have been applied
successfully for more than two decades to constrained systems in multibody dynamics. For large
scale systems, Newmark type integrators are considered to be an interesting alternative in terms
of numerical effort and stability. In the present paper we study the time integration of constrained
mechanical systems
M(q)¨q = −g(q, ˙q, t) − B ⊤ (q)λ , Φ(q) = 0
by a generalized-α time integration method
with
qn+1 = qn + h ˙qn + (0.5 − β)han + βhan+1
˙qn+1 = ˙qn + (1 − γ)han + γhan+1
(1 − αm)an+1 + αman = (1 − αf)¨qn+1 + αf ¨qn ,
M(qn)¨qn = −g(qn, ˙qn, tn) − B ⊤ (qn)λn , Φ(qn) = 0
and appropriate parameters αf, αm, β, γ, see [1] and the recent extension to constrained systems
in a Lie group setting [2].
The order condition γ = 0.5 + αf − αm guarantees second order convergence in the classical
case as well as for the Lie group integrator [3]. A potential drawback of the methods are spurious
transient oscillations of the constrained forces that result from an order reduction in the transient
phase. We present a strict mathematical analysis of this phenomenon and show how to avoid the
spurious oscillations by perturbed starting values ˙q0, a0.
[1] J. Chung and G. Hulbert: A time integration algorithm for structural dynamics with improved
numerical dissipation: The generalized-α method. ASME Journal of Applied Mechanics,
60:371–375, 1993.
[2] O. Brüls and A. Cardona: On the use of Lie group time integrators in multibody dynamics.
J. Comput. Nonlinear Dynam., 5:031002, 2010.
[3] O. Brüls, A. Cardona, and M. Arnold: Lie group generalized-α time integration of constrained
flexible multibody systems. Mechanism and Machine Theory, in press, 2011. DOI: 10.1016/
j.mechmachtheory.2011.07.017
High-order time integration methods in molecular dynamics
Florian Niederhöfer, Jens Wackerfuß (TU Darmstadt) Schedule
The mechanical behaviour of molecular structures can be described by a system of stiff differential
equations, which can not be solved analytically. Several numerical time integration schemes can
be find in the literature. The aim of this talk is to give a survey of partitioned Runge-Kutta
methods applied in molecular dynamics. This class of methods includes a wide range of explicit
and implicit, single- and multi-stage, symplectic and non-symplectic, low- and high-order time

Section 1: Multi-body dynamics 51
integration schemes. Also most of the classical methods like explicit and implicit Euler, explicit and
implicit midpoint rule, Störmer-Verlet and Newmark are also partitioned Runge-Kutta methods.
The schemes are implemented in a finite element code which can serve as a numerical plattform
for molecular dynamics [1]. To evaluate the different methods several criteria are formulated and
analyzed. The visualization of the simulations is another tool to compare the different methods.
The effectiveness of the methods are demonstrated by means of several numerical simulations.
[1] Wackerfuß, J., Molecular mechanics in the context of the finite element method, International
Journal for Numerical Methods in Engineering, Volume 77, Issue 7, Pages 969-997, 2009
Convergence Study of Explicit Co-Simulation Approaches with Respect to Subsystem
Solver Settings
Robert Schmoll, Bernhard Schweizer (Universität Kassel) Schedule
Coupling different subsystem simulators can be accomplished by a co-simulation [1]. For this
purpose, the subsystem solvers are coupled by appropriate input and output variables. In order to
analyze the stability of the coupled simulation, not only the coupling technique must be taken into
account, but also the subsystem integrators. One the one hand, the stability of the co-simulation
is influenced by the extrapolation of the coupling variables and the macro-step size. On the other
hand, the numerical errors arising from the subsystem solvers may directly affect the coupled
simulation. The focus of this paper lies on the question, how the subsystem solvers influence the
co-simulation. Therefore, numerical studies regarding the numerical stability and the convergence
order have been carried out by using a co-simulation test model [2]. We restrict ourselves to explicit
co-simulation techniques, based on a zero-stable applied-force coupling approach [3]. Furthermore,
stability and convergence are examined for the case that an explicit macro-step size controller is
applied [4].
[1] M. Valasek, Modeling, simulation and control of mechatronical systems, in: Simulation Techniques
for Applied Dynamics, CISM Courses and Lectures Vol. 507 (Springer, 2008), 75 -
140.
[2] M. Busch and B. Schweizer, Numerical stability and accuracy of different co-simulation techniques:
Analytical investigations based on a 2-dof test model, in: The 1st Joint International
Conference on Multibody System Dynamics, (Lappeenranta, Finland, 2010).
[3] R. Kübler and W. Schiehlen, Two Methods of Simulator Coupling, Mathematical and Computer
Modelling of Dynamical Systems 6 (2000), 93 - 113.
[4] M. Busch and B. Schweizer, An explicit approach for controlling the macro-step size of cosimulation
methods, in: 7th European Nonlinear Dynamics Conference, (Rome, Italy, 2011).
Alternative approaches to the incorporation of control constraints in multibody dynamics
Yinping Yang, Peter Betsch (Universität Siegen) Schedule
Control constraints can be used to prescribe the motion in the inverse dynamics of multibody
systems. If the number of control inputs is lower than the degrees of freedom, this kind of mechanical
system is called underactuated system. The solution of such partly specified system is a

52 Section 1: Multi-body dynamics
challenging task due to the underactuation property. The description of underactuated systems
can be based on either minimal coordinates or redundant coordinates. The resulting governing
equations show the form of differential-algebraic equations (DAEs) with a mixed set of holonomic
and control constraints. The index of the DAEs may exceed three and alternative projection
methods will be applied to reduce the index to three. Numerical examples are used to compare
the alternative projection methods.
A discrete Cosserat rod model taking into account the effect of torsion warping
suitable for the dynamic simulation of wind turbine rotor blades
Holger Lang (Universität Erlangen-Nürnberg) Schedule
In our talk, we present a non-standard discretisation scheme for Cosserat rods. The discrete Cosserat
model is — as the continuum one itself — geometrically exact; in particular, it satisfies
the axiom of objectivity: The discrete internal strain measures are invariant with respect to rigid
body motions. The key to receive objectivity is the use of finite quotients (instead of differences)
in order to discretise the curvature of the rod. Finite quotients are obtained naturally, if one uses
quaternions and spherically linear ansatz functions.
In contrast to the standard finite element approach, where the primary unknowns are situated
on the nodes of the grid, we use a staggered grid: Here the translatory and rotatory degrees of
freedom are ordered in an alternating fashion. This ansatz yields a decisive advantage: For the
evaluation of the internal shearing energy, it is not necessary to interpolate the rotations onto the
Gauss point within the element.
On the one hand, the right-hand side of the equations of motion becomes significantly cheaper.
On the other hand — interesting from the numerical point of view — the shearing modes and
frequencies of the continuum model are approximated consistently. (The latter is not the case for
example, if one uses linear shear flexible rod elements in ABAQUS.)
For the time integration of the equations of motions, we use integrators that are well established
in multibody dynamics simulation, e.g. DASSL/DASPK or RADAU5. With these, we arrive at
computational times below the real time barrier, if we use the model for the simulation of flexible
cables and hoses. The model is nowadays used by the industry in assembly simulations.
If, in addition, one takes into account possible warping of the cross sections, e.g. due to
assymetric, open or hollow profiles, an extended continuous version of the Cosserat rod model is
obtained, which exhibits coupling of shearing and torsion. Of course, this effect has a considerable
influence on the defection of the rod centreline.
An enhancement of our discrete model is able to cover these effects for wind turbine rotor
blades up to the accuracy that is required by the manufacturer. For that reason and because of
its low complexity, the new modified discrete model is well suited for MBS simulations in wind
turbine industry.
S1.7: Applications Thu, 16:00–18:00
Chair: Bernd Simeon S2|02–C110
Modeling and Simulation of Ride Dynamics of High-Rise Elevators
Michael Beitelschmidt (TU Dresden), Heinz Widmer (Schindler Aufzüge AG Ebikon) Schedule
Elevators in high-rise buildings ascend altitudes of several hundred meters and achieve a maximum
velocity of more than ten meters per second. During technical development the ride quality
and the safety under extreme load conditions are subject of investigation. The numerical simulation
of a normal ride of the cabin or of special load cases is an important assistance for this
issue. The simulation model presented covers the whole movement in riding direction of cabin and

Section 1: Multi-body dynamics 53
counterweight, the rotation of all pulleys and traction sheaves, vertical movements of compensating
pulleys, control of electrical drives, and at least the longitudinal movement of the ropes.
The elastic conveying ropes of high-rise elevators have a weight within the range of the cabin or
the counterweight respectively. Therefore, the ropes can be modeled neither as massless springs
nor as rigid bodies. The rope model established in the simulation system makes use of the theory
of the longitudinal dynamics of a onedimensional elastic continuum. Because of the change of
length during ride, a mixed Eulerian-Lagrangian ansatz for the ropes to cover different boundary
conditions at the rope ends is used. Stick-slip of the ropes at the contact to the sheaves is included
in the system as well as a simplified model for slack rope which can occur under extreme load
situations. The simulation model is a versatile system implemented in Matlab using its object
oriented programing facilities. The bodies mentioned above and several types of force elements
including driving torque control and rheonomic kinematical excitation elements for different purposes
are implemented. All elements have hooks and eyes for their connection to neighboring
elements. This leads to a tree-structured multi-body system topology, which is suitable for any
elevator system. Different elevator system topologies, e.g. simple setups with or without connecting
rope, additional rope systems for overspeed limiting or even more complex setups resembling
block and tackle configurations can be assembled easily. The presentation covers the modeling of
the systems elements, the compilation to a multibody system using the hookeye logic, numerical
aspects, and simulation results compared to measurements of real rides in the hoistway.
A Discrete Element Model for Degradation of Ballast Tracks
Christian Ergenzinger, Robert Seifried, Peter Eberhard (Universität Stuttgart) Schedule
Track settlement due to degradation of ballast is a severe issue in railway operation. The dynamics
of trains are frequently modeled using multibody systems. However, the simulation of track
dynamics and especially consideration of degradation effects such as breakage of stones requires
other approaches. The Discrete Element Method, which can be regarded as a special case of a
multibody system, is suitable to model these effects. In the Discrete Element Method the system
comprises many thousand rigid bodies, which are often called particles. The interaction of these
particles is governed by unilateral and bilateral penalty forces, respectively.
In this contribution, a model is presented that considers interaction and failure of individual
ballast stones. The stones themselves consist of breakably bonded particles on a meso-scale. The
granular solid generated by bonding of adjacent particles of a dense packing is calibrated to
granite, which is a typical material for railway ballast. Uniaxial and confined compression tests
are used to evaluate strength and failure modes. In a second step, a number of tangent planes
on ellipsoids of appropriate size and aspect ratios are used to define angular ballast stones. The
strength of these stones is determined by compression between parallel platens. From statistical
evaluation of a number of simulations, it is found that based on calibration of the material strength
in compression tests, the strength of the stones in the model compares well to experimental results
from literature. Finally, aggregates of ballast stones are constructed. Strength and failure of these
aggregates are assessed in exemplary load cases such as oedometric compression or indentation
of a sleeper into a railroad ballast bed.
Influence of Internal Actuator Properties of Active Anti-Roll Systems on the Vehicle
Driving Behaviour
Thomas Mirwaldt, Manfred Harrer (Dr. Ing. h.c. F. Porsche AG, Weissach), Peter Eberhard
(Universität Stuttgart) Schedule
Active anti-roll systems - as part of vehicle chassis - are able to adapt their system behaviour to
the current driving situation. It is possible to vary between comfortable or sportive setups. The

54 Section 1: Multi-body dynamics
forces applied to the chassis are determined by ECU-controlled actuators. These ECU includes a
global chassis control which generates set points for an internal actuator feed back control. The
set points are calculated by measured vehicle states.
It has been proven useful to go for a model based design method for the development of such
complex systems. This method consists of simulation models in combination with system testrig
results. Thus, it is possible to achieve early model based predictions about the pre-designed
system. It also gives basic information for the following control strategy synthesis. Test-rigs are
development tools that achieve objective precise system measurements and whose results are used
to verify the simulation models.
The final system application always takes place in the real car. Typically it consists of a
manual parameter adjustment which is based on driver’s subjective criteria. An objective and
efficient way to setup system parameters is given by an implementation of numerical optimization
routines. Hence, these routines enable an automated calibration of the anti-roll system. The
optimization objectives consist of drive comfort criteria as well as factors which describe sportive
driving behaviour. The current states are calculated online from vehicle measurement variables.
With regard to a global vehicle behaviour optimization it is not sufficient to consider global
chassis control parameters only. The dynamic actuator setup and the internal feed back control
set the boundary conditions for the superior body control. The influence of these internal actuator
properties on the global chassis control and thus on the vehicle optimization objectives will be
illustrated.
Stability of vehicles under nonstationary crosswind excitation
Xiaoyu Zhang, Carsten Proppe (KIT) Schedule
Abstract: Strong crosswind gusts have great influence on the stability of railway and road vehicles,
they may lead to accidents and also to a discomfort for the road vehicle driver. Risk assessment
for overturning of railway and road vehicles is usually calculated based on the stationary situation
or at least on wind-tunnel experiments that are carried out with a static vehicle model. Nonstationary
excitation due to wind turbulence occurs if the vehicle accelerates or decelerates. Increasing
vehicle speed relative to wind speed will move the energy content in spectrum to a higher frequency
range. It has been realized that nonstationary wind turbulence has a great influence to
vehicles especially when the vehicle speed is high. Thus in order to assess the overturning risk in
a more realistic way, a nonstationary wind model together with its interaction with the vehicle
should be taken into consideration.
This paper proposes a nonstationary turbulence wind model for the investigation of crosswind
stability of ground vehicles. A wind model with nonstationary turbulence as well as the wind
effects to the moving vehicle in a nonstationary situation (acceleration/deceleration) are described.
Nonstationary aerodynamic forces are considered together with the interaction between the
moving vehicle system and the wind turbulence. Failure probabilities are computed and reliability
analyses are carried out.
Keywords: Vehicles, crosswind stability, nonstationary excitation, reliability analysis.
Zur Wechselwirkung in Elastomerlagern und deren Auswirkung auf das Fahrverhalten
von PKW
Christian Lohse, Matthias Kröger (TU Bergakadmie Freiberg) Schedule
Die Steifigkeit und Dämpfung von Fahrwerkslagern beeinflussen direkt das Fahrverhalten und den
Fahrkomfort. Der Konstrukteur versucht im Entwicklungsprozess die optimale Lösung für den
Zielkonflikt von gutem dynamischen Verhalten inbesondere bei Kurvenfahrt und hohem Kom-

Section 1: Multi-body dynamics 55
fort zu finden. Als Stellgrößen zur Beeinflussung dienen hier die Lagersteifigkeit und -dämpfung,
welche nach den Vorgaben des Lastenheftes für das Bauteil in allen relevanten Beanspruchungsrichtungen
definiert werden. Der Parameter Steifigkeit wird dabei durch die Geometrie ( Form
des enthaltenen Elastomers und die etwaige Verwendung von Zwischenblechen) sowie durch das
verwendete Material beeinflusst. Durch die gezielte Wahl des Werkstoffs kann auch die Dämpfung
und somit das Schwingungsverhalten eingestellt werden. Als gängige Größe für die Beschreibung
der Dämpfung hat sich in den letzten Jahren der Verlustwinkel etabliert.
Im Einsatz wird davon ausgegangen, dass die Kennlinien konstant bleiben und keiner Veränderung
unterliegen. Überlagerungen von eingeleiteten Kräften und Momenten beeinflussen jedoch
die Lagersteifigkeit in den einzelnen Raumrichtungen. Diese Kopplungen können durch ein allgemein
gültiges Elastizitätsgesetz beschrieben werden und finden nur in einer vollständigen, für das
Bauteil, spezifischen Steifigkeitsmatrix Berücksichtigung. Die Kenntnis dieser Kopplungen und
die damit verbundenen Änderungen der Steifkeitskennlinien sind für virtuelle Untersuchungen
aus dem Grund der Genauigkeitserhöhung von Simulationen wünschenswert.
In experimentellen Untersuchungen an einem ausgewählten Elastomerlager sind die, für eine FEA
notwendigen, Kennlinien bestimmt worden. Anschließend wurde ein Finite-Elemente-Modell erarbeitet,
das die Bestimmung der Matrizenelemente erlaubt. Für darauf aufbauende Untersuchungen
kam eine, in der Praxis gängige, Mehrkörpersimulationssoftware zum Einsatz. Es wurden Untersuchungen
an einem starrkörperbasierenden Zwei-Spur-Fahrzeugmodell mit hohem fahrwerkspezifischen
Detaillierungsgrad durchgeführt, in das elastische Fahrwerkslager, auf Grundlage eines
speziellen Elementtyps, eingebracht wurden.
[1] Heißing B., Ersoy M., Gies S.; Fahrwerkhandbuch; Springerverlag; 2011
[2] Matschinsky W.; Radführung der Straßenfahrzeuge; Springerverlag; 2007
[3] Leister G.; Fahrzeugreifen und Fahrwerkentwicklung; Vieweg Teubner Verlag; 2008
[4] Gross D., Hauger W., Schröder J., Wall. W. A.; Technische Mechanik; Springerverlag; 2007
Perspectives on constructive and functional optimizing of a serial robot with four
degrees of liberty destined for special applications
Petrisor Silviu Mihai, Barsan Ghita (Nicolae Balcescu Land Forces Academy, Sibiu, Romania)
Schedule
Serial-modular robots are mainly built from translation, rotation and orientation modules, prehension
devices and connectors. By differently assembling these modules, various robot architectures
result, adequate to operations within military industrial applications. Modulisation implies
building a number of standard modules, common to the same robot family, which, thoroughly
combined, would lead to a variety of constructions in terms of complexity and application.
With this as a starting point, the authors of this paper managed, within the Advanced Logistics
Technologies Laboratory of the Nicolae Bălcescu Land Forces Academy from Sibiu, Romania, to
develop a mathematical algorithm, to ideate and design three modules (basic, arm and prehension
device), which, combined and taking into account the actual mechanical application, would result
in the modeling and configuration of a TTRT robot.
This paper deals with aspects on the dynamic modulation of the robots mechanical structure,
using Langrangian formalism, choosing the adequate DC servomotors, translation modules
constituting the TTRT robot, the constructive solution and modeling the three translation subassemblies
of the studied robot, with the intention that, in the end, based on a dynamic-organologic

56 Section 1: Multi-body dynamics
algorithm, a functional optimization of the robot be brought out within a workcell destined for
special applications, so that the energetic consumption be as low as possible. This paper also
presents the organological calculi and solutions for the efficient design of modules specific to
mechanical structures of industrial serial-modular robots.

Section 2: Biomechanics 57
Section 2: Biomechanics
Organizers: Markus Böl (TU Braunschweig), Oliver Röhrle (Universität Stuttgart)
S2.1: Multi-Phasic Modelling in Biomechanics Tue, 13:30–15:30
Chair: Tim Ricken S1|03–23
Multiphasic Modelling of Human Brain Tissue for Intracranial Drug Infusion Studies
Arndt Wagner, Wolfgang Ehlers (Universität Stuttgart) Schedule
A direct intracranial infusion of a therapeutic solution into the extra-cellular space of human
brain tissue is a promising medical application for the effective treatment of malignant brain
tumours [1]. The advantage of this method, in comparison with an intra-vascular medication, is
the targeted delivery with a circumvention of the blood-brain barrier (BBB), which prohibits the
passing of therapeutic macro-molecules across the vascular walls into the brain parenchyma.
The prediction of the resulting therapeutic distribution by a numerical simulation is challenging,
since the spreading is affected by the complex nature of living brain tissue. Therefore, a macroscopic
continuum-mechanical model is established within the Theory of Porous Media (TPM), proceeding
from a homogenisation of the underlying micro-structure [2]. The biphasic four-constituent
model consists of an elastically deformable solid skeleton (composite of tissue cells and vascular
walls), which is perfused by two mobile but separated liquid phases, the blood plasma and the
overall interstitial fluid (treated as a two-component mixture of the liquid solvent and the dissolved
therapeutic solute). The strongly coupled solid-liquid-transport problem is simultaneously
approximated in all primary unknowns using mixed finite elements (uppc-formulation) and solved
in a monolithic manner with an implicit time-integration scheme.
This numerical investigation allows the computational study of several conditions influencing the
irregular distribution of infused drugs, observed in clinical studies. Therefore, the micro-structural
perfusion characteristics in the extra-cellular space of the white-matter tracts are considered by a
spatial diversification of the anisotropic permeability tensors, provided by Diffusion Tensor Imaging
(DTI). Furthermore, Magnetic Resonance Angiography (MRA) enables the in vivo location
of blood vessels within the brain tissue. Finally, the selection of appropriate material parameters
has a crucial influence on the drug distribution profil and further occurring effects beyond.
[1] R.H. Bobo, D.W. Laske, A. Akbasak, P.F. Morrison, R.L. Dedrick, E.H. Oldfield, Convectionenhanced
delivery of macromolecules in the brain, PNAS 91 (1994), 2076 – 2080.
[2] A. Wagner, W. Ehlers, Continuum-mechanical analysis of human brain tissue, Proc. Appl.
Math. Mech. 10 (2010), 99 – 100.
A Scale Bridging Model For Sinusoidal Liver Perfusion
Daniel Werner, Tim Ricken (TU Dortmund), Uta Dahmen, Olaf Dirsch (Universitätsklinikum
Jena) Schedule
In this talk we will discuss a three-scale finite element model for sinusoidal liver perfusion. Starting
from the macro-scale we use information about blood pressure and blood flux, gathered and
obtained by our collaborators in T. Preusser’s group from the Fraunhofer Institute, as boundary
conditions for our simulation. Regarding the micro-scale, we incorporate a coupled ODE model,
provided by the group of H.-G. Holzhütter from the Charité Berlin, to describe the metabolism
in a singular liver cell. The combination of the macro- and the micro- scale leads to a coupled

58 Section 2: Biomechanics
multiphase simulation on the meso-scale, which is based on a 2-D model for sinusoidal liver
perfusion [1].
Since the liver is composed of a fluid (blood) that flows through a solid biological structure
(tissue), the liver can be described as a multiphase material. Multiphase materials consist of two
or more interacting components with strong coupling between solid deformation, fluid pressure,
and fluid flow. Due to the consistent theoretical framework and its proven applicability, the
Theory of Porous Media (TPM) is chosen as the underlying framework for this project. After
giving a short motivation and introduction to the TPM, we will present numerical examples to
demonstrate our model’s ability to provide information about stresses, strains, blood flow and
pressure, concentrations, sinusoidal organization, and remodeling from the micro- to macro- scale.
[1] T. Ricken, U. Dahmen, O. Dirsch, A Multiphase Model for remodeling in liver lobes during
resection, Biomechanics and Modeling in Mechanobiology 9 (2010), 435 – 450.
A Biphasic Approach for the Simulation of Growth Processes in Soft Biological Tissues
Incorporating Damage-Induced Stress Softening
Thomas Schmidt, Daniel Balzani (Universität Duisburg-Essen), Tim Ricken, Daniel Werner (TU
Dortmund) Schedule
In the context of cardiovascular diseases such as cardiac hypertrophy growth processes play a
predominant role. Myocardial tissues can be characterized as a multiphase material containing
a solid phase which can mechanically be characterized as a fiber-reinforced material, and a fluid
phase which is assumed to transport nutrients required for the growth process. The passive behavior
of myocardial tissues shows a strain softening which is found to be a result of microscopic
damage, see [1] and which thus strongly influences the overall mechanical behavior during growth.
In this contribution a multiphase model, cf. [2], is proposed for the simulation of growth processes
which occur in myocardial tissues based on the theory of porous media. The solid phase is modeled
by applying the approach proposed in [3], which is formulated in terms of the concept of internal
variables and continuum damage mechanics. The fiber damage is represented by a scalar-valued
damage variable and remanent strains in fiber direction due to supra-physiological loading situations
can be captured. Numerical Examples are given in order to show the performance of the
proposed model.
[1] J.L. Emery, J.H. Omens, and A.D. McCulloch: Strain Softening in Rat Left Ventricular
Myocardium, Transactions of the ASME - Journal of Biomechanical Engineering, 119:6–12,
1997.
[2] T. Ricken and J. Bluhm: Remodeling and Growth of Living Tissue - A Multiphase Approach,
Archive of Applied Mechanics, 80/5:453-465, 2010.
[3] D. Balzani, S. Brinkhues, and G.A. Holzapfel: Constitutive Framework for the Modeling of
Damage in Collagenous Soft Tissues with Application to Arterial Walls, Computer Methods
in Applied Mechanics and Engineering, submitted.
Towards a Method for Parameter Estimation of Articular Cartilage
and a Staggered Procedure for Synovial Fluid-Cartilage Interaction
Joffrey Mabuma, Bernd Markert, Wolfgang Ehlers (Universität Stuttgart) Schedule

Section 2: Biomechanics 59
Up to now, the interaction mechanisms between cartilage and synovial fluid within diarthrodial
joints are not yet fully understood. These joints are able to function effectively over the lifetime of
an individualeven under very high loads, which requires minimal wear of cartilage. In particular,
the reason for the extremely low coefficients of friction has still to be explained.The goal of
this contribution is to numerically investigate the interaction between articular cartilage and
synovial fluid in diarthrodial joints. In this connection, we already developed an appropriate
continuum model of the articulating tissue layers as highly anisotropic [1] and heteregeneously
[3] charged biphasic solid-fluid aggregates based on the Theory of Porous Media (TPM) [2]. The
next step is now concerned with the calibration of the previously elaborated model. To this
end, a sensitivity analysis is performed to identify the relevant constitutive parameters under
physiological loading conditions. The remaining parameters are then obtained using a direct
search algorithm. In order to solve the complex contact problem at the interface between synovial
fluid and articular cartilage, a sequential solution algorithm is applied, in which the fluid and
cartilage domains are iteratively calculated until equilibrium is reached. The applied staggered
method considers, on the one hand, a synovial fluid flow formulation described by the Reynolds
equation and, on the other hand, the continuum-mechanical description of the cartilage layers.
Moreover, the simulations are performed on 3-d hip-joint geometries reconstructed from MRI
data.
[1] Markert B., Ehlers W. & Karajan N.: A general polyconvex strain-energy function for fiberreinforced
materials. Proceedings in Applied Mathematics and Mechanics 5 (2005), 245-246.
[2] Ehlers W., Markert B. & Röhrle O.: Computational continuum biomechanics with application
to swelling media and growth phenomena. GAMM-Mitteilungen 32, (2009), 135-156.
[3] Wilson W., Huyghe J. M. and Van Donkelaar C.: A Composition-based cartilage model for the
assessment of compositional changes during cartilage damage and adaptation. Biomechanics
and Modeling in Mechanobiology 6 (2007), 43-53.
A biphasic transverse isotropic FEM model for cartilage
Daniel Albrecht, Tim Ricken (TU Dortmund), David M. Pierce (TU Graz), Gerhard A. Holzapfel
(TU Graz; Royal Institute of Technology (KTH)) Schedule
In this talk we discuss cartilage, a multi-phase material composed of fluids and electrolytes.
From the mechanical point of view, cartilage is a porous, incompressible material combined with
transversely isotropic solid and fluid behavior. Moreover, in studying cartilage it is essential to
account for the poro-viscosity of the porous matrix as well as material viscoelasticity of the
collagen fibers.
In order to describe this complex material, and the resulting mechanical behavior, we propose
a homogenized mixture model based on the theory of porous media which allows for a coupled
description of the solid-fluid interaction. The transverse isotropic behavior of the solid impacts
both the stress response and the internal fluid permeability, which is modeled by using an invariant
formulation of the Helmholtz free energy and a transverse isotropic permeability. The latter is
modeled by using an invariant formulation of Helmholtz free energy and a transverse isotropic
permeability function. Fluid permeability is further influenced by the inhomogenous, dispersed
fiber fabric of the solid and an intrafibrillar portion that can not be „squeezed out“ from the tissue.
The collagen fibers show both a principal orientation distribution within cartilage (superficial,
middle and deep zones are commonly identified) and a local dispersion (the fiber fabric is locally
composed of dispersed fibers).

60 Section 2: Biomechanics
Representative numerical examples are shown and compared to experimental data from cartilage
mechanics in the literature.
[1] Pierce, D.M., Ricken, T., Holzapfel, G.A. 2011. A Hyperelastic Biphasic Fiber-Reinforced Model
of Articular Cartilage Considering Distributed Collagen Fiber Orientations: Continuum
Basis, Computational Aspects and Applications. In: Computer Methods in Biomechanic and
Biomedical Engineering, submitted for publication
S2.2: Skeletal Muscle Modelling Tue, 16:00–18:00
Chair: Markus Böl S1|03–23
Elastic properties of muscle tissue: comparison of an inverse finite element approach
and homogeneous deformation
Roland Kruse, Christine Weichert, Markus Böl (TU Braunschweig) Schedule
The passive elastic properties of skeletal muscle tissue are important for the simulation of surgical
procedures and to find mechanically compatible materials. The parameters of a chosen material
model have to be identified by measurements. Two approaches were compared in this study, both
based on compressive tests on cuboid samples of the soleus muscle of domestic rabbits: On the
one hand, a finite element model of the samples has been created using surface shape information
from a three-dimensional camera system and the test, including the friction between the sample
and the sample holder, has been simulated. On the other hand, homogeneous deformation has
been assumed so that the sample could be represented by a single cube with known cross-sectional
area and height, and without friction effects. In both cases, the optimal parameters were deduced
by minimizing the difference between observed and predicted load-deflection curves, for three
orientations of the muscle fibers. The results indicate, firstly, that the chosen model is able to
describe the behavior of the muscle tissue well, and, secondly, that there can be a quite severe
differences between the two procedures as a consequence of the ”homogeneous deformation” assumption.
In conclusion, though the inverse finite element method is very time consuming, it is still
recommended because it better takes into account the experimental conditions and consequently
is expected to yield more realistic parameter estimates.
Numerical investigations of muscle contraction by using an optical measurement
technique
Maike Sturmat, Christine Weichert, Tobias Siebert, Markus Böl (TU Braunschweig) Schedule
For a better understanding of essential mechanical muscle properties during contraction we proposed
a new approach in this paper by using an optical measurement technique. A method has
been developed to measure the three-dimensional shape during the contraction process. In doing
so, the surface of an ex situ isolated rabbit soleus muscle has been coated by a special technology
whereby the optical three-dimensional deforming analysis system was able to detect deformation
changes on the muscle surface. Thus, a three-dimensional geometry model could be reconstructed
for several deformation states. Hence, the region of less deformation could be determine as tendon
tissue due to the fact that tendon has certainly a higher stiffness than muscle tissue. The complex
architecture of muscle fibres has a huge influence of the whole muscle deformation. Therefore,
the fascicle distribution has been taken into account by scanning the muscle via a special manual
digitising technique.
In a second step a recently developed numerical model [1] has been validated by these optical
data for two contraction modes, namely isometric and isotonic. Main idea of the numerical model

Section 2: Biomechanics 61
was a non-additive decomposition of the free energy function into an active and passive part. The
transversal isotropic muscle behaviour has been described by a hyperelastic constitutive law whereas
the activation could be inserting by a single parameter. The ability of the proposed modelling
approach has been shown by three-dimensional numerical experiments.
[1] A. E. Ehret, M. Böl, M. Itskov, A continuum constitutive model fort the active behaviour of
skeletal muscle, Journal of the Mechanics and Physics of Solid 59 (2011), 625 – 636.
A neuronal-recruited geometrical model of skeletal muscle
Thomas Heidlauf, Oliver Röhrle (Universität Stuttgart) Schedule
Mathematical models of neurophysiology and continuum biomechanics are combined to include
mechanisms of motor unit recruitment and rate coding in a geometrical model of skeletal muscle.
Couplings between the models occur at the neuromuscular junction and through afferent sensory
neurons that emerge from muscle spindles.
Neurophysiological models [1] describe how the motoneuron pool in the central nervous system
(CNS) operates as an ensemble to control force. Muscle force production in these models is
based on simple analytical equations that do not involve any spatial components. On the other
hand, continuum-biomechanical models of skeletal muscle [2] focus on the generation of force.
The biochemical reactions that lead from excitation of a muscle fibre to its contraction and force
generation are in continuum models often described by cellular models of systems biology [3].
Geometrical aspects, such as complex fibre architectures or local motor unit distributions, can be
adequately represented in three-dimensional (3D) continuum models.
Various couplings between the models or within the models are required, whereat the individual
models or sub-models are based on different dimensionalities (0D, 1D, and 3D), and different
length and time scales. In this contribution, we demonstrate how such couplings can be efficiently
implemented within a parallel-computing architecture considering the example of the open-source
software library OpenCMISS [4].
The aim of the development of such a model is to answer questions of neurophysiology that involve
spatial components of the muscular system.
[1] J.L. Dideriksen, F. Negro, D. Farina, Motor Unit Recruitment Strategies and Muscle Properties
Determine the Influence of Synaptic Noise on Motor Output Variablitlty, submitted.
[2] O. Röhrle, J.B. Davidson, A. Pullan, Bridging scales: a three-dimensional electromechanical
finite element model of skeletal muscle, SIAM Journal on Scientific Computing 30 (2008),
2882–2904.
[3] P. Shorten, P. O‘Callaghan, J.B. Davidson, T. Soboleva, A mathematical model of fatigue in
skeletal muscle force contraction, Journal of Muscle Research and Cell Motility 28 (2007),
293–313.
[4] C. Bradley et al., OpenCMISS: A multi-physics & multi-scale computational infrastructure
for the VPH/Physiome project, Progress in Biophysics and Molecular Biology 107 (2011),
32–47.
Optimal control simulations of human arm motion
Ramona Maas, Sigrid Leyendecker (Universität Erlangen-Nürnberg) Schedule

62 Section 2: Biomechanics
The simulation of ordinary, athletic or pathologic human motion has been in the focus of several
investigations for a long time. Simulating such motions usually yields boundary value problems,
like moving the body from a predefined initial to a given final configuration, that can not be
solved via forward dynamics simulation. Furthermore, one has to account for the natural linking
of joint movements in a coordinated way which is typical for human motion. This is frequently
treated via linear relations between the single velocities [1].
Another approach is to assume that human movements are optimally controlled by the central
nervous system in the sense that a physiologically motivated cost function is minimised during
the motion [1]. We follow this approach and use a method called DMOCC (Discrete mechanics
and optimal control for constrained systems [2]) to simulate such problems. Since DMOCC is a
structure preserving method, the resulting trajectories are consistent in the evolution of momentum
maps and show good energy behaviour.
We apply the method to simulations of arm movements, in particular to the simulation of steering
(torque or muscle actuated) and extend it to include parameter optimisation to investigate an
optimal steering environment.
[1] J. Friedman and T. Flash. Trajectory of the index finger during grasping. Exp. Brain Res
196 (2009), 497-509.
[2] S. Leyendecker, S. Ober-Blöbaum, J.E. Marsden and M. Ortiz. Discrete Mechanics and Optimal
Control for Constrained Systems. Optim Contr Appl Met 31 (2010), 505-528.
Coupling 3D and 1D Skeletal Muscle Models
Michael Sprenger, Oliver Röhrle, Syn Schmitt (Universität Stuttgart) Schedule
This work introduces a modelling framework for skeletal muscle mechanics that couples a threedimensional
(3D) continuum-mechanical-based Finite Element (FE) model [1] to a one-dimensional
(1D) lumped-parameter Hill model. In this regard, this is a methodological approach which incorporates
different skeletal muscle models to realise simulations, which are at a present state still
computationally not feasible. The new model framework enables to investigate systems, which
are able to consider both local force distributionwhile incorporating movement patterns of (parts
of) the musculoskeletal system.
State of the art computer models simulating the muscle activities during posture or movement
are based on Multibody Simulations (MBS) incorporating 1D lumped-parameter Hill muscles [2].
Due to the simplicity of such models, they cannot account for local and geometrical effects such
as the muscle’s shape, the interaction of muscles with its surrounding tissues, local activation
principles, or the muscle fibre distribution. Simulating (parts of) the musculoskeletal system with
full 3D continuum-mechanically based skeletal muscle models [1], which can take into account
such structural and functional information, are currently not feasible due to limited computational
power.
Here, we present, based on the upper limp, an overall modelling framework that couples 3D
FE models with MBS. This is justified as geometrical measures, like muscle force direction and
muscle force lever arms, have a strong influence on the mechanical state and movement pattern
in MBS [3]. The coupling is achieved through a nested iteration procedure, where MBS deliver
an initial guess to FE simulations. The FE model improves the physiological reliability of MBS
by providing detailed geometrical information.
[1] O. Röhrle, A.J. Pullan, Three-dimensional finite element analysis of muscle forces during
mastication, Journal of Biomechanics 40 (2007), 3363–3372.

Section 2: Biomechanics 63
[2] M. Günther, H. Ruder, Synthesis of two-dimensional human walking: a test of the λ-model,
Biological Cybernetics 8 (2003), 89–106.
[3] M. A. Nussbaum, D.B. Chaffin, C. J. Rechtien, Muscle Lines-of-Action Affect Predicted
Forces in Optimization-Based Spine Muscle Modeling, Biomechanics 28 (2003), 401–409.
Modeling and Control of hair-shaped Vibrissae as biological Sensors
Carsten Behn, Tonia Schmitz, Hartmut Witte, Klaus Zimmermann (TU Ilmenau) Schedule
The reception of vibrations is a special sense of touch, important for many insects and vertebrates.
Scorpions, cats and rats use a sophisticated sensory systems (sensilla or vibrissae) to acquire tactile
information about their surroundings. Vibrissae, located in the mystacial pad, are either used
passively to sense environmental forces (wind, contact with an obstacle) or actively, when they
are rhythmically moved to scan objects or surfaces. Inspired by this biological sensory system,
several types of mechanical models are developed based on ndings in the literature. We present
three models with a stiff rod-like vibrissa, taking into account the viscoelastic support in the
mystacial pad (follicle-sinus complex and skin). The muscles (extrinsic and intrinsic) enabling the
animals to whisk actively are simulated by adaptive control algorithms. Numerical simulations
with chosen perturbation forces show that specic control variables contain adequate information
on the force to be identied. All models represent a single vibrissa of the mystacial pad, we do not
model a field of vibrissae. Therefore, these models can be transferred to model a carpal vibrissa,
too.
S2.3: General Biomechanics Wed, 13:30–15:30
Chair: Arndt Wagner S1|03–23
Model-based therapy - new methods of model reduction for non-linar mechanics
Annika Radermacher, Stefanie Reese (RWTH Aachen) Schedule
The constantly rising requirements for simulations of biomechanical problems yield numerical
models with increasing number of degrees-of-freedom. Due to significant nonlinearity computational
effort increases constantly. Simulations which serve for surgery training or online support
demand minimal computational time possibly even in real time. A real time simulation without
a significant loss of accuracy would be very valuable. To achieve this and to minimize the computational
effort model reduction is needed. The Functional Endoscopic Sinus Surgery (FESS) is a
minimally invasive surgery, which removes blockage from the nasal cavity. A training program or
an online support would help the surgeon by supplying import data like stress and displacements
during the process. We can generally differentiate between two ways of model reduction methods:
the singular value decomposition (SVD)-based methods and the Krylov-based methods. These
methods were developed and are widely used for solving linear problems. There exist concepts to
expand these methods to nonlinear problems. A general method for model reduction in nonlinear
solid mechanics, in particular, is not available yet. This contribution discusses the performance
and efficiency of three SVD-based methods for nonlinear structuralproblems: the modal basis, the
load dependent Ritz and the proper orthogonal decomposition (POD) method. A complex biomechanical
model with nonlinear behavior will be investigated. It turns out that the performance
of the POD is very promising. It significantly reduces the effort within a good agreement to the
unreduced results.

64 Section 2: Biomechanics
Modelling and simulation of injecting acrylic bone cement into osteoportic vertebral
bones within percutaneous vertebroplasty
Sebastian Kolmeder, Alexander Lion (Universität der Bundeswehr München), Ralf Landgraf, Jörn
Ihlemann (TU Chemnitz) Schedule
According to the world health organisation osteoporosis is among the most important diseases
worldwide. People affected by osteoporosis often suffer from severe back pain and fractured vertebral
bones due to decreasing bone density. Vertebroplasty is a common clinical procedure, whereat
osteoporotic vertebral bones are stabilised by means of an acrylic glue called bone cement. Therefore
initially liquid bone cement is injected through a biopsy needle into the porous vertebral
bone. The cement penetrates the cavities, cures by an exothermal polymerisation and strengthens
the vertebral body within the spinal column [1]. However, this operation technique is accompanied
by risks like cement leakage and heat necrosis as well as long term load redistribution in the
spinal column [2].
In order to obtain a better physical understanding of the process of vertebroplasty and to reduce
the complications, a detailed thermomechanical-chemical coupled material model of acrylic bone
cement has been developed [3]. The flow behaviour of bone cement is modelled incompressible
and purely viscous but depending on shear rate and temperature. An evolving internal state
variable is used to represent the dissolution of liquid monomer within polymer powder, the two
initial components of bone cement. This temperature dependent dissolution also effects the viscosity.
Moreover, the heat transfer equation of the model includes temperature dependent material
properties, such as specific heat capacity and thermal conductivity. Based on an extended experimental
data pool the developed model is adapted and parameterised.
For true in detail simulations an accurate geometrical model is indispensable. To this end a human
vertebral body, affected by osteoporosis, was scanned by a micro CT apparatus and further
converted to a surface tesselation language file, which can be processed by standard meshing tools.
The open source CFD toolbox OpenFOAM was chosen to handle this injection simulation task,
because of free accessibility of the program code and its sophisticated meshing tool. To implement
the described material model, the volume of fluid solver interFoam was used as a foundation
and extended by a heat transfer equation and a transport and evolution equation regarding the
dissolution process.
Having accomplished the injection simulation, the distribution of bone cement within the geometry,
i.e. the vertebral body and the temperature field can be passed to a finite element simulation,
that takes into account the internal stresses and temperature field during the main curing process.
First results encourage the objective of simulating the procedure of vertebroplasty in detail, but
of course have to be validated.
ACKNOWLEDGEMENTS: The authors would like to thank Prof. Dr. Cornelia Kober and Helena
Lebsack from HAW Hamburg as well as Prof. Dr. med. Thomas R. Blattert from OFK Schwarzach
for making geometric data available. This research project is funded by the German Research
Foundation (DFG).
[1] M. E. Jensen, A. J. Evans, J. M. Mathis, D. F. Kallmes, H. J. Cloft, J. E. Dion, Percutaneous
polymethylmethacrylate vertebroplasty in the treatment of osteoporotic vertebral
body compression fractures: technical aspects, Am. J. Neuroradiol 18 (1997), 1897 – 1904.
[2] P.F. Heini, U. Berlemann, M. Kaufmann, K. Lippuner, C. Fankhauser, P. v. Landuyt, Augmentation
of mechanical properties in osteoporotic vertebral bones: a biomechanical investigation
of vertebroplasty with different bone cements Eur Spine J. 10 (2001), 164 –

Section 2: Biomechanics 65
171.
[3] S. Kolmeder, A. Lion, R. Landgraf, J. Ihlemann, Thermophysical properties and material
modelling of acrylic bone cements used in vertebroplasty, J. Therm Anal Calorim 105
(2011), 705 – 718.
Marker based in-vivo analysis of 3D spinal motion during gait using spline curves
Dietmar Rosenthal, Andres Kecskeméthy (Universität Duisburg-Essen), Harald Hefter (Universitätsklinikum
Düsseldorf), Alejandro A. Espinoza Orias, Gunnar Andersson, Markus A. Wimmer
(Rush University Medical Center, Chicago, IL) Schedule
We propose a numerical framework for the fitting of a 3D spline curve model to measured marker
positions that is less sensitive to skin artifacts. We consider for this a quintic B-spline curve
representation of the posterior vertebral line
r(u) =
nS�
ciNi,5(u) (1)
i=0
with control points ci and normalized quintic basis functions Ni,5 corresponding to a specific knot
vector û, see [2]. The curve is related to a set of nM measured skin markers Mj by introducing
movable ’sliders’ Sj with a perpendicular lever of fixed length dj attached to the curve. The sliders
are allowed to move along and around the curve to account for skin motion. Let s denote the arclength
parameter of a curve. The fitting result is given as the curve minimizing the deformation
energy functional, defined as the elastic energy stored between a given reference curve rref(s) and
the sought curve r(s):
�
f(c0, ..., cnS ) = kκ(s)(κref(s) − κ(s)) 2 �
ds + kτ(s)(τ ∗ ref(s) − τ ∗ (s)) 2 ds (2)
Ω
such that (a) the tips of the sliders Sj, � Mj coincide with the measured positions Mj and (b) the
curve length agrees with subject anatomy. In (2), κ denotes Euclidian curvature and
Ω
τ ∗ (s) = (1 − exp(−||r ′ (s) × r ′′ (s)|| 4 ) · τ(s) (3)
denotes the modified torsion with Frenet-Serret torsion τ associated to r(s) and rref(s). The scalar
functions kκ(s) and kτ(s) in (2) define the local stiffness properties along the curve, modeled as
splines with the same parameter domain Ω as r. Some sample evaluations are compared with
published results.
[1] Berthonnaud, E.; Fougier, P.; Hilmi, R.; Labelle, H.; Dimnet, J.: Relationship Between Sagittal
Spinal Curves and Back Surface Profiles Obtained With Radiographs. Journal of
Mechanics in Medicine and Biology, Vol. 10, No. 2,pp. 313–325, 2010.
[2] De Boor, C.: A Practical Guide to Splines. New York: Springer, 2001.
Study of the biomechanical behaviour of structurally stable/unstable motion segments
of the sheep spine
Strampe M, Stoffel M, Weichert D (RWTH Aachen), Sellei R, Pape H-C (Universitätsklinikum
Aachen) Schedule

66 Section 2: Biomechanics
The effects of damage of intervertebral discs on their biomechanical behaviour and the factors
favouring the progression of instability are studied. Healthy and damaged movement segments
are analyzed experimentally and numerically. The aim is to represent and predict the effects of
tissue damage and changes in the spine by comparison with healthy segments. Since the intervertebral
disc acts as a mechanical damper, relaxation tests are performed in addition to pressure
experiments. The experiments are carried out in a bioreactor with tempered nutrient solution.
A cultivation period in the bioreactor allows detecting cell viability, solute diffusion rates and
gene expression of the discs. Numerically, the nonlinear, viscoelastic, anisotropic and diffusiondependent
behaviour of the intervertebral disc is modelled with the FE-program Abaqus, using
a modular material law as a UMAT subroutine. With the measurement results, the relevant
parameters can be determined so that the mechanical behaviour of intervertebral discs can be
simulated.
3D Analysis of Stresses within Molars during Natural Clenching
Harnoor Saini, Oliver Röhrle (Universität Stuttgart) Schedule
Teeth are subjected to some of the highest physiological loads during clenching and biting. The
highest loads occur in the region about the first molars [1]. Clinically, this is reflected by the higher
incidence of cuspal-fractures in posterior teeth, more specifically at the maxillary and mandibular
first molars [2]. Cuspal-fractures of natural and restored teeth cause a significant amount of nonrestorable
tooth damage [3], which subsequently require complete dental implantation. Analysis
of internal stresses and strains within molars, can provide insight into designing more robust
dental implants. Currently, stress analyses have not implemented a combination of 3D geometric
descriptions with naturally captured masticatory movements.
The aim of this study is to analyse internal stresses and strains in mandibular and maxillary
molars during natural masticatory movements, which were recorded with 6 degrees of freedom.
The investigation was performed by simulating a real world clenching experiment via the use of a
quasi-static FE model, implemented in a commercially available FE-software. Three-dimensional
models of the opposing first and second molars were generated along with a model of the rubber
piece used in the real world experiment. In the first step, teeth were taken as rigid and rubber
as hyperelastic. Captured clenching movements were then applied to the mandibular molars, and
contact pressures calculated at each time increment. In a second step, assuming no dissipation
of energy, the contact pressures will be applied as boundary conditions to the now deformable
maxillary and mandibular molars. The resulting internal stress and strain distributions should
provide insight into the deformation behavior of the molars during clenching.
[1] Bates JF, Stafford GD, Harrison A. Masticatory function – a review of the literature. J Oral
Rehabil 2 (1975), 281-301.
[2] Bader JD, Martin JA, Shugars DA. Incidence rates for complete cusp fracture. Community
Dent Oral Epidemiol 29 (2001), 346-353.
[3] McDaniel RJ, Davis RD, Murchison DF, Cohen RB. Causes of failure among cuspal-coverage
amalgam restorations: a clinical survey. J Am Dent Assoc 131 (2000), 173-177.
S2.4: Modelling Vibrations of Tools Wed, 16:00–18:00
Chair: Roland Kruse S1|03–23

Section 2: Biomechanics 67
Vibrations action of the trilling machine MA750 on the human operator hand
Mariana Arghir, Mariana Rus, Sorin Constantin Macovescu (Technical University of Cluj-
Napoca) Schedule
Work includes identifying and analyzing vibrations produced by a trilling machine within space
work. To identify vibration is used a special method, which has not been used so far in identifying
vibrations, with the action on the human body. For obtaining a very good identification of
the human body vibrations has been used the Moiré projection method. General conditions were
applied human hand operator during working hours on a trilling machine, with different speeds
of main shaft. Human operator has been informed of action risks vibration on his hand and he
has accepted experiment. In the paper are presented successively two methods of measuring of
the vibrations: the Moiré projection method and conventional method of measuring with the vibrometer.
Because Moiré projection method was not used until this moment from the another
researchers for the human body vibrations, was necessary to realize the calibration of the method
with an experimental device made by the authors of this paper. The successive operations for
applying this method were possible using a signal generator, an amplificatory device of the signal,
a system of illumination, a computer having a corresponding software for the analyzing the databases
of the results. The Moiré projection method used human operator during processing parts
on the trilling machine has gave results comparable to conventional method of measuring using
a vibrometer with three-axial accelerometer. The results in the both situation were in the same
order of unit scale, and in this situation the optical method named Moiré projection method can
be considered a valid method for the human vibrations measurements without surface taste. The
Moiré projection method can be used to the vibrations measurement with success because this is
a method without contact.
[1] Borza, Dan, Nicolae, Mechanical vibration measurement by high-resolution time-averaged
digital holography, Measurement Science & Technology, vol. 16, No. 9, Pages 1853-1864,
ISSN: 0957-0233, 2005.
[2] Borza, Dan, Nicolae, Evolutions in Full-field Optoelectronic Coherent Metrology as Applied
in Numerical Model Validation, Microscopy and Vibroacoustics, Automation, Quality and
Testing, Robotics, IEEE International Conference on Volume 2, Pages: 99 104, Cluj-Napoca,
Romania, 2006.
[3] Runcan, Mariana, Arghir, Mariana, La technique Moiré de projection, Acta Technica Napocensis,
Series: Applied Mathematics and Mechanics, Vol. IV, Nr. 51, pag. 117-120, ISSN:
1221-5872, Cluj-Napoca, 2008.
Vibrating Portable Machine-Tools Acting on Human Operator
Anamaria Gligor, Alina-Sabina Țepeş-Bobescu, Mariana Arghir (Technical University of Cluj-
Napoca) Schedule
This paper is designed to be an information to the public about the importance of vibration
action of portable machine-tools on the human body and particularly on the hand-arm system.
Mechanical vibrations are non-periodic motions of a material system around a static or dynamic
equilibrium position. Generally in the production of vibrations interfere forces of inertia (seeking
to bring the mobile in static or dynamic equilibrium position), elastic forces, resistance forces
(given by friction and can be an outside or inside force for the system) and disturbing forces
(acting from the outside and maintaining oscillatory motion). An excessive exposure to vibration
can cause blood circulation disorders in hands (ex: Reynauds phenomenon), the alteration of

68 Section 2: Biomechanics
the neurological and musculoskeletal functions of the hands and arms (carpal tunnel syndrom).
Machine tools in operation expose those who use them to mechanical vibrations transmitted by
hand this affects the comfort, efficiency and in some cases the security of the human operator.
Exposure to vibration can vary widely from one operation to another, due to the use of different
machines or powered tools or because of different operating modes of a powered tool or a machine
and this paper is mainly aimed to do a comparison between different vibrating powered tools.
Exposure to harmful vibrations can lead to health problems and disorders, especially in the upper
joints and dorsal region of the human body. A detailed understanding of the undesirable effects of
vibration on the human body is essential to achieve administrative and technical prevention. In
modern times, vibration studies become more frequent, decisive for the many machines, vehicles,
construction.
[1] SR EN ISO 5349-1, Mechanical vibration. Measurement and evaluation of human exposure
to vibration through hand. Part 1: General requirements. 2003.
[2] SR EN ISO 5349-2, Mechanical vibration. Measurement and evaluation of human exposure
to vibration through hand. Part 2: Practical guidance for measurement at the workplace.
2003.
[3] SR ISO 2631 -1, Mechanical vibration and shock. Assessment of human exposure to wholebody
vibration. Part 1: General requirements.
[4] Harris, C., M., Harris’ shock and vibration handbook, ISBN: 0-07-137081-1, 2002.
The Study of Psychoacoustic Effects of Noise Emitted by the Machine Tools Structure
Alina-Sabina Țepeş-Bobescu, Florin Țepeş-Bobescu, Anamaria Gligor, Mariana Arghir (Technical
University of Cluj-Napoca) Schedule
Cause-effect relationship between noise and hearing loss is considered relevant to human health in
the workplace. Psychoacoustics can be described as the study of how people react to sound, hearing
and perception. Any noise problem may be described in terms of a sound source, a transmission
path and a receiver. If complaints arise from the work place, then regulations should be satisfied,
but to minimize hearing damage compensation claims, the goal of any noise-control program
should be to reach a level of no more than 85 dB(A) [1]. By [5], specific occupational noise effects
are hearing loss and deafness. Occupational hearing loss represents permanent decrease in hearing
threshold at a frequency of 4000 Hz, including more than 30 dB, type of perception, generally
bilateral and symmetric, without involving conversational frequencies. Occupational deafness is
based on a permanent hearing loss at low conversational frequencies, the arithmetic mean of the
three frequencies deficits exceeding 25dB. This paper provides ways for the prediction of noise
radiated by the single part structure of the machine-tool using vibration measurement and an
estimation method for the hearing deterioration or hearing impaired individual people. There are
the following conclusions: noise and vibration have a close physical relationship; noise induced
permanent threshold shift values depending on frequencies, exposure time, the noise exposure
level, LEX,8h; exposure time of noise is longer even the risk of hearing impairment is greater.
[1] Mariana, Arghir, ş.a., Monitorizarea zgomotului traficului rutier, EDP, 644 pag., ISBN 978-
973-30-2314-2, Bucureşti, 2008
[2] SR ISO/TR 7849:1995 Acoustics- Estimation of airborne noise emitted by machinery using
vibration measurement

Section 2: Biomechanics 69
[3] STAS 1999:1996 Acoustics-Determination of occupational noise exposure and estimation of
noise induced hearing impairment
[4] ***www.scribd.com/doc/29247889/7-Bioacustica-MG
S2.5: Growth and Remodelling I Thu, 13:30–15:30
Chair: Ellen Kuhl S1|03–175
A network model for the EPS matrix of microbial biofilms
Alexander E. Ehret, Antonio Bolea Albero, Markus Böl (TU Braunschweig) Schedule
Microbial biofilms exist on a multitude of surfaces and interfaces. While some of these bacterial
colonies play vital roles for human health and ecology, others pose severe health risks and cause
large problems in industrial processes [1-3]. Generally, a biofilm is considered as immobilised cells
which are embedded in a matrix of extracellular polymeric substances (EPS) produced by these
cells themselves [1,3]. Although not the only possible component of EPS, many biofilms contain
highly hydrated gel-forming polysaccharide networks [4].
In the present contribution, the latter characteristic is exploited in order to model the mechanical
behaviour displayed by microbial biofilms. As a particular example, the relatively well
explored networks formed by bacterial alginates are considered. The polysaccharide molecules
are represented by worm-like chains and incorporated into a suitable network description. The
effects of crosslinking and swelling on the mechanical behaviour of this polysaccharide network
are studied. Finally, the model is discussed in comparison with recent rheological and stress-strain
data of biofilms.
[1] W.G. Characklis, K.C. Marshall, Biofilms: A basis for an interdisciplinary approach, in: W.G.
Characklis, K.C. Marshall (eds.) Biofilms, John Wiley & Sons, New York (1990), pp. 3 –
15.
[2] H.-C. Flemming, J. Wingender, Biofilme – die bevorzugte Lebensform der Bakterien, Biologie
in unserer Zeit 31 (2001), 169 – 180.
[3] R.M. Donlan, J.W. Costerton, Biofilms: Survival Mechanisms of Clinically Relevant Microorganisms,
Clin. Microbiol. Rev. 15 (2002), 167 – 193.
[4] H.-C. Flemming, J. Wingender, The biofilm matrix, Nat. Rev. Microbiol. 8 (2010), 623 – 633.
Theoretical and experimental investigation of cartilage replacement material for medical
applications
Bei Zhou, Marcus Stoffel, Dieter Weichert, Björn Rath (RWTH Aachen) Schedule
Soft tissues are commonly applied in surgery to replace the injured articular cartilage. Many
biological researches were carried out through mechanical and histological experiments. They
focus on the function, degeneration and regeneration of the articular cartilage and fibrocartilage.
In the present work a theoretical material model, which takes elasticity and deformation dependent
diffusion into account, is proposed to identify the mechanical properties of soft tissues during the
remodeling process. This approach includes experimental investigation of the soft tissue implants
and numerical simulation. Through simulating the stress-relaxation response of materials under

70 Section 2: Biomechanics
unconfined compression by means of finite element method based on an optimization algorithm,
material parameters can be identified. For a widely application, this material model was validated
with different experimental method, specimens with different dimensions and different kinds of
soft tissues.
Mechanical modeling of medical mesh implants at the meso-scale
Barbara Röhrnbauer, Gerald Kress, Edoardo Mazza (ETH Zürich) Schedule
The present study aims at developing a physically based mechanical model for medical mesh
implants at the mesoscale. Medical mesh implants are knitted two-dimensional fiber-networks
used for soft body tissue support, such as in case of a prolapse. At the mesoscale, the geometry
and the local kinematics of a representative unit cell are mapped in an abstracted, but still
physically relevant description. Such a model allows to understand the interplay between local
deformation patterns and the resulting global anisotropic and nonlinear force response. It is
expected to provide design criteria for mesh implant optimization, not only accounting for the
global mechanical behavior but also for local mesh-tissue interactions.
A representative unit cell is modeled as a 20 degree of freedom system based on multi-body
theory. It is composed of discrete force elements, such as translational and rotational springs.
The system equations are the projected Newton-Euler equations, reducing for the static case to
a simple equilibrium of active forces and constraint forces. There are 21 parameters to adjust the
force laws of the whole model. These parameters can be related to the mechanical behavior of
single elements at the micro-scale, involving stretching and bending of filaments. An experimental
study has been conducted subjecting the dry mesh to cyclic load cases of uniaxial stress and
uniaxial strain respectively, in four different loading directions.
Single sets of parameters can be found simulating the global force and kinematic response of
all eight experimental load cases in an appropriate way. Moreover, preconditioning effects, i.e. an
alteration of the force response due to cyclic loading are adequately described based on an altered
reference configuration. Preconditioning of the meshes is thus interpreted as a mainly geometry
related phenomenon, caused by a load history dependent inelastic deformation of each unit cell.
Analysis at different length scales allows to link macroscale phenomena of mesh implants to
mechanical contributions of single elements at the mesoscale. With respect to mesh design control,
the mechanical properties of these elements have to be translated to material and structural
properties at the microscale, such as filament material and diameter or knitting pattern.
Red Blood Cell Shape Transformations
Stefan Wolf, Justyna Czerwinska (ARTORG Center, Universität Bern) Schedule
Several red blood cell (RBC) diseases such as sickle cell anaemia and spherocytosis are related
to the shape and the deformability of RBCs. Furthermore, it has been reported that RBC ageing
is connected to stiffening and the loss of volume and area. The vesicles acquire shapes for which
appropriate constraints are minimal. The global energy of a vesicle shape is related to osmotic
pressure, lipid densities, constraints on the area, the volume and the area-difference in elasticity.
Several energy models [1] were studied for the evolution of the vesicle curvature such as: the minimal
local curvature, the spontaneous curvature, the bilayer couple, the area-difference-elasticity
and their combinations.
The information about the shape of the lowest energy for given parameters can be obtained
by solving the Euler-Lagrange equations or by using trail shapes which could be obtained by numerical
simulations. For that purpose we have used the finite element simulations. The different
red blood cell shapes can then be grouped in the phase space diagram and we plot the trajectories
related to the deformation of the different shapes . Furthermore, the effect of the different

Section 2: Biomechanics 71
energy models on the phase space trajectories is analysed. These results are compared with the
experimental data for optical tweezers stretching [2,3].
[1] U. Seifert, Configurations of Fluid Membranes and Vesicles, Adv. Phys. 46 (1997), 13 – 137.
[2] M. Dao, C.T. Lim, S. Suresh , Mechanics of the Human Red Blood Cell Deformed by Optical
Tweezers, J. Mech. Phys. Solids. 51 (2003), 2259 – 2280.
[3] D. A. Fedosov, B. Caswell, G. E. Karniadakis, A Multiscale Red Blood Cell Model with
Accurate Mechanics, Rheology, and Dynamics, Biophys. J. 98 (2010), 2215 – 2225.
Investigation of regenerative tissues for replacing the Bruch’s membrane
W. Willenberg, M. Stoffel, D. Weichert, A.-K. Salz, G. Thumann (RWTH Aachen) Schedule
Age-related macular degeneration (AMD) is one of the leading causes of blindness in developed
countries. One of the contributing factors appears to be alterations of Bruch’s membrane such as
change in elasticity and filtration properties. According to medical research it will be a promising
approach to transplant cells as pre-formed monolayers on an artificial substratum. For this reason,
in the present study, artificial substratums in form of collagen foils are investigated numerically
and experimentally. Consequently, animal specimens and collagen foils are studies first in material
tests. Based on the measured phenomena a structural and material model are proposed taking
into account elastic material behaviour and diffusion properties. After implementation into a finite
element code simulation results are compared to measurements. In order to investigate the
remodeling process in the replacement material, a bioreactor is developed. Hereby, mechanical
stimulations are subjected to cultivated cellular collagen samples while the load history and reaction
forces are measured during the cultivation period.
S2.6: Growth and Remodelling II Thu, 16:00–18:00
Chair: Alexander Ehret S1|03–175
The mechanics of growing skin
Ellen Kuhl, Alexander Zollner, Adrian Buganza Tepole (Stanford University) Schedule
Tissue expansion is a common surgical procedure to grow extra skin through controlled mechanical
over-stretch. It creates skin that matches the color, texture, and thickness of the surrounding
tissue, while minimizing scars and risk of rejection. Despite intense research in tissue expansion
and skin growth, the biomechanical and mechanobiological mechanisms behind skin growth
remain unclear. Here, we show that a continuum mechanics approach, embedded in a customdesigned
finite element model, informed by medical imaging, provides valuable insight into the
biomechanics of skin growth. In particular, we model skin growth using the concept of an incompatible
growth configuration. We characterize its evolution in time using a second-order growth
tensor parameterized in terms of a scalar-valued internal variable, the in-plane area growth [1].
When stretched beyond the physiological level, new skin is created, and the in-plane area growth
increases. We simulate tissue expansion on a patient-specific geometric model, and predict stress,
strain, and area gain [2]. Our results may help the surgeon to prevent tissue over-stretch and
make informed decisions about expander geometry, size, placement, and inflation. We anticipate
our study to open new avenues in reconstructive surgery, and enhance treatment for patients with
birth defects, burn injuries, or breast tumor removal.

72 Section 2: Biomechanics
[1] Buganza Tepole A, Ploch CJ, Wong J, Gosain AK, Kuhl E. Growing skin: A computational
model for skin expansion in reconstructive surgery. J Mech Phys Solids, 2011;59:2177-2190.
[2] Zollner AM, Buganza Tepole A, Gosain AK, Kuhl E. Growing skin: Tissue expansion in
pediatric forehead reconstruction. Biomech Mod Mechanobio, doi:10.1007/s10237-011-0357-
4.
A continuum model for free growth in living materials
Antonio Bolea Albero, Alexander E. Ehret, Markus Böl (TU Braunschweig) Schedule
Living materials can grow in volume in two different ways: following a predefined process or
depending on the current state of the body. In bodies that have a set growth path, we can
observe residual stresses that appear if the boundary conditions or loads do not fit with its path.
In the other kind of volume growth, the tissue has a feed-back that behaves depending on a
growth kinetic. We can find this growth behaviour for example in muscles (they increment their
mass if we train them) or in biofilms. Biofilms grow isotropically if there are no boundaries or
loads, in other case, the biofilm will follow a more favourable growth direction.
We focus in this work on the growth kinetic for isotropically growing materials. An adaptive
algorithm is used in order to satisfy the boundary conditions of the system, trying to stay in
a stress free state if no external loads are applied, but keeping the volume growth defined by a
growth kinetic. The proposed model based on a modified multiplicative split of the deformation
gradient into a growth part and an elastic part. The growth part will be isotropic if the elastic
deformations are favourable, otherwise the growth will find a more comfortable direction. Several
three-dimensional examples based on different growth kinematics are presented and discussed
using the numerical model.
Growth and Remodelling of Biological Tissue: A Biphasic Porous Media Description
Robert Krause, Bernd Markert, Wolfgang Ehlers (Universität Stuttgart) Schedule
In the context of the Theory of Porous Media (TPM) [1], a continuum-mechanical model is
introduced to describe the complex fluid-structure interaction in biological tissue on the macroscale.
The tissue is treated as an aggregate of two immiscible constituents, where the cells and the
extracellular matrix (ECM) are summarised to the solid phase, and the fluid phase summaries
the extracellular fluids and its components. Growth and remodelling processes are described
on the macro-scale by a distinct mass exchange that also causes a change of the constituents’
material properties. To guarantee the compliance with the entropy principle, the growth energy
is introduced as an additional quantity [2]. It measures the average of chemical energy available
for cell metabolism and, thus, controls the growth and remodelling processes.
In addition to a purely mechanical description, systems-biological control mechanisms are included
into the model by an evaluation of a systems-biological cell interaction model at every integration
point of the finite-element mesh.
To set an example, the remodelling of a human femur under physiological loading conditions is
implemented and numerically solved. Thereby, tailored programs are used for the mechanical and
the systems-biological simulation. The execution of the different programs and the data exchange
between the programs is controlled via Scientific Workflows.
[1] W. Ehlers: Challenges of porous media models in geo- and biomechanical engineering including
electro-chemically active polymers and gels. Int. J. Adv. Eng. Sci. Appl. Math. 1 (2009),
1–24.

Section 2: Biomechanics 73
[2] W. Ehlers, R. Krause, B. Markert: Modelling and remodelling of biological
tissue in the framework of continuum biomechanics. PAMM 11 (2011), 35–38.
On the global dynamics of the dePillis- Radunskaya tumor growth model
Konstantin E. Starkov (Instituto Politecnico Nacional, CITEDI), Alexander P. Krishchenko
(Bauman Moscow State Technical University) Schedule
In this work we examine dynamical properties of one cancer tumor growth model with help of
studies of a localization of its compact invariant sets. This model was elaborated in [1] and has the
form: ˙x1 = x1(1−x1)−a12x1x2−a13x1x3, ˙x2 = r2x2(1−x2)−a21x1x2, ˙x3 = r3x1x3
x1+k3 −a31x1x3−d3x3,
where by x(t) we denote the vector of cell populations: x1(t) is the number of tumour cells at the
moment t; x2(t) is the number of healthy host cells at t; x3(t) is the number of effector immune
cells at t. Here a localization means a description of the locus of all compact invariant sets by
using equations and inequalities expressed in terms of parameters of a system, [2]. Our main
results are as follows: 1) we compute upper and lower bounds for the global attractor in R3 + ;
2) we study cases when each trajectory in R3 + may tend to 2i) tumor-free or ”dead” equilibrium
points only; 2ii) small tumor mass equilibrium point only; 2iii) tumor-free equilibrium point only
and some other related topics.
Acknowledgment. This work is supported by the CONACYT project N. 78890, MEXICO.
[1] de Pillis LG, Radunskaya A, [2003] Math and Comput. Modelling, 37, 1221;
[2] Krishchenko AP, Starkov KE, [2006] Phys. Lett. A 353, 383.
Experimental and theoretical investigations on soft tissue remodeling enhanced by
cell activity
Jeong-Hun Yi, Marcus Stoffel, Dieter Weichert (RWTH Aachen), Sven Nebelung and Björn Rath
(Universitätsklinikum Aachen) Schedule
The aim of the paper is to investigate the remodeling phenomenon of a cell-seeded material. For
the experiments, a cell-seeded condensed collagen gel is mechanically stimulated in a bioreactor
for two or four weeks and histological investigations are carried out. Collagen type-II newly
synthesized by cells causes a change of the material’s mechanical properties. In this study the
new remodeled stiffness of the material is subsequently measured by a compression test. For this
phenomenon, a viscoelastic-diffusion material model is proposed, which incorporates an evolution
equation for the observed, long-term change of stiffness.

74 Section 3: Damage and fracture mechanics
Section 3: Damage and fracture mechanics
Organizers: Jörn Mosler (TU Dortmund), Manuela Sander (Universität Rostock)
S3.1: Modeling material failure Tue, 13:30–15:30
Chair: Ragnar Larsson, Jörn Mosler S1|03–116
Ductile dynamic fracture modeling using embedded discontinuities in CGI machining
simulations
Ragnar Larsson, Goran Ljustina, Martin Fagerström (Chalmers University of Technology Göteborg)
Schedule
A major driving force for the industry to simulate various manufacturing processes is the incorporation
of new design materials e.g. in order to promote lightweight design often leading to
significant changes in manufacturing conditions, which can be assessed in an efficient way by simulation
rather than more expensive testing. In the current contribution we are concerned with the
constitutive modeling of Compacted Graphite Iron (CGI) with respect to orthogonal machining
simulations. Although CGI consists in general of pearlite, graphite and ferrite, focus is placed
on the constitutive modeling of the pearlitic phase since this is the dominating constituent with
respect to the machinability issues. In this study, the continuum hardening response is modeled
using the Johnson-Cook (JC) plasticity model; a model that has been extensively used in the
literature for the modeling effects of large strains, high strain rates and high temperatures related
to machining. In earlier works, the JC plasticity model has been used along with ductile fracture
response that has been described with the element deletion based on Johnson-Cook dynamic failure
criterion. In the current development we it is proposed to use a continuum damage approach
for the continuous behavior up to the critical stress-strain states where discontinuous bifurcation
occurs. Whenever a critical state has been diagnosed, a Cohesive Zone (CZ) is established so that
the actual critical stress state is located right at the onset of stress degradation in the CZ. Both
pre-peak continuum damage and post-peak CZ damage, representing distributed and localized
damage evolution, respectively, are considered in the formulation. Both the pre- and post-peak
damage evolutions are defined as a post-processing of the effective stress response. The localized
cohesive zone damage is kinematically realized as an element embedded discontinuity which is
introduced elementwise, thereby facilitating the model developments in standard FE-packages.
The orthogonal machining simulations show that the new continuum damage model appears to
be sensitive to element locking as well as significant element size dependence without the cohesive
zone enhancement of the model. In order to investigate the extent of locking behavior in simulations
and also the possible pathological mesh dependency the series of 2D shear test simulations
with both triangular and rectangular elements with different sizes have been conducted and results
are compared.
New three-dimensional finite elements with embedded strong discontinuities to model
solids at failure
Christian Linder, Xiaoxuan Zhang (Universität Stuttgart) Schedule
This work presents new finite elements that incorporate strong discontinuities with linear interpolations
of the displacement jumps for three-dimensional finite elements within the infinitesimal
theory to model solids at failure. The cases of interest are characterized by a localized cohesive
law along a propagating discontinuity representing a crack in the solid, with this propagation
occurring in a general finite element mesh without remeshing. As in [1] for plane problems, the
new elements are constructed by enhancing the strain field of existing displacement based, as-

Section 3: Damage and fracture mechanics 75
sumed strain based, and enhanced strain based 3D finite elements. The enhancement is driven
by the incorporation of 9 separation modes directly into the finite element framework which are
chosen so that stress locking in general brick finite elements is avoided. This results in an efficient
formulation where all the introduced enhanced parameters can be statically condensed out at the
element level.
A series of numerical tests including single element tests and convergence studies outline
the performance of the new finite elements. To drive the crack propagation for sophisticated
and realistic numerical simulations in three dimensions, a global tracking algorithm is employed.
The obtained results are close to experimentally observed crack paths and reaction force versus
displacement relations.
[1] C. Linder, F. Armero, Finite elements with embedded strong discontinuities for the modeling
of failure in solids, Int. J. Numer. Meth. Engng. 72 (2007), 1391 – 1433.
On the size-dependent damage behaviour of short fibre reinforced composites
Ingo Scheider, Yongjun Chen, Norbert Huber (Helmholtz-Zentrum Geesthacht), Jörn Mosler (TU
Dortmund, Helmholtz-Zentrum Geesthacht) Schedule
The present paper is concerned with the analysis of size effects of short fibre reinforced composites.
The microstructure of such composites often represents the first hierarchy level of a bioinspired
material, and thus an elastic organic matrix material with strong but brittle ceramic fibres has
been investigated. For modelling the various failure mechanisms occuring in heterogeneous materials,
i.e. fibre cracking, debonding between fibre and matrix material, and matrix cracking, a fully
three-dimensional cohesive zone model is applied. It is shown that this model indeed captures the
size effect associated with material failure of fibre reinforced materials. More explicitly and in line
with previous investigations by Gao (Int. J. Fract. 2006; 138:101-137), it is shown that a surface
precracked fibre reaches its theoretical strength, if its diameter is smaller than a certain threshold.
However, the one-dimensional model advocated by Gao usually leads to an overestimation
of the flaw tolerance due to their simplifying assumptions. Based on these findings, a representative
volume element (RVE) containing ceramic fibres with fixed aspect ratios embedded within a
polymer matrix is considered. Similar to the single fibre, the RVE also shows a pronounced size
effect, but the underlying physical process is significantly more complex. More explicitly, the size
effect of the RVE is a superposition of that related to the isolated fibres (i.e. fibre breaking) as
well as of that induced by debonding of the fibres from the matrix material.
Analysis of Break Up Events in Antarctic Ice Shelves Using Configurational Forces
Carolin Plate (TU Kaiserslautern), Dietmar Gross (TU Darmstadt), Angelika Humbert (Universität
Hamburg), Ralf Müller (TU Kaiserslautern) Schedule
Previous studies on the sensitivity of cracks in ice shelves with different boundary conditions,
stress states and density profiles revealed the need for further analyses. Therefore, the aim of this
presentation is to discuss new findings on the effect of freezing water in surface crevasses and
the influence of depth dependent material parameters, e.g. Youngs modulus and Poissons ratio
on the criticality of cracks. The numerical simulations are conducted using Finite Elements utilizing
the concept of configurational forces. Therefore, a 2-dimensional geometry with mode-I loads
and additional body forces is analyzed. As the transfer of boundary conditions from dynamic ice
flow simulations to the linear elastic fracture analyses proved to be a critical aspect in previous
studies, preliminary results on visco-elastic fracture simulations of ice shelves will be provided.

76 Section 3: Damage and fracture mechanics
These results yield the opportunity of finding a measure on how cracks of different size influence
the viscosity of the ice shelf in dynamic flow simulations.
Modeling of deformation and failure in rubber-toughened polymers – effect of distributed
crazing
Martin Helbig, Thomas Seelig (KIT) Schedule
The improved ductility and toughness of rubber-modified polymers, e.g. ABS, relies on microscale
deformation and damage mechanisms such as rubber particle cavitation, matrix shear yielding
and crazing. The present work focusses on the effect of distributed crazing, i.e. the formation of
cohesive crack-like defects, between the fine dispersed rubber particles. A macroscopic material
model for the inelastic deformation behavior of ABS is developed that describes distributed crazing
as an anisotropic flow process. Scaling of the overall yield strength and failure strain with the
rubber volume fraction is explicitly accounted for through micromechanical considerations. The
suitability of the model is analyzed by comparison of finite element simulations with experimental
findings.
S3.2: Continuum damage mechanics and phase field models Tue, 16:00–18:00
Chair: Daniel Balzani, Jörn Mosler S1|03–116
Relaxed Incremental Variational Formulation for Damage in Fiber-Reinforced Materials
Daniel Balzani (Universität Duisburg-Essen), Michael Ortiz (Caltech) Schedule
An incremental variational formulation for damage at finite strains is proposed based on the
classical continuum damage mechanics. Since loss of convexity is obtained at some critical deformations
a relaxed incremental stress potential is constructed which convexifies the original
non-convex problem, see also [1] for the small strain framework. This approach is in line with
the general approach for standard dissipative solids presented in [2]. The resulting model can be
interpreted as the homogenization of a micro-heterogeneous material bifurcated into a strongly
and weakly damaged phase at the microscale, cf. [3]. A one-dimensional relaxed formulation is
derived and based thereon, a model for fiber-reinforced materials is given, see [4]. Finally, some
numerical examples illustrate the performance of the model.
[1] E. Gürses, Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures
and Crack Propagation, Bericht Nr.: I-19, Institut für Mechanik (Bauwesen),
Lehrstuhl I, Professor C. Miehe, 2007
[2] C. Miehe and M. Lambrecht, A two-scale finite element relaxation analysis of shear bands in
non-convex inelastic solids: small strain theory for standard dissipative materials, Computer
Methods in Applied Mechanics and Engineering, 192:473-508, 2003.
[3] G.A. Francfort and A. Garroni, A variational view of partial brittle damage evolution, Archive
of Rational Mech. and Analysis, 182:125-152, 2006.
[4] D. Balzani and M. Ortiz, Relaxed Incremental Variational Formulation for Damage at Large
Strains with Application to Fiber-Reinforced Materials and Materials with Truss-like Microstructures,
Computer Methods in Applied Mechanics and Engineering, submitted.
Interpretation of parameters in phase field models for fracture
Charlotte Kuhn, Ralf Müller (TU Kaiserslautern) Schedule

Section 3: Damage and fracture mechanics 77
Based on Bourdin’s regularization of a variational fracture criterion, a phase field fracture model
is formulated. This model, as virtually any phase field fracture model, features a length scale parameter
which controls the width of the transition zone between broken and undamaged areas. In
the limit case of a vanishing length parameter, the model converges to the underlying sharp crack
model. From this point of view, the length scale parameter is a purely auxiliary numerical quantity.
The study of the model in an one-dimensional quasi-static setting yields another interpretation
of the length parameter. Qualitatively, there are two different solutions to the one-dimensional
quasi-static problem: a homogeneous solution with a constant crack field, and an inhomogeneous
solution, where the crack field localizes at a certain point which leads to the nucleation of a crack.
In the homogeneous setting, it is observed that there is a critical stress value, at which the material
starts to soften. It can be shown, that this stress level coincides with the stability point of
the homogeneous solution. At this point, the numerical solution bifurcates to the inhomogeneous
solution and a crack forms. The value of this critical stress is determined by the stiffness and
cracking resistance of the material in conjunction with the introduced length parameter. In this
regard, the length parameter may be seen as a material parameter since is related to the critical
stress at which crack nucleation occurs. The analytical findings are approved in finite element
simulations.
Phase Field Modeling of Fracture in Plates and Shells
H. Ulmer, M. Hofacker, C. Miehe (Universität Stuttgart) Schedule
The numerical modeling of failure mechanisms in plates and shells due to fracture based on sharp
crack discontinuities is extremely demanding and suffers in situations with complex crack topologies.
This drawback can be overcome by a diffusive crack modeling, which is based on the
introduction of a crack phase field. Such an approach to brittle fracture is conceptually in line
with gradient-extended continuum damage models which include internal length scales. In this
lecture, we extend ideas recently outlined in [1,2] towards the phase field modeling of fracture in
dimension-reduced continua with application to plates and shells. We start our investigation with
a regularized crack line functional that converges for vanishing length-scale parameter to a sharp
crack topology functional. This functional provides the basis for the definition of suitable dissipation
functions, which govern the evolution of the crack phase field. Next, we define energy storage
functions for Kirchhoff plates and shells, which degrade with increasing phase field. Finally, we
propose rate-type variational principles, whose Euler equations are the quasi-static form of the
balance of momentum and a partial differential equation that describes the evolution of the crack
phase field. The introduction of history fields, containing the maximum reference energy obtained
in history, provides a very transparent representation of these coupled equations. In particular,
it allows the construction of an extremely robust operator split technique. An important aspect
of the modeling is the separation of bending and membrane source terms in the evolution equation
of the crack phase field. A very simple and robust discretization of the coupled problem is
obtained by C 0 continuous rotation-free finite elements for plates and shells, whose only nodal
degrees of freedom are the displacement and the phase field. We demonstrate the performance of
the proposed models by means of some representative numerical examples showing complex crack
patterns and failure modes in plates and shells.
[1] C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically consistent phase-field models of
fracture: Variational principles and multi-field FE implementations, Int. J. Numer. Meth.
Eng., 83 (2010), 1273–1311.
[2] C. Miehe, M. Hofacker, F. Welschinger, A phase field model for rate-independent crack
propagation: Robust algorithmic implementation based on operator splits, Comput. Method.

78 Section 3: Damage and fracture mechanics
Appl. M. 199 (2010), 2765–2778.
Damage processes coupled with phase separation in elastically stressed alloys
Christian Heinemann, Christiane Kraus (WIAS Berlin) Schedule
Diffuse interface models can be used to describe phase separation and coarsening as well as damage
processes in elastic multi-component alloys.
This talk first introduces a model where both processes, phase separation and incomplete
damage, are coupled. The phase separation is here described by a elastic Cahn-Hilliard equation
and the damage process by a doubly nonlinear differential inclusion. In incomplete damage models,
the material maintains its elastic behavior even in a region of maximal damage. We are interested
in free energies of the system which may contain a chemical energy of polynomial or logarithmic
type, an inhomogeneous elastic energy and a quadratic term of the gradient of the damage variable.
An important example of an elastic energy density which is covered in our framework is
W = 1
2 (z + ε)C(c)(e(u) − e⋆ (c)) : (e(u) − e ⋆ (c))
with concentration c, damage z and deformation u. Existence theorems are presented for polynomial
and logarithmic chemical potentials.
Additionally, the complete damage case, i.e. ε = 0, where the diffusion mobility also depends
on the damage and degenerates on the completely damaged parts is studied. Using the previous
framework, the problems arising in the transition ε → 0 + are discussed. The limit model can be
formulated in terms of a free boundary which borders the region of the not completely damaged
parts with Dirichlet boundary from the parts where no deformation field can be established.
The influence of viscoelastic material behaviour on the interface failure in composite
materials
Sebastian Müller, Markus Kästner, Volker Ulbricht (TU Dresden) Schedule
The nonlinear macroscopic material behaviour of composites is amongst others driven by damage
effects and the strain-rate dependent material behaviour of typical polymeric matrices. As a result
of the complex geometry of textile reinforcing architectures, the application of the standard finite
element method tends to result in an extensive modelling and meshing effort including problems
related to distorted element shapes and a poor numerical condition of the system of equations to
be solved. Therefore, the authors have implemented XFEM [1] to model the local heterogeneous
material structure in an RVE.
For the description of curved material interfaces a higher order XFEM formulation including
quadratic basis functions and integration subdomains which are consistent to the curved path
of the discontinuity has been developed. In order to incorporate microscopic damage effects, the
modelling procedure has been enhanced to model the failure of the fibre-matrix interface. To
this end, a second enrichment term [2] accounting for the strong discontinuity is added to the
displacement approximation. The mechanical behaviour in the fracture zone is represented by an
cohesive zone model.
In addition to these approaches, which account for the material structure and the interface
failure, a fractional viscoelastic material model has been developed for the polymeric matrix
material [3]. The combination with the XFEM model and homogenisation techniques allows for
the calculation of effective inelastic material behaviour of the composite material.
[1] M. Kästner, G. Haasemann and V. Ulbricht, Multiscale XFEM-modelling and simulation of

Section 3: Damage and fracture mechanics 79
the inelastic material behaviour of textile-reinforced polymers, Int. J. Numer. Meth. Engng.
86 (2011), 477 – 498.
[2] G. Zi and T. Belytschko, New crack-tip elements for XFEM and applications to cohesive
cracks, Int. J. Numer. Meth. Engng. 57 (2003), 2221 – 2240.
[3] S. Müller, M. Käestner, J. Brummund, V. Ulbricht, A nonlinear fractional viscoelastic material
model for polymers, Computational Materials Science 50 (2011), 2938-2949.
Creep damage modeling of a polycrystalline material
Oksana Ozhoga-Maslovskaja, Holm Altenbach, Konstantin Naumenko, Oleksandr Prygorniev
(Universität Magdeburg) Schedule
A polycrystal unit cell is simulated and investigated under creep conditions within the framework
of continuum micromechanics. Geometrical 3D model of a polycrystalline microstructure is represented
as a unit cell with grains of random crystallographical orientation and shape. Thickness of
the plains, separating neighboring grains in the unit cell, has non-zero value. Obtained geometry
assigns a special zone in the vicinity of grain boundaries, possessing unordered crystalline structure.
Within the grain interior crystalline structure is ordered, what prescribes cubic symmetry
of a material. According to this the anisotropic material model with the cubic symmetry is implemented
in ABAQUS and used to assign elastic and creep behavior of a grain interior. Material
parameters are identified from creep tests for single crystals copper. In order to describe damage
processes in a polycrystalline material, accompanying the tertiary creep stage, micromechanical
damage model is involved. The continuum damage model, based on grain boundary cavitation is
implemented in the grain boundary zone of the unit cell. Stress redistribution within the grains
is investigated. Overall response of the unit cell is analyzed during the primary, secondary and
tertiary creep.
S3.3: Fracture Mechanics Wed, 13:30–15:30
Chair: Manuela Sander, Geralf Hütter S1|03–116
Recovery based error estimation for 3D multiscale computations within the XFEM
for cracks
Corinna Prange, Stefan Loehnert, Peter Wriggers (Universität Hannover) Schedule
The extended finite element method (XFEM) is established as a reasonable method to simulate
cracks. Using the XFEM, cracks can be modelled independent of the mesh. Even coarse meshes
usually lead to suitable results for displacements and stresses. Nevertheless, the solution is more
accurate for finer meshes. Therefore, an adaptive mesh refinement based on a discretization error
estimation technique is applied.
In many materials in the vicinity of a propagating macrocrack microcracks develop. Considering
these microckracks is important for crack growth since they can lead to crack shielding
or crack amplification effects. Microcracks further away to the crack front are of less influence.
Therefore, only those microcracks in the vicinity to a macrocrack front need to be considered.
To model the microcracks in an accurate way the mesh has to be finer than for the macrocrack
description. A twoscale technique based on a projection method enables the consideration of
microcracks around each crack front with low computational effort.
To improve the results of the microscale computation the above mentioned recovery based
discretization error estimation is utilised. The adaptive mesh refinement causes incompatible

80 Section 3: Damage and fracture mechanics
’hanging’ nodes. Applied to the XFEM some specialties occur, e.g. in our approach those hanging
nodes are not allowed to be enriched with additional degrees of freedom.
The error estimator is presented for 3D single- and multiscale computations. Effects of the
radius of the microdomain around a crack front are analysed.
Modeling of quasi-static crack growth with a multilevel embedded FEM
Arun Raina, Christian Linder (Universität Stuttgart) Schedule
Modern engineering applications sometimes subject materials to external forces beyond their
design limit. It is of utmost importance for the integrity of the structure and general safety that
material behavior beyond design limit is understood. Cracks or shearbands are the starting point of
any material failure subjected to high stresses which appear as jumps in the displacement field also
called as ’strong discontinuities’. Some advanced numerical techniques like the ”embedded finite
element method (EFEM)” [1] can model failure of solids with a very good approximation. The key
advantages of EFEM over other available methods are its mesh independency and computational
efficiency that makes the method suitable for the newly developed multilevel approach as described
below. The multilevel embedded finite element method facilitates the use of even coarser meshes
at the failure zone with improved accuracy. The methodology also enables the development of
multiple strong discontinuities in a single finite element which can be used to model certain
complex failure phenomena.
The multilevel approach of using the EFEM is derived from the method of domain decomposition
[2]. For a discretized domain, the finite elements at the zone where a strong discontinuity
can form and propagate based on some failure criterion are treated as separate sub-boundary
value problems. Each global finite element representing a sub-boundary value problem is adaptively
discretized during the run time into a number of sub-elements which are subjected to a
kinematic constraint at the degrees of freedom associated with its boundary. The newly created
sub-boundary problem therefore becomes a constrained minimization problem which is solved in
every Newton iteration of an incremental time step. Each sub-element in a sub-boundary value
problem is equally capable of developing a strong discontinuity depending upon its state of stress.
The kinematic constraint at the boundary is a linear displacement based interface which is modified
accordingly as soon as a strong discontinuity crosses the global finite element boundary. For
the local equilibrium, the coupling between the quantities at two different levels of discretization
is obtained by matching the virtual energies due to admissible variations of the global finite
element and its constituent sub-elements.
[1] C. Linder, F. Armero, Finite elements with embedded strong discontinuities for the modeling
of failure in solids, Int. J. Numer. Methods Engrg. 72 (2007), 1391-1433.
[2] K.C. Park, C.A. Felippa, A variational principle for the formulation of the partitioned structural
systems, Int. J. Numer. Methods Engrg. 47 (2000), 395–418.
Crack growth in elastic materials with internal boundaries and interfaces
P. Judt, A. Ricoeur (Universität Kassel) Schedule
This work presents numerical methods used for predicting crack paths in technical structures
based on the theory of linear elastic fracture mechanics. The FE-method is used in combination
with an efficient remeshing algorithm to simulate crack growth. Different post processors providing
loading parameters such as the J-integral and stress intensity factors (SIF) are presented.
Path-independent contour integrals [1] are used to avoid special requirements concerning crack tip

Section 3: Damage and fracture mechanics 81
meshing and to enable efficient calculations for domains including interfaces and internal boundaries.
Several crack growth criteria are compared with respect to the resulting crack paths. In
particular, the interaction of cracks and internal boundaries and interfaces is investigated. The
simulation combines crack propagation within elastic bodies and at bimaterial interfaces. The latter
is based on a cohesive zone model. The presented numerical results of crack paths are verified
by experiments.
[1] Rice, J.R.; Journal of Applied Mechanics 35, 379-386 (1968)
Simulation of Crack Propagation with Competing Brittle and Ductile Damage Mechanisms
Geralf Hütter (TU Freiberg), Thomas Linse (TU Dresden), Uwe Mühlich, Meinhard Kuna (TU
Freiberg) Schedule
For decreasing temperatures, typical engineering metals show a transition from ductile to brittle
failure. The accompanied loss of toughness, e.g. measured as Charpy-energy or crack growth resistance,
is a problem in many technical applications. Today, the so-called local approach to fracture
got state-of-the-art, whereby the damage is computed equivalently to stresses and deformations.
However, in most cases only the ductile damage is taken into account as damage variable whereas
possible cleavage is still evaluated by post-processing criteria. Mostly, it is argued that cleavage
cracks propagate instably coinciding with structural failure. Certainly, this type of approach does
not account for the interaction of ductile and cleavage mechanisms which is important in the
upper ductile-brittle transition region as well as for phenomena like crack arrest.
For our contribution we employ a non-local model of Gurson-type together with a cohesive
zone to model the ductile-brittle transition region. This consistent formulation of a boundary
value problem allows arbitrary mesh resolutions. The crack propagation is simulated within the
limiting case of small-scale yielding.
The results show that the model captures qualitative effects of corresponding experiments
such as pop-ins, the formation of a stretch zone and secondary cracks. The influence of the temperature
on the predicted toughness is reproduced in the whole ductile-brittle transition region
without introducing temperature dependent fit parameters. The pop-in mechanism of secondary
cracks and unloading zones is highlighted.
Monitoring fatigue cracks and stress intensity factors based on local strains
Ramdane Boukellif, Andreas Ricoeur (Universität Kassel) Schedule
We present a method for crack detection and stress intensity factor measurement in plate structures
by using strain gauges and applying the Body Force Method (BFM) as well as the dislocation
method. The BFM is based on elastic solutions for concentrated loads and the principle of linear
superposition allowing e.g. the calculation of the strain field in a cracked body. The dislocation
method is based on a similar idea, however the crack is here represented by a line of point dislocations.
Thus, the approach is based on the weighted superposition of elastic Greens functions
representing the strain field due to the presence of a crack, where the weights are being identified
by inverse problem solution. Since the strain fields are controlled by both external loads and
the crack growth the unknown parameters are crack position and inclination as well as loading
quantities. First, the algorithms are verified based on numerical simulations. The particle swarm
algorithm came out to be most suitable for parameter identification in a high dimensional space.
Experimentally, we use strain gauges at different positions to measure the remote strain field on
the surface of a plate structure. Experiments are carried out under cyclic loading using pre-cracked

82 Section 3: Damage and fracture mechanics
plates made of aluminum alloy.
Investigation of the local behavior of different cohesive zone models
Claudio Balzani (Universität Hannover) Schedule
Cohesive interface elements are well suited for three-dimensional crack propagation analyses as
long as the crack path is well known. This is the case e.g. in delamination analyses of laminated
composite structures or failure analyses of adhesively bonded joints. Actually, they are widely
used in such applications for both brittle and ductile systems.
As long as the strength and fracture toughness of the material are accurately captured it is
generally accepted that the shape of the cohesive law describing the nonlinear softening behavior
has little to no influence on the mechanical behavior of the investigated structures. The author
agrees if the global structural response is of interest.
However, when having a look on the local behavior of different cohesive zone models, such as
stress distribution in the fracture process zone, the results exhibit certain differences. These will
be studied in the present contribution. Especially the local stress distribution will be investigated
and the effect on the computational efficiency will be pointed out based on relevant numerical
examples with experimental evidence.
S3.4: Dynamic Fracture Mechanics Wed, 16:00–18:00
Chair: Manuela Sander, Martina Hofacker S1|03–116
Dynamic crack analysis in 2D elastic solids with the singular edge-based smoothed
finite element method
Tinh Q. Bui, Chuanzeng Zhang (Universität Siegen) Schedule
In this work, the recently developed singular edge-based smoothed finite element method (sES-
FEM) [1] is further developed for dynamic crack analysis in two-dimensional elastic solids. The
objective of this paper is to provide a better understanding of the dynamic fracture behaviors of
linear elastic solids in the framework of the strain smoothing approach. Following this approach,
the strains are smoothed and the system stiffness matrix is thus performed using the strain
smoothing technique over the smoothing domains associated with the element edges. In order
to accurately capture the singular fields at the crack tip, a two-layer singular five-node crack-tip
element is employed. Due to the unique feature of the present sES-FEM formulation, such singular
crack-tip element is constructed based on the assumed displacement values on the boundary of the
smoothing domains without the need of the derivatives. The singular shape functions are generated
by a simple point interpolation with a fractional order basis without the mapping procedure. The
governing dynamic equations are transformed into a standard weak-form, which is then discretized
into a sES-FEM system of time-dependent equations to be solved by the unconditionally stable
implicit Newmark time integration method. To analyze the fracture behaviors of linear elastic
solids, mixed-mode dynamic stress intensity factors (DSIFs) are evaluated using the domain forms
of the interaction integrals in terms of the smoothing technique. Various numerical examples are
considered to illustrate the accuracy of the proposed approach, and the computed results for the
normalized DSIFs are compared with reference solutions in a wide range of benchmark dynamic
crack problems which shows high accuracy of the proposed sES-FEM.
[1] G. R. Liu, N. Nourbakhshnia, L. Chen, Y. W. Zhang. A novel general formulation for singular
stress field using the ES-FEM method for the analysis of mixed-mode cracks. Int J Comput
Methods 7 (2010), 191–214

Section 3: Damage and fracture mechanics 83
A New Phase Field Model for Dynamic Fracture Accounting for Brittle to Ductile
Failure Mode Transition
M. Hofacker, C. Miehe (Universität Stuttgart) Schedule
The computational modeling of failure mechanisms in solids due to fracture based on sharp crack
discontinuities suffers in dynamic problems with complex crack topologies including branching.
This can be overcome by a diffusive crack modeling based on the introduction of a crack phase
field as suggested in [1,2]. In this work, we extend these recent models of brittle crack propagation
towards the analysis of ductile fracture in elastic-plastic solids. In particular, we propose a
formulation that is able to predict the brittle-to-ductile failure mode transition under dynamic
loading. The proposed model is able to reproduce the classical impact test performed by Kalthoff
and Winkler, which shows brittle-to-ductile failure mode transition for increasing impact velocity.
We start our investigation with an intuitive and descriptive derivation of a regularized crack
surface functional that converges for vanishing length-scale parameter to a sharp crack topology
functional. This functional provides the basis for the construction of suitable energy storage and
dissipation functions, which govern the degrading stress response in ductile materials and the
evolution of both the plastic strain as well as the crack phase field. The governing equations are
derived in a consistent manner from a rate-type variational principle. We then introduce local
history fields which contain suitably defined crack sources which accumulate in the deformation
history. It is shown that these local variables drive the evolution of the crack phase field. The
introduction of the history fields inspires the construction of extremely robust operator split schemes
of phase-field-type fracture which successively update in a typical time step the history fields,
the crack phase field and finally the displacement field. We demonstrate the performance of the
proposed phase field formulation of fracture by means of the simulation of the Kalthoff Winkler
experiment and show the failure mode transition.
[1] C. Miehe, M. Hofacker, F. Welschinger, A phase field model forrate-independent crack propagation:
Robust algorithmic implementation based onoperator splits, Comput. Method. Appl.
M. 199 (2010), 2765–2778.
[2] M. Hofacker, C. Miehe, A phase field model of dynamic fracture: Robust field updates for
the analysis of complex crack patterns, submitted to Int. J. Numer. Meth. Eng.
Debonding propagation analysis of sandwich beams subjected to dynamic bending
loading
Vyacheslav N. Burlayenko (National Technical University KhPI, Kharkov), Tomasz Sadowski
(Lublin University of Technology) Schedule
Sandwich materials are an assembly of generally orthotropic layers, consisting of rigid face sheets
sandwiched by the lightweight and soft core. The resin rich interface between the basic layers are
susceptible to damage from occurring large stresses that can be the prelude to debonding initiation
and its advancing under loading conditions. In this study an assessment of the debonding advance
within a sandwich beam is examined. The sandwich beam with an embedded debonding zone
is subjected to both a static and a dynamic transverse load. The finite element model of the
sandwich beam is simulated by using the finite element code ABAQUS. Both the linear fracture
mechanics approach, based on the virtual crack closure technique and the damage mechanics
approach, implemented in ABAQUS through cohesive elements are applied to consideration of
the stress regimes at the damaged interface to predict the debonding capability to propagate. For
this application the behavior of cohesive elements is defined in terms of the traction-separation

84 Section 3: Damage and fracture mechanics
law along with a progressive damage model. Stress-based damage initiation criteria are used to
evaluate the propensity of the sandwich beam to undergo damage. Both implicit and explicit
solvers available in ABAQUS are applied for analyzing damage tolerance of partially debonded
sandwich beams under conditions of static and dynamic loading. Distributions of stresses and
components of strain energy release rate are calculated at the debonding front so that to make a
conclusion on debonding propagation process.
Microcrack Evolution in Functionally Graded Material under Dynamic Loading
Ralf Mueller, Natalia Konchakova (Universität Kaiserslautern) Schedule
The damage process of metal-ceramic functionally graded material (FGM) is investigated. The
microcrack evolution in a layered structure is analyzed using numerical simulation (FEM) of stresses
and configurational forces. The modelling of an FGM of alumina ceramic and a metalic phase
with gradually changing volume fraction of alumina is performed. A structure of two different
layers bonded to a substrate is used. The stiffness and density of the three materials are varying.
The evolution of configurational forces is simulated.
The influence of crack length on the crack driving force is studied for the case of a stress wave
loading. The stress loading is applied in the horizontal direction as a dead load.
The comparison with an uncracked FGM is considered. It is shown that in the case of an
uncracked FGM the zone of maximal stress is placed in the central part of the specimen in the
material with maximal volume fraction of alumina, which yields maximal Young Modulus and
minimal density.
Boundary Integral Equations in the Frequency Domain for Interface Cracks under
Impact Loading
Oleksandr V. Menshykov, Maryna V. Menshykova (University of Aberdeen), Michael Wuensche,
Chuanzeng Zhang (Universität Siegen) Schedule
It is common knowledge that all existing structural materials contain various inter- and intracomponent
cracks which appear in materials during fabrication or in-service. The presence of
structural defects considerably decreases the strength and the reliability of materials.
Under deformation the opposite faces of the existing cracks interact with each other, altering
significantly the stress fields near the crack tips. The analysis of static problems demonstrates
that the contact interaction considerably changes the solution. It takes on special significance for
the case of high rate deformations as found in impact and high-frequency dynamics, which covers
an extremely wide range of situations, where the contact interaction can change the response substantially.
Unfortunately, due to the non-linearity of the problem and substantial computational
difficulties, the overwhelming majority of studies neglect the contact interaction of crack faces in
spite of its evident significance.
In the current study we investigate 2D interface cracks between two dissimilar homogeneous
isotropic half-spaces undergoing impact loading. In order to take the contact interaction of crack
faces into account the Signorini constraints are imposed for normal components of displacements
and forces. The problem is solved using the boundary integral equations in the frequency domain.
The distributions of the displacements and tractions at the bonding interface and surfaces of the
cracks are obtained and analysed. The stress intensity factors (opening and shear modes) are
computed for different values of the wave frequency and different properties of the bimaterial.

Section 3: Damage and fracture mechanics 85
BEM for transient thermoelastic analysis of a functionally graded layer on a homogeneous
substrate under thermal shock
A. Ekhlakov (Universität Siegen), Oksana M. Khay (Universität Siegen, Pidstryhach Institute for
Applied Problems of Mechanics and Mathematics Lviv), Chuanzeng Zhang (Universität Siegen)
Schedule
In this paper, transient thermoelastic analysis of two-dimensional, isotropic and linear elastic bimaterials,
which are constituted by a functionally graded (FG) layer attached to a homogeneous
substrate, subjected to thermal shock is investigated. For this purpose, a boundary element method
(BEM) for coupled and linear thermoelasticity is developed. The material properties of the
FG layer are assumed to be continuous functions of the spatial coordinates, while Poissons ratio is
taken as constant. The Laplace-transform technique is applied to eliminate the time-dependence
in the governing partial differential equations.
Fundamental solutions of linear coupled thermoelasticity for homogeneous, isotropic and linear
elastic materials in the Laplace-transformed domain are used to derive boundary-domain integral
representations for the mechanical and thermal fields. The FG/homogeneous bimaterials are modeled
by using a sub-domain technique. The bimaterial system is divided into a homogeneous and
a non-homogeneous sub-domain along the interface. The boundary-domain integral equations are
applied to each sub-domain and the continuity conditions are employed on the interface boundary.
Due to the material non-homogeneity in the FG layer, this approach leads to domain integrals
involving the unknown quantities in addition to the conventional boundary integrals. The domain
integrals are transformed into boundary integrals by using the radial integration method (RIM).
For the homogeneous and linear elastic substrate, only boundary integrals need to be considered
in the boundary integral equations. A collocation method is implemented for the spatial discretization
of the boundary-domain integral equations. Numerical solutions are first obtained in the
Laplace-transformed domain for discrete values of the Laplace-transform parameter. To obtain
time-dependent solutions, an inverse Laplace-transform by using Stehfests algorithm is performed.
Numerical examples for an exponential gradation of the material parameters are presented
and discussed to demonstrate the accuracy and the efficiency of the present BEM.
S3.5: Different advanced aspects in damage modeling Thu, 13:30–15:30
Chair: Maksim Zapara, Vladimir Shneider S1|03–116
Strain induced damage of ductile materials under compression
Maksim Zapara (TU Berlin), Nikolai Tutyshkin (Universität Tula, Russia), Wolfgang H. Müller,
Ralf Wille (TU Berlin) Schedule
The scheme of plastic compression has been successfully implemented in many metal forming
processes and can be characterized by negative values of stress triaxiality. Damage mechanics
considers ductile failure as a kinetic deterioration of the deformed material. The difficulties of the
analysis of damage kinetics are related to the determination of the material functions which appear
in the constitutive equations. Stress triaxiality under plastic compression varies considerably both
over the specimen volume (in the meridian section) and over the strain path. The averaged values
of stress triaxiality are commonly used for the analysis of plastic compression.
In this paper the problem of ductile damage and failure prediction is solved by taking a change
in stress triaxiality under plastic compression of cylindrical specimens made of low-carbon lowalloy
steel, aluminum alloy, and pure copper into account. It is shown that such a more accurate
assessment leads to a greater shift of stress triaxialities into a range of negative values (compared
to their averaged values). At such values of stress triaxiality the material can be subjected to

86 Section 3: Damage and fracture mechanics
plastic compression without failure under arbitrarily large deformations (due to the healing of
micro-defects). The constitutive equations of the tensorial framework for ductile damage recently
developed by the authors are applied to modeling.
Investigation of gradient-enhanced damage evolution in viscoplastic plates under propagating
disturbance
An Danh Nguyen, Marcus Stoffel, Dieter Weichert (RWTH Aachen) Schedule
This work investigates gradient-enhanced damage evolution by performing a parameter study for
the authors’s finite element shell model, in which the free energy function is enhanced phenomenologically
in terms of a non-local damage variable and its gradient on the mid-surface of shell
structures. This enhancement gives rise to an introduction of gradient parameters in terms of a
substructure-related intrisic length-scale and a relationship between non-local and local damage
variable. Based on the global displacement-force curves obtained from shock-tube tests on aluminium
plate specimens, the gradient parameters are determined to validate the proposed shell
model. The influence of spatial gradient of loading on the material behaviour within a macroscopic
continuum element will be discussed through several examples.
Enhancement of the micro mechanical basis for local approach cleavage models
Volker Hardenacke, Jörg Hohe (Fraunhofer IWM Freiburg) Schedule
The present study is concerned with the investigation of the micro mechanisms of micro defect
nucleation in ferritic steels in order to provide an enhanced basis for probabilistic cleavage models.
Brittle fracture of ferritic steels is a probabilistic process, triggered by the failure of randomly
distributed second phase particles. These particles fracture due to plastic deformation of the surrounding
matrix, resulting in the nucleation of micro defects. Once nucleated, the local stress
state controls the possible instability of the defects. In this context, the local stress triaxiality is
assumed to govern the blunting of freshly nucleated micro cracks. By a micro mechanical modelling
of the cleavage initiation process the effects and the interactions of the relevant parameters
can be identified. For this purpose Representative Volume Elements (RVE) of the micro structure
are utilised, accounting for both, the grain structure as well as the brittle particles at the
grain boundaries. The RVEs are loaded based on the local mechanical field quantities determined
numerically for different fracture mechanics specimen types at the cleavage origins. Thus, the
behaviour of the particles against the micromechanical conditions can be specified, resulting in a
better understanding of the processes at cleavage fracture initiation.
Marciniak-Kuczynski type modelling of the effect of complex loading on the forming
limits of sheet metal
D.K.Teslenko, V.P.Shneider, Yu.A.Chernyakov (Dnepropetrovsk National University) Schedule
Formability of sheet metal is limited to the beginning of localized shear or necking. In connection
with the application value, recently interest to the problem of determining the maximum allowable
strain in the biaxial tension of elastoplastic thin plates is increased. Most articles on this subject
use the classical model of Marciniak-Kuczynski (MK) [1]. Later, in a number of studies, this
model has been improved, allowing taking into account all possible orientations of localization,
including through-thickness shear [2].
Despite the substantial progress made in modeling the limiting conditions of formation, virtually
all studies that describe the elastic-plastic behavior of materials are limited to using the
simplest theories of plasticity. However, the processes of forming of sheet metal is generally accompanied
by large deformations and complex loading and improving of prediction of sheet forming
simulation often requires physically based model defining.

Section 3: Damage and fracture mechanics 87
In this paper for describing the behavior of elastic-plastic material we use the theory of plasticity,
taking into account microstrain [3].
In the framework of this theory, a comparative analysis of the MK approach and the bifurcation
analysis, followed by the construction of afterbifurcational solutions for the plate, are made.
The dependences of the limit of formability of the material under load (with a given strain)
on two-tier broken are calculated. A comparison of ultimate strains with the values obtained with
the proportional deformation are made. It is shown that under non-proportional deformation the
ultimate strain may increase. We studied the dependence of the formability limit under cyclic
loading and ratcheting. It was found that in this case the limit of formability depends on the
cyclic properties of the material and can both increase and decrease.
[1] Marciniak, Z., Kuczynski, K. Limit strains in the processes of stretch-forming sheet metal,
International Journal of Mechanical Sciences 9 (1967), 609620.
[2] Eyckens P., Van Bael A., Van Houtte P. MarciniakKuczynski type modelling of the effect
of Through-Thickness Shear on the forming limits of sheet metal, International Journal of
Plasticity 25 (2009), 22492268.
[3] Kadashevich Yu.I., Chernyakov Yu.A. Theory of plasticity, taking into account micro stresses
Advances in Mechanics 15 (1992), 3-39.
Mechanical properties of hybrid composites made of a steel plate and a laminate
connected with screw rivets
Zolkiewski Slawomir (Silesian University of Technology) Schedule
In this paper the research results of hybrid composite materials made of a steel plate and laminates
will be presented. The tested composites were made of a metal sheet plate and a laminate
plate connected with screw rivets. The laminates were made of three different types of fabrics
with: fibreglass, carbon fibres and aramid fibres. As a warp, epoxide resin and polyester resin
were used. The FML (fibre-metal laminate) hybrid composites connect advantages of metal sheet
plates and laminates, especially locking of expansion of cracks on the composite surface (avoiding
delamination) under multiple loading [1]. They also have very good force versus displacement
characteristics, strain characteristics, percussive resistance and a strength versus total mass ratio.
In the work the following characteristics and the juxtaposition of results of experimental tests will
be presented. The application of the hybrid composite materials is very wide and popular. These
composites can be applied in: connecting systems made of different fabrics, connecting systems
with a large number of layers in their structure and in a system with a variety of configurations
between metals and laminates. The experimental tests were carried out in the Dynamic Machines
Laboratory on the dedicated laboratory stands. The laboratory stand consists of the carrying frame,
fixing frame, manual hydraulic actuator and measuring elements: displacement sensor and/or
extensometers [2] and force gauge. The laminates were the handmade ones and fabricated in the
same conditions in the laboratory. This fact is important when comparing sample results. The
maximal and minimal strains were derived and average strain was calculated. The strain in the
time function graphs were presented. The tests relies on fixing of the specimen in the fixation
frame and loading it by means of the manual hydraulic actuator. The specimen was fixed in
the frame by hand screws. The force gauge was situated between the specimen and the manual
hydraulic actuator. The force gauge U2B-50kN was used for force measurements. The specimen
was loaded in the centre point with the force originating from the manual hydraulic actuator.

88 Section 3: Damage and fracture mechanics
The displacement sensor WA L-20 was used on the other side of the laboratory stand. The extensometers
were stuck on the specimen surface. The stand allows measuring the displacement
of the centre point of the sample under the given load and displacements in a place where the
extensometers were applied.
[1] B. Surowska, Functional and hybrid materials in air transport, Eksploatacja i Niezawodnosc
Maintenance and Reliability, 3 (2008), 30 – 40.
[2] S. Zolkiewski, Laboratory Test Of The Composite Material Provided By Extensometer, Sev-
NTU Journal, 110 (2010), 128 – 129.
Predicting ductile fracture under multi-axial loading: comparison of modified Mohr-
Coulomb with shear modified Gurson model
Matthieu Dunand, Dirk Mohr (MIT and École Polytechnique) Schedule
Substantial progress has been made over the past decade in characterizing and modeling the effect
of the Lode angle parameter on ductile fracture at low stress triaxialities. In this talk, we compare
the performance of shear-modified Gurson models with that of the Modified Mohr-Coulomb
(MMC) damage indicator model in view of predicting the onset of fracture over a wide range of
stress-states. The experimental program on TRIP780 steel sheets includes notched tension tests,
a punch test and combined tension/shear experiments on butterfly specimens. It is found that
onset of fracture in all nine experiments is predicted correctly by the MMC fracture model. The
predictions of the shear-modified Gurson model are found to be less accurate. The differences and
shortcomings of both models are discussed in detail along with important underlying experimental
challenges.
Keywords: Ductile fracture, stress triaxiality, Lode angle,

Section 4: Structural mechanics 89
Section 4: Structural mechanics
Organizers: Christian Hellmich (TU Wien), Martin Schagerl (Johannes Kepler Universität
Linz)
S4.1: Numerical Methods 1 Tue, 13:30–15:30
Chair: Jochen Hebel S2|02–C205
An Efficient Scheme for Stochastic Finite Element Solutions
Philipp-Paul Jablonski, Udo Nackenhorst (Universität Hannover) Schedule
Results from computational mechanics analysis are unsure due to uncertain model parameters
like boundary conditions, constitutive models and process development. Increasing computer performance
and sophisticated modeling approaches enable for stochastic analysis of mechanical
processes. However, a broad variety of methods for the treatment of stochastic partial differential
equations are under discussion in the related literature.
In this presentation the concept of Polynomical Chaos expansion is investigated with regard
to the analysis of welded steel joints. The constitutive parameters in the zone of interest are
assumed to be uncertain with a priory statistical distribution.
With regard to the computational efficiency it has to be notices, that with each stochastic
variable an additional infinite dimension is added to the problem. In order to treat these problems
within a finite element computational framework, a novel staggered iterative scheme is suggested
to solve the resulting linear system. Furthermore, sophisticated schemes for the postprocessing,
e.g. the computation of equivalent stresses from uncertain displacement fields and uncertain material
properties will be introduced.
Computational results are compared with results obtained from well defined experimental
investigations. The fatigue under cyclic loading will be discussed.
Application of isogeometric analysis to domain decomposition and phase separation
problems
Christian Hesch, Peter Betsch (Universität Siegen) Schedule
During the past decate various new spatial discretization techniques have been developed. In
particular, the usage of NURBS based shape functions, well known to the CAD community, has
been adapted to finite element technology, used to solve different types of PDEs.
Within this talk we concentrate on two different aspects: First, we search for a remedy of a
major drawback of NURBS based shape functions: The discretization relies on a specific index
space, imposing restrictions to h-refinements and the possible geometry. In the field of CAD
applications this is resolved by using unconnected patches or by introducing T-Splines. Contrary
to the mentioned solutions for CAD applications, we resolve this by introducing a variational
consistent and non conform domain decomposition method, based on Mortar projections of the
displacement field.
Second, we search for the limitations of NURBS based shape functions. In particular, a specific
higher order phase separation model, based on the Cahn-Hilliard model, is discretized with C 1
continuous NURBS in space and a modified mid-point type discretization scheme in time. It turns
out, that the spatial discretization imposes restrictions to the time integration if applied to this
type of transport equations.
Bayesian Inference of Linear Time-Varying Systems Based on Hilbert-Huang Transform
Han Hu, Carsten Proppe (KIT) Schedule

90 Section 4: Structural mechanics
This paper proposes an identification method for general linear time-varying MDOF systems
(including chainlike and non-chainlike systems) based on the Hilbert-Huang Transform. The main
procedures of the identification for system with n degrees of freedom are: First, by using Bayesian
Inference and a Transitional Markov Chain Monte Carlo algorithm, initial knowledge about the
free vibration system responses and the white noise in system responses is updated based on
measured system responses, which yields the posterior distributions of the noise parameters.
Second, each sample system responses are obtained in accordance with the posterior distribution
and are processed by Hilbert-Huang Transform in order to obtain n intrinsic mode functions
(IMFs) and the residue as well as the corresponding n analytical IMFs and the analytical residue
for each degree of freedom. Finally, the above signals for each degree of freedom are summed
respectively to form new responses and new analytical responses for each set of sample system
responses, which are then used in the proposed identification equations to identify the distributions
of system parameters.
The proposed method is applied to chainlike and non-chainlike linear time-varying systems with
three types of stiffness variations: smooth, abrupt and periodical variations. The effectiveness and
accuracy of the proposed method on SDOF and MDOF systems is discussed in numerical simulations.
System responses are perturbed by white noise, and the identified results demonstrate the
robustness of the method.
Keywords: System identification, Linear systems, Special transforms (Legendre, Hilbert, etc.),
Bayesian inference, Transitional Markov Chain Monte Carlo algorithm
Energy-consistent time-integration for a dynamic finite deformation thermoviscoelastic
continuum
Melanie Krüger (Universität Siegen), Michael Groß (TU Chemnitz), Peter Betsch (Universität
Siegen) Schedule
The main goal of the present paper is the description of a dynamic finite deformation thermoviscoelastic
continuum in the enhanced GENERIC (General equations for non-equilibrium reversible
irreversible coupling) format, which is based on the works of Romero [1] (thermoelasticity)
and a work of Krüger et al. [2] (enhanced GENERIC for masspoint systems). The time integration
for the energy-momentum consistent or thermodynamically consistent system is done with
partitioned discrete derivatives, which are well known from Gonzalez [3]. The underlying structure,
in which the system of partial differential equations is described, is the enhancement of the
so called GENERIC format. This GENERIC format was introduced by Öttinger [4] for thermoelastodynamic
systems. The considered variables of the system are the Poissonian variables, which
are here the linear momentum, the configuration, the entropy and the internal variable.
The thermo-viscoelastic continuum needs two constitutive equations for the thermoelastic and
viscoelastic part of the system. The thermal evolution equation is described with Fourier’s law of
isotropic heat conduction and the viscous part is given by an fourth order compliance tensor.
The enhanced numerical stability of the newly developed structure-preserving integrators in
comparison to standard integrators is demonstrated by means of numerical examples.
[1] I. Romero, Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics,
Part I: Monolithic integrators and their application to finite strain thermoelasticity,
Computer Methods in Applied Mechanics and Engineering, 2010, 199:1841-1858
[2] M. Krüger, M. Groß and P. Betsch, Energy-consistent time-integration for dynamic finite
deformation thermo-viscoelasticity, PAMM, 2011, submitted for publication

Section 4: Structural mechanics 91
[3] O. Gonzalez, Design and analysis of conserving integrators for nonlinear Hamiltonian systems
with symmetry, Ph.D. Thesis, Department of Mechnical Engineering, Stanford University,
1996
[4] H.C. Öttinger, Beyond equilibrium thermodynamics, Wiley, New York, 2005
System Identification based on Selective Sensitivity Analysis
Billmaier Maximilian, Bucher Christian (TU Wien) Schedule
Dynamical measurements are applied to assess structural reliability in the context of health
monitoring or design evaluation. However, system identification requires the solution of inverse
problems, which usually leads to rather ill-conditioned formulations.
The selective sensitivity analysis provides a way out of this dilemma. In this analysis, the output
of a structure is only sensitive to a few model parameters (to be identified), but insensitive to the
others.
These essential few parameters are then identified by applying selective sensitive excitations. It is
shown that the updating algorithms for selective sensitive excitations are always better conditioned
than those for any other excitation combination. A limitation of this method has often been
called the realization of theoretically derived excitations in dynamical experiments.
In a first laboratory application, the analysis is applied. With only a very limited prior knowledge
of the structure, a robust converging mathematical model is presented. It is shown that the
selective sensitive excitations can be experimentally realized in a convenient approach.
Adaptive FEM with Stabilized Elements for Parameter Identification of Incompressible
Hyperelastic Materials
Kai-Uwe Widany, Rolf Mahnken (Universität Paderborn) Schedule
This work is concerned with the identification of material parameters for isotropic, incompressible
hyperelastic material models. Besides the principal stretch-based strain-energy function by Ogden
an invariant-based strain-energy function by Rivlin/Saunders is considered for which parameter
sensitivities are derived. The identification is formulated as a least-squares minimization problem
based on the finite element method to account for inhomogeneous states of stresses and strains
in the experimental data which is obtained by optical measurements [2]. For the finite element
method low-order tetrahedral elements in a mixed displacement-pressure formulation with stabilization
are considered [3]. Special attention is payed to an adaptive mesh-refinement based on a
goal-oriented a posteriori error indicator to gain reliable material parameters [1]. To approximate
error terms an element-wise recovery technique based on enhanced gradients is introduced.
[1] R. Becker, B. Vexler, A posteriori error estimation for finite element discretization of parameter
identification problems. Numerische Mathematik 96(3) (2004), 435 – 459.
[2] R. Mahnken, E. Stein, Parameter identification for finite deformation elasto-plasticity in
principal directions. Comp. Meths. Appl. Mech. Eng. (1997) 147, 17 – 39.
[3] K.-U. Widany, I. Caylak, R. Mahnken, Stabilized Mixed Tetrahedrals with Volume and Area
Bubble Functions at Large Deformations, Proc. Appl. Math. Mech. 10 (2010), 227 – 228.
S4.2: Numerical Methods 2 Tue, 16:00–18:00
Chair: Vadim Potapov S2|02–C205

92 Section 4: Structural mechanics
Incompatible Modes for Volumetric Shell Elements in Explicit Time Integration
Steffen Mattern, Christoph Schmied, Karl Schweizerhof (KIT) Schedule
Explicit time integration methods as the widely-used central difference scheme are characterized
by efficient vector equations on the global level due to the application of diagonalized mass
matrices. Together with a limitation of the time step size by a critical value, this leads to a
domination of the numerical effort on element level.
Volumetric shell elements as presented e. g. in [1], are formulated only with displacement
degrees of freedom and hence allow the simulation of shell-like structures with full representation
of its continuum properties. As all lower order displacement based element formulations with
standard numerical integration, they show artificial stiffness effects, the so-called locking. One
well-known strategy for the treatment of locking is the enhanced assumed strain (EAS) method [2],
based on an enhancement of the compatible strain field by introducing additional degrees of
freedom, which are condensed-out by local equation solving. This leads to a significant increase of
the numerical effort on element level. The method of incompatible modes (IM) has originally been
the basis for the variational principle presented in [2]. As presented in [3] for 2D-plane elements,
it is possible to generally formulate the method in order to reproduce any EAS-element with
corresponding incompatible modes also for the 3D volumetric shell elements. In order to achieve
an efficient element formulation, the additional displacement degrees of freedom are treated as
regular unknowns in the global equations, so the formulation of a diagonalized mass matrix for
the additional degrees of freedom has to be discussed.
The implementation of efficient element routines is supported by the programming tool Ace-
Gen [4], which allows the application of symbolic operations and the generation of highly optimized
program code. Both EAS- and IM-elements are implemented using AceGen and compared
regarding the treatment of locking effects and their numerical performance.
[1] R. Hauptmann & K. Schweizerhof: A systematic development of ‘solid-shell’ element formulations
for linear and non-linear analyses employing only displacement degrees of freedom,
IJNME, 42(1): 49–69, 1998.
[2] J.C. Simo & M.S. Rifai: A class of mixed assumed strain methods and the method of incompatible
modes, IJNME, 29(8): 1595–1638, 1990.
[3] M. Bischoff & I. Romero: A generalization of the method of incompatible modes, IJNME,
69(9): 1851–1868, 2007.
[4] J. Korelc: http://www.fgg.uni-lj.si/Symech/, 2011.
Solid-shell finite elements for tesselated geometries
Johannes Wimmer, Stefanie Reese (RWTH Aachen) Schedule
Tesselated folded sheets have a multitude of applications in sandwich panel cores or impact absorbing
elements while allowing for additional functionality like cooling and moisture removal.
Particularly in transportation industry applications, the lightweight but stiff combination of tesselated
cores with smooth top and bottom sheets is of huge interest. Furthermore, these structures
are very economical in terms of usage of raw materials.
The tesselation can be chosen to fulfil specific structural requirements, but the production of
these tailor-made sheets has proven to be troublesome. E.g. zig-zag fold-patterns cause a strong
coupling between the facets and the transformation from a planar to a three-dimensional structure

Section 4: Structural mechanics 93
leads to significant biaxial contraction. In order to reduce time- and cost-intensive prototype production,
finite element analysis can provide an alternative to experimental testing, but this only
holds if the representation of both the structure and the material behaviour is sufficiently accurate.
Currently, typical simulations make use of standard finite elements, which are based on the
classical shell, beam or plate theory, respectively. High requirements towards precision, especially
for the transverse stress distribution, yield a high computational effort. Here, the solid-shell concept
provides an alternative with potential benefits in accuracy and performance.
In addition, solid-shell elements can overcome several numerical difficulties in finite element
simulations, such as locking phenomena. Volumetric, as well as membrane and thickness locking
are removed directly within the solid-shell formulation. Application of the assumed natural strain
concept provides a remedy for the transverse shear and curvature thickness locking. Furthermore,
we use reduced integration together with hourglass stabilisation.
Thus, the proposed elements are quite attractive from a numerical point of view due to their
computational efficiency and provide a suitable approach to the representation of tesselated sheets.
Keywords: tesselated geometry, folded sheet, solid-shell, locking
Coupled multiscale finite element analysis of shell structures
Jochen Hebel, Friedrich Gruttmann (TU Darmstadt) Schedule
In this study, a coupled multiscale finite element procedure (FE 2 ) for the analysis of shell structures
is proposed. On the macrolevel, a shell element with Reissner-Mindlin kinematic assumptions
is employed. On the microlevel, a representative volume element (RVE) ranging through the full
shell thickness is formulated. Numerical homogenisation in terms of shell stress resultants and
strains is used for coupling both scales. The resulting moduli are obtained by means of static
condensation of the internal degrees of freedom of the RVE. The finite element analyses on the
microlevel are solved efficiently in a parallel manner. A fully three-dimensional stress state is
obtained from the microproblem allowing an accurate analysis of even thick shells or composite
sections including inelastic material behaviour. Numerical examples demonstrate the effectiveness
and efficiency of the approach.
An Extended Product Ansatz for the Computation of Interlaminar Stresses in a
Mixed Finite Element
M. Schürg, J. Wackerfuß, F. Gruttmann (TU Darmstadt) Schedule
In this paper we enlarge on an extended shell kinematic which is implemented in a mixed four-node
shell element and described in detail in [1]. It is able to describe the complete three-dimensional
strain state. An extended product ansatz is introduced, so that additionally to the conventional
degrees of freedom of the shell based on the Reissner-Mindlin theory with inextensible director
vector also warping and thickness changes can be described. For the second part, it is considered
that the derivatives to the two coordinates in the plane are zero. In the context of the related
finite element formulation this leads to values that are constant in each element.
In this paper we consider that the derivatives to the two coordinates are not zero and describe
the corresponding finite element equations. In the context of the used finite element implemention,
this approach leads to a higher number of degrees of freedom on element level and it means that
an ansatz in the domain has to be made. The results of the two considerations are compared.
[1] M. Schürg, J. Wackerfuß, F. Gruttmann, Using A Mixed Shell Formulation To Compute

94 Section 4: Structural mechanics
Interlaminar Stresses In Layered Composite Shell Structures, 3rd ECCOMAS Thematic
Conference on the Mechanical Response of Composites 21st - 23rd September (2011).
Solving hyperelastic problems using mixed LSFEM
Karl Steeger, Alexander Schwarz, Jörg Schröder (Universität Duisburg-Essen), Gerhard Starke,
Benjamin Müller (Universität Hannover) Schedule
The focus of this contribution is the solution of hyperelastic problems using the least-squares
finite element method (LSFEM). In particular a mixed least-squares finite element formulation is
provided and applied on geometrically nonlinear problems. The basis for the element formulation is
a div-grad first order system consisting of the equilibrium condition and the constitutive equation
both written in a residual form. An L2-norm is adopted on the residuals leading to a functional
depending on displacements and stresses which has to be minimized. Therefore the first variations
with respect to both free variables have to be zero. The solution can then be found by applying
Newton’s Method. For the continuous approximation of the displacements in W 1,p with p > 2,
standard polynomials are used. Shape functions belonging to a Raviart-Thomas space are applied
for the stress interpolation. These vector-valued functions ensure a conforming discretization of
the Sobolev space H(div, Ω). Finally the proposed formulation is tested on several numerical
examples.
FEM system matrix modifications for structural optimization problems
Andreas Wagner, Gottfried Spelsberg-Korspeter, Peter Hagedorn (TU Darmstadt) Schedule
Design engineers frequently rely on the finite element method since it offers a broad range of
possibilities and is available in many powerful commercial tools. Also, finite element models can
be a basis for structural optimization. There are many optimization strategies and tools available,
however, if the finite element method is used in the context of structural optimization, it is often
necessary to change the mesh of the structure in every or at least some optimization steps. In order
to avoid this remeshing process, a new modeling approach for structures with modifications is
proposed. The approach can be of great advantage if the optimization aims for global properties
of the structure, e.g. the distribution of eigenfrequencies, and not local properties like stress
concentrations. The basic idea of the approach is to combine separate finite element meshes of
the basis structure and of the modifications by kinematical relations, leading to mass and stiffness
matrices of the complete structure. The approach will be demonstrated by a concise example.
S4.3: Shells and Plates Wed, 13:30–15:30
Chair: Wolfgang Müller S2|02–C205
Some geometrically nonlinear problems of thin periodic plates
Jarosław Jędrysiak, Łukasz Domagalski, Michał Gajdzicki (Technical University of Łódź) Schedule
Thin plates with periodic structure in planes parallel to the midplane are considered in this note.
In these plates we can distinguish many small, repeated elements called periodic cells, treated
as thin plates. The size of periodic, being a diameter of the cell, is called the microstructure
parameter l. It is assumed that on the microlevel properties of these plates are described by
periodic, highly oscillating, non-continuous functions. Such plates are called periodic plates.
Deflections of these plates are of the order of their thickness. Hence, they are usually analysed
in the framework of geometrically nonlinear theories, such as the well-known von Karman theory,
cf. [6]. But, for thin periodic plates the obtained governing equations have highly-oscillating, pe-

Section 4: Structural mechanics 95
riodic, non-continuous functional coefficients. Thus, it is rather difficult to apply these equations
to investigate special problems. In order to replace these equations by equations with constant
coefficients, various averaging techniques are used, e.g. asymptotic homogenization, cf. [4]. Unfortunately,
obtained governing equations usually neglect the effect of the microstructure size.
To avoid this drawback the tolerance averaging technique can be applied, proposed and developed
to analyse periodic composites and structures in a series of papers, e.g. for thin periodic
plates in [3], for periodic plates with a moderately thickness in [1], for periodic wavy-type plates
in [5], for periodic shells in [7]. An extended list of publications related to applications of this
approach can be found in the books [9, 8].
In this paper the governing equations with constant coefficients of the tolerance model for elastostatics
of periodic geometrically non-linear plates are applied to analyse some special problems,
cf. [2]. Moreover, results obtained in the framework of the proposed tolerance model and using
the orthogonality method are compared to results calculated using the finite element method.
[1] BARON E.: On modelling of periodic plates having the inhomogeneity period of an order of
the plate thickness, J. Theor. Appl. Mech., 44, 2006, 3-18.
[2] DOMAGALSKI Ł., JĘDRYSIAK J.: Modelling of thin periodic plates subjected to large
deflections, Civ. Env. Eng. Rep., 5, 2010, 121-136.
[3] JĘDRYSIAK J.: Dispersive models of thin periodic plates, Łódź, Wyd. Politechniki Łódzkiej
2001, (in Polish).
[4] KOHN R.V., VOGELIUS M.: A new model of thin plates with rapidly varying thickness,
Int. J. Solids Struct., 20, 1984, 333-350.
[5] MICHALAK B.: The meso-shape functions for the meso-structural models of wavy-plates,
ZAMM, 81, 2001, 639-641.
[6] TIMOSHENKO S., WOINOWSKY-KRIEGER S.: Theory of plates and shells, New York,
McGraw-Hill 1959.
[7] TOMCZYK B.: A non-asymptotic model for the stability analysis of thin biperiodic cylindrical
shells., Thin Walled Struct., 45, 2007, 941-944.
[8] WOŹNIAK CZ., ET AL. [eds]: Mathematical modelling and analysis in continuum mechanics
of microstructured media, Gliwice, Wyd. Politechniki Śląskiej 2010.
[9] WOŹNIAK CZ., MICHALAK B., JĘDRYSIAK J. [eds]: Thermomechanics of microheterogeneous
solids and structures, Łódź, Wyd. Politechniki Łódzkiej 2008.
Analysis of notches and cracks in circular Kirchhoff plates using the scaled boundary
finite element method
Rolf Dieringer, Wilfried Becker (TU Darmstadt) Schedule
In this contribution, a new formulation of the scaled boundary finite element method (SBFEM)
is presented for the analysis of circular plates in the framework of Kirchhoff’s plate theory. The
basic characteristic of the method is that a domain is described by the mapping of its boundary
with respect to a scaling centre. The governing partial differential equations are transformed into
scaled boundary coordinates and are reduced to a set of ordinary differential equations applying

96 Section 4: Structural mechanics
a discrete form of the Kantorovich reduction method. If the scaling centre is selected at the crack
tip, the SBFEM enables the effective and precise calculation of stress intensity factors of cracked
and notched structures, solving the corresponding eigenvalue problem. Although the method has
been applied successfully to many problems of continuum mechanics, its application to plate
bending problems is rather unexploited. The study provides the employment of the method for
the static analysis of circular plates using Kirchhoff kinematics. The element stiffness matrices
for bounded and unbounded media are derived. Numerical examples show the performance and
efficiency of the method, applied to plate bending problems.
Stress concentrations at free edges of shear webs
Christoph Kralovec, Kai-Uwe Schröder, Martin Schagerl (Universität Linz) Schedule
Shear webs with free edges occur frequently in lightweight constructions. A typical example in aircraft
design is the attachment of the circumferential frames to the fuselage skin. This attachment
is predominately loaded by the shear between the frame and skin. The web of this attachment
is interrupted by so-called “mouse-holes” at crossing of the stringers, so that the longitudinal
stringers can run through without interruption. Due to these holes the web has free edges at the
stringer positions. The other two opposite edges of the web are loaded by shear, which is brought
in by the frame and the skin, respectively. In this short communication we discuss the in-plane
strength of the shear web under these loading and boundary conditions. For analysis we use both,
analytical and numerical considerations.
For our study we consider a rectangular plate, which is loaded by shear on two simply supported
opposite sides. The other opposite sides can move freely and remain unloaded. Analyzing the
plates in-plane stress state it is obvious that at the corners the maximum equivalent stress occurs.
If no buckling occurs this stress determines the strength of the plate. However, the evaluation of
the stress-state at the corners raises some difficulties, as at these points the loaded and unloaded
edges meet, which indicates the development of stress concentrations.
A comparative study of deformations of elastic-viscoplastic plates using different
structural hypotheses
Marcus Stoffel, Duy Thang Vu, Rüdiger Schmidt, Dieter Weichert, (RWTH Aachen) Schedule
In the present study the geometrically and physically non-linear response of ductile structures
under shock wave loading conditions is investigated. The considered elastic-viscoplastic deformations
are occurring during time ranges of several microseconds. A finite element algorithm of
the transient structural response is based on shell theories taking first- and third-order transverse
shear deformations into account. In order to consider material non-linear effects, viscoplastic
constitutive equations are combined with the structural theory. The aim is to determine which
structural model predicts deformations under blast loading conditions most accurately. For this
reason, an experimental investigation with developed shock tubes is introduced as well. By subjecting
pressure waves in shock tubes to plate specimens, deflections and loading histories can be
measured during the impulse period and can be compared to simulation results.
Analysis of magnetoelectric laminated plates using a coupled zig-zag model
C.L. Zhang (Universität Siegen/Zhejiang University Hangzhou), W.Q. Chen (Zhejiang University
Hangzhou), Chuanzeng Zhang (Universität Siegen) Schedule
Two-dimensional equations (2D) for the analysis of magnetoelectric laminated (MEL) plates are
derived based on a coupled zig-zag model. A layer-wise linear zig-zag approximation is adopted
for the in-plane displacements and the transverse displacement is approximated by taking
account of the normal strain in the thickness direction of the MEL plates as a result of the piezo-

Section 4: Structural mechanics 97
electric/piezomagnetic coupling effects. The electrical and magnetic potentials in each layer are
assumed to be a piecewise quadratic function across the thickness. Numerical examples will be
presented and discussed to compare the present theory with the available 2D theories of MEL
plates and investigate the static behavior of simply supported MEL plates under different loads.
S4.4: Composites and Structured Materials Wed, 16:00–18:00
Chair: Jaroslaw Jedrysiak S2|02–C205
Numerical modelling of layered composite struts
C. Völlmecke, W.H. Müller (TU Berlin) Schedule
Composite components are on the forefront in most engineering applications these days. They
are increasingly employed in a broad range of applications from mechanical via structural engineering
components to marine and aerospace applications. In particular they are utilized when
lightweight principles are a dominant design criteria since they possess a high stiffness-to-weight
ratio. Thereby they effectively reduce a structures overall weight whilst allowing for loadings to be
transferred efficiently. However, owing to the manufacturing process of laminating several layers
of fibre-matrix plies interlaminar defects may occur. Once this so-called delamination is present,
the residual capacity of a component may be severely affected under compression.
In order to investigate the effects of an interlaminar defect on the buckling and postbuckling
behaviour of a strut, a numerical representation of a delaminated strut is developed based on a
previously developed analytical model. The underlying variational formulations are derived based
on continuum mechanics. The model is then discretized using an open source finite element
code and investigated carefully whilst varying system parameters. Subsequently the results are
validated against a previously developed analytical model. The numerical model allows a very
efficient investigation of the behaviour of the delaminated component. Moreover, the requirement
of imposing imperfections is superfluous which is usually necessary when the (post-) buckling
behaviour of structures is attempted to be simulated via finite elements.
Modal Response Design for Efficient Configuration Control of Bistable Structures
Andres F. Arrieta, Peter Hagedorn (TU Darmstadt) Schedule
Composite laminates are becoming increasingly important in a wide variety of applications, particularly
in aerospace engineering. Within this context, anisotropic composites allowing for a
high degree of directional stiffness tailoring are increasingly been developed as a solution for the
conflicting aerospace requirements of light-weight and high-strength structural materials. This
capability in the design of aerospace structures is particularly important to achieve conformal
change of shape, or morphing. This idea has attracted much attention from researchers within
the aerospace community given the offered potential performance gains and, in particular, the
possibility of augmented optimal operation over a wide range of different mission objectives and
environmental conditions. One example of structural materials offering the stated capabilities are
multi-stable composites. These composite laminates are structures capable of adopting multiple
statically stable configurations [1]. The multi-stability property has drawn considerable attention
from the adaptive structure community for its potential applications in morphing structures, as
no energy is required to hold each of the stable configurations [2]. The mechanism for changes
between stable states known as snap-through is strongly nonlinear in nature, resulting on rich
dynamic behaviour. Recently, the idea to exploit the dynamics of bistable composites, a class of
multi-stable composites, to allow for less energy intensive actuation, and hence lighter actuators,
has been proposed showing encouraging results [3].

98 Section 4: Structural mechanics
In this paper the structural tailoring of the dynamic response of multi-stable composites
to obtain desired modal properties to allow for easier actuation is proposed. The response is
design such that resonant oscillations are easily induced in order to trigger controlled snapthrough,
i.e. changes between stable states, of the multi-stable structures resulting in minimum
actuation effort. In this work the effects on the dynamic response of varying dimensions, stacking
sequence and discrete inclusions adding inertia or stiffness are studied for bistable composites. In
particular, the effect of introducing asymmetry in the structure to ensure the responses of each
stable configuration are slightly different avoiding complex dynamics involving constant snapthrough,
such as large amplitude limit cycles or chaotic oscillations, is studied. The effect of
the attached flexible piezoelectric actuators on the dynamics of the morphing structures is also
considered and used to achieve minimum morphing actuation.
[1] M. W. Hyer. Some observations on the cured shapes of thin unsymmetric laminates. Journal
of Composite Materials, 15:175194, 1981.
[2] C. G. Diaconu, P. M. Weaver, and F. Mattioni. Concepts for morphing airfoil sections using
bi-stable laminated composite structures. Thin-Walled Structures, 46:689701, 2008.
[3] A. F. Arrieta, D. J. Wagg, and S. A. Neild. Dynamic snap-through for morphing of bi-stable
composite plates. Journal of Intelligent Material Systems and Structures, 22:103112, 2011.
Microstructural Model of a Closed-Cell Foam on the Basis of Image Analysis
Nina-Carolin Fahlbusch, Wilfried Becker (TU Darmstadt) Schedule
Polymer foams combine an excellent weight-specific stiffness and strength with advantageous properties
such as a low density, thermal conductivity and cost-effective production. Therefore, they
are suited for many lightweight applications. The focus of this work is the identification of a unit
cell that is able to represent the microstructure of a closed-cell foam. For the investigation, a
finite element model consisting of a repeating unit cell with periodical boundary conditions is
implemented. As simplified cell geometry a tetrakaidecahedral foam microstructure is considered
and a strain-energy based homogenisation concept is utilized. On the basis of image analysis
imperfections are applied to the cell. These imperfections can be curved cell walls and edges,
geometric irregularities of corner nodes and material concentrations at the cell edges. Some input
data, for example Young’s modulus of the matrix material, are difficult to test experimentally.
Consequently, these parameters are identified by an optimization. The obtained model is used
as representative volume element (RVE) for further investigations of the postbuckling behaviour
of the foams. Different analyses are performed and the results are compared to literature and
experimental data.
Homogenization of thin structured sheet metals by using FEM
T. de Silva, A. Kühhorn, M. Golze (TU Cottbus) Schedule
Thin structured sheet metals promise high potential concerning lightweight design in industrial
applications regarding the classical mechanical engineering and vehicle construction as well as the
aeronautics.
Compared to flat, unstructured sheet metals the component stiffness and buckling behavior can
significantly be improved by structuring especially in out of plane direction.
To be able to calculate the elastic behavior of large structures from structured sheet metals a
mechanical surrogate model is developed which describes effectively average material parameters
based on processes of homogenization.

Section 4: Structural mechanics 99
For the surrogate properties symmetry and antisymmetry boundaries and periodic boundaries respectively
are contemplated on elementary cells whose structural mechanical behavior is decisive.
By using an energetic approach the stiffness’s of large plate and shell structures can be determined
by a cooperatively small amount of finite elements. By means of these material properties elastic
behavior can easily be calculated. With it an efficient numerical design is guaranteed.
This explained analysis can be applied to other periodically built up plate structures.
[1] J. Hohe. Elastizitätsverhalten von Sandwich-Zellkernen und zweidimensionalen Modellschäumen.
Shaker Verlag, Aachen, 2003.
Material libraries for texturized thin metal sheets in elastic range
Jonathan Montalvo-Urquizo (Universität Bremen) Schedule
Thin metal sheets are highly determined by the rolling process during production, causing the
material grains to have preferred orientations. The existence of such preferences is known as
texture and cannot be modeled as a deterministic process.
We present a simulation approach for the simulation of the elastic material responses based
in stochastic generation of material samples and a subdomain-based FEM simulation. Both the
single grain geometries and the lattice orientations are stochastically simulated.
Combining a series of material samples with FEM simulations it is possible to generate a
Material Library (ML) of responses. Being constructed only once for a given material, the ML
can be used in a fast two-scale simulation avoiding any detailed computation in the microscale.
Using Steel DC01 we show the simulated texture and its comparison with experimental data
and present some results in the microscale and main ideas towards the two-scale method.
S4.5: Material behavior I Thu, 13:30–15:30
Chair: Christian Hellmich S2|02–C120
Plastic deformation of rough surfaces
Kai Willner, Franz Hauer (Universität Erlangen-Nürnberg) Schedule
We present a fully elasto-plastic halfspace contact formulation based on the work of Jacq et al.
[1]. Linear elastic-plastic material behavior is modeled based on v.Mises plasticity with isotropic
hardening. The algorithm gives the residual stress as well as the full plastic deformation field due
to a frictionless normal contact.
The general algorithm is outlined and demonstrated using Hertzian type contact problems,
showing for example the influence of the discretization and hardening effects. The results are
compared to finite element solutions and a simplified elasto-plastic halfspace contact algorithm
[2], showing the limits of the simplified algorithm.
Use of FFT based convolutions of the influence functions allows the introduction of periodic
boundary conditions suitable for the simulation of representative surface elements of rough surfaces.
As an example, a typical contact pairing of a rough workpiece and a smooth die in a metal
forming situation is simulated, allowing the identification of a constitutive contact law which can
be used in a finite element simulation of the forming process.
[1] C. Jacq, D. Nelias, G. Lormand, and D. Girodin. Development of a Three-Dimensional Semi-
Analytical Elastic-Plastic Contact Code. Journal of Tribology (124) pp. 653–667, 2002.
[2] K. Willner. Elasto-Plastic Normal Contact of Three-Dimensional Fractal Surfaces Using
Halfspace Theory. Journal of Tribology (126) pp. 28–33, 2004.

100 Section 4: Structural mechanics
Sensitivity analysis of elastic beams on Winkler foundation with stiffness weakening
by Greens functions
Kai Schwartpaul, Chuanzeng Zhang (Universität Siegen), Oliver Carl (C + P Engineering) Schedule
This paper presents a sensitivity analysis of elastic beams on Winkler foundation with stiffness
weakening. A local method is developed that enables us to predict the changes in the solution of
the structure resulting from the stiffness weakening by considering only the weakened or damaged
parts. The advantage of this method is that it results in a local analysis instead of recalculating
the whole structure. Consequently, it is computationally less time-consuming than the commonly
used conventional method. The key idea of this method is based on the comparison between the
elastic strain energies of the original and the weakened structures.
As a suitable tool for the sensitivity analysis, the Green’s functions are applied [2]. If the
different elastic strain energies of the original and the weakened systems are considered, then the
solution for the changes of the internal forces, displacements or reaction forces can be obtained
by substituting the virtual displacements by the corresponding Green’s functions.
Furthermore, an approximate approach for the sensitivity analysis is presented which is described
in detail in [1,3]. This approach enables us to predict the changes in the results due to the
stiffness weakening within the beam or the elastic Winkler foundation by considering only the
internal forces or the deflections of the initial system.
In addition, an iterative method is developed to enhance the accuracy of the present approach.
Numerical examples will be presented and discussed to show the accuracy and efficiency of the
proposed method.
[1] O. Carl: Static and dynamic sensitivity analysis of damaged structures by Green’s functions
(in German). Dissertation, University of Siegen, 2011.
[2] F. Hartmann; C. Katz: Structural Analysis with Finite Elements. Springer-Verlag, 2nd Edition,
Berlin, 2007.
[3] K. Schwartpaul: Sensitivity analysis with Green’s functions of weakened beams on elastic
foundation (in German). Master Thesis, University of Siegen, 2011.
Elastic-plastic States of Two-layer Curved Bar Under Pure Bending
İsmail Y. Sülü, Eray Arslan (Inonu University, Turkey) Schedule
An elastic-partially plastic two-layer curved bar with a narrow rectangular cross section subjected
to couples at both ends is considered. In state of plane stress, small deformations and cylindrical
symmetry are assumed. Trescas yield criterion and its associated flow rule initiate an analytical
solution of the problem. A governing differential equation describing elastic and plastic behaviors
of the two layers is derived. Field equations for elastic regions in two layers are obtained by
integration of the governing equation and the solutions onset of yielding are investigated. The
results show that yielding may emerge at the inner surface, at the outer surface of the whole
bar or at the interface between two layers depending on selected materials and the geometry of
the layers. It is noted that in case of a homogeneous bar, however, plastic deformation always
commences on the inner surface at the elastic limit. Furthermore, a critical case, in which yielding
commences at the outer and the interface surfaces of the two-layer bar simultaneously, is observed.
In the critical case, solutions of the governing equation for plastic regions enclose different Trescas

Section 4: Structural mechanics 101
yield condition are obtained. Numerical results for real engineering materials in partially plastic
state, which consists of elastic and plastic regions, are presented in graphical form.
Analysis of the coupling effects of the longitudinal and transversal displacements on
the deformation and internal forces of functionally graded beams
Pedro D. Villamil, Chuanzeng Zhang (Universität Siegen) Schedule
In this contribution, functionally graded beams (FGBs) with an arbitrary gradation of the material
properties along the thickness of the beams are analyzed. Such FGBs are of special interest in
civil and mechanical engineering to improve both the thermal and the mechanical behaviour of
the beams.
In [1] free vibrations of functionally graded Timoshenko and Euler-Bernoulli beams have been
considered. The described analytical solutions are based on the work of Li [2], where closed-form
solutions of stress distributions, eigenfrequencies and eigenfunctions have been derived by means
of a single differential equation of motion for the deflection.
However, these previous considerations did not take into account the coupling between the
longitudinal and the transversal displacements and its effect on the deformation and internal
forces of the FGBs. This approximation is exact only for a symmetrical material gradation but it
may not be valid for general cases with an arbitrary material gradation.
In this contribution, the coupling effects of the longitudinal and transverse displacements on
the deformation and internal forces of FGBs are investigated for different boundary conditions.
An analytical solution of the corresponding boundary problem is derived. A comparison is also
made with the numerical results obtained by the Finite Element Method. The obtained solution
and its applications to FGBs with or without an elastic foundation are discussed.
[1] P. D. Villamil, Vibrations of Functionally Graded Bars and Beams (in German), Diploma
Thesis, Chair of Structural Mechanics, University of Siegen (2010).
[2] X.-F. Li, A unified approach for analyzing static and dynamic behaviors of functionally graded
Timoshenko and Euler-Bernoulli beams, Journal of Sound and Vibration 318 (2008), 1210
– 1229.
Asymptotic formulae for the flexibility of an infinite row of pin-loaded holes
Jan Kratochvil, Wilfried Becker (TU Darmstadt) Schedule
The problem of the flexibility of an infinite row of pin-loaded holes in an elastic plane or halfplane
is considered within the framework of the complex potential method [1] and the theory of
compound asymptotic expansions [2]. First, the relative radius of the holes is introduced as a small
parameter. The holes are loaded by an arbitrary distribution of radial and tangential stresses with
a resultant equal to the overall transmitted force. Then, an asymptotic expansion of the complex
potentials in terms of this small parameter is constructed. This expansion is uniformly valid in the
whole domain, i.e. in the vicinity of the holes as well as in the far-field. Finally, the flexibility of
the row of pin-loaded holes is evaluated using this solution. In this manner, closed-form analytical
approximations of the flexibility of several configurations of rows of pin-loaded holes are obtained.
It appears that the results to a sufficient order of approximation do not depend on the complete
information about the distribution of the contact pressure but only on several so called load
coefficients that can be easily fitted from the experiment. The presented results are compared
to the semi-empirical Huth’s formula [3] for the fastener flexibility which is widely used in the
engineering practice.

102 Section 4: Structural mechanics
[1] Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, P.
Nordhoof Ltd, 1963
[2] Maz’ya, V.; Nazarov, S.; Plamenevskij, B., Asymptotic Theory of Elliptic Boundary Value
Problems in Singularly Perturbed Domains, Birkhäuser, 2000
[3] Huth, H., Zum Einfluss der Nietnachgiebigkeit mehrreihiger Nietverbindungen auf die Lastübertragungs-
und Lebensdauervorhersage, Frauenhofer-Institut für Betriebsfestigkeit Darmstadt,
1984
S4.6: Dynamics of Structures Thu, 13:30–15:30
Chair: Jonathan Montalvo-Urquizo S2|02–C205
Analysis of the lamition stack influence on the stiffness of stator active component
Vera Luchscheider, Kai Willner (Universität Erlangen-Nürnberg) Schedule
For electric motors light weight construction becomes increasingly important. This is why the
nearly unknown stiffness and dynamical characteristic of the lamination stack has a bigger influence
on the strength and oscillation calculation. For this reason in a first step the stiffness
behavior is identified with quasi-static tests. Subsequently dynamical tests are to carry out.
In the quasi-static tests the electric sheets are just stacked and an axial load is applied. At first a
pressure of 1.5 or 3 N/mm 2 is exerted, representing the packaging process. Then a cyclic loading
is superposed to simulate the forces acting during the motors life. The analysis of the lamination
stack behavior at uniform loading has a progressive characteristic and a settling. The behavior at
cyclic loading is hysteretic. The settling and some of the progression can be explained with the
sheets waviness. Reason for this are the internal stresses, which are an effect of the sheets rolling
and which release at the blanking process. The lamination stack behavior is also influenced by the
coreplate varnish and the contacts of the sheets. Their mechanical characteristics are unknown
and have to be modeled in this project. It is done with springs, dampers and frictional elements,
which are coupeled parallel and in series. For this the models of Maxwell, Biot or Zener are
often used [1]. Usually the frictional elements are Coulomb elements. The influence of the dampers
is identified in dynamical tests, because they are dependent on the velocity. The stiffness of
the springs is mostly nonlinear and often exponetial dependent on the surfaces intersection. This
aspect is motivated by the increasing contact of the surfaces by loading and the roughness heights,
which are normally distributed and therefore follow an exponential function [2]. The hysteresis
area is direct proportional to the dissipated work. With the dissipated work the sort of damping
can be determined [1].
After characterizing the lamination stack behavior in axial direction, there will be a tangential loading
superposed and a model for the tangential direction developed. Therefor the just mentioned
elements and procedure are used too.
[1] G. Siegl, Das Biegeschwingungsverhalten von Rotoren, die mit Blechpaketen besetzt sind,
Dissertation, Technische Universität Berlin (1981)
[2] D. Görke, Experimentelle und numerische Untersuchung der Normal- und Tangenialkontaktverhaltens
rauer metallischer Oberflächen, Dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg
(2010)

Section 4: Structural mechanics 103
Shaking table tests of a model-scale building with 2DOF pendulum mass damper
Krzysztof Majcher (Wroclaw University of Technology) Schedule
In this paper, the numerical and experimental studies of a tall buildings model with 2DOF pendulum
mass damper (PMD) are considered. It is assumed that the model excitation is in the
form of horizontal and/or torsional motion of the ground caused by earthquake. The construction
consists of the main system (tall buildings model) and a double pendulum mass damper,
which is attuned to the first (bending) and the second (torsional) eigenfrequencies of the main
structure. The analysis focuses on reduction of structure vibration caused by horizontal or torsional
component of ground motions. Therefore, results presented in this work show efficiency of
2DOF PMD for vibration reduction. The numerical analysis of the problem is performed with
using COSMOS/M system (a FEM numerical model is defined), while experimental analysis is
carried out on a physical model-scale building with 2DOF PMD. Model consists of twenty five
recurrent storeys (total height 2,5m) and on the highest storey there is a PMD located. Shaking
table device is used to simulate an earthquake excitation in horizontal and torsional component
independently.
Application of the Proper Orthogonal Decomposition for structures under earthquake
excitations
Franz Bamer (TU Wien), Christian Bucher Schedule
Model reduction has become very important in order to save calculation time. Especially in Structural
Mechanics computations become very time consuming when the critical timestep of explicit
integrators gets very small. The main focus of this work is to use the Proper Orthogonal Decomposition
(POD) method for an earthquake loaded structure and to compare its results to
those according to the classical method of modal truncation. After testing the applicability of the
Proper Orthogonal Decomposition on linear systems, nonlinear friction base isolation systems are
integrated. The POD is a very powerful and elegant method if the snapshots within a certain
chosen time interval describe the main behavior of the system. Both in the linear and in the
nonlinear case the approximation of the POD reduced system is very accurate by using only a
few POD modes. The advantage over the method of Modal Truncation is the optimality of the
POD modes, which are not only dependent on the system but also on the excitation.
Analysis of macro- and micro-vibrations of transversally graded thin plates
Magda Kaźmierczak, Jarosław Jędrysiak (Technical University of Łódź) Schedule
Thin plates having tolerance-periodic microstructure in planes parallel to the plate midplane are
considered in this note. But their macrostructure is functionally graded. These plates consist of
many small elements. Distant elements can be very different, but adjacent elements can be nearly
identical. All elements are treated as thin plates and called cells. The size of the microstructure
is described by a diameter of the cell l, called microstructure parameter. Plates of this kind will
be treated as made of functionally graded materials, cf. [7], and called transversally graded thin
plates.
Vibrations of these functionally graded plates are described by differential equations which
coefficients are highly oscillating, tolerance-periodic and non-continuous functions. Thus, these
governing equations are not a proper tool to analyse specials engineering problems.
In order to obtain equations with continuous, slowly-varying coefficients there are proposed
various averaging techniques. Functionally graded structures are often described by averaging
approaches, which are applied for macroscopically homogeneous structures, e.g. periodic, cf. [7].

104 Section 4: Structural mechanics
Unfortunately, governing equations of these models neglect usually the effect of the microstructure.
However, to avoid this drawback and to describe the effect of the microstructure the tolerance
averaging technique can be applied. This modelling method was proposed and developed for
various periodic structures, cf. [9], [8]. Then it has been also adopted to analyse various thermomechanical
problems of functionally graded media with a microstructure, e.g. for heat conduction
in composites, cf. [2, 6], for thermoelasticity problems in laminates, cf. [1], for functionally graded
plates, cf. [3, 4, 5]. These different problems are shown in a series of papers. Extended lists of
publications can be found in monographs [9, 8].
The main aim of this paper is to show and apply an asymptotic-tolerance model of the plates
under consideration. The model equations are obtained using both the asymptotic and the
tolerance modelling procedures, cf. [8]. In the framework of this model macro- and micro-vibrations
of transversally graded plates can be analysed.
[1] JĘDRYSIAK J.: On the tolerance modelling of thermoelasticity problems for transversally
graded laminates, Arch. Civ. Mech. Engn., 11, 2011, 61-74.
[2] JĘDRYSIAK J., RADZIKOWSKA A.: Tolerance averaging of heat conduction in transversally
graded laminates, Meccanica, 2011, Doi:10.1007/s11012-010-9420-y.
[3] KAŹMIERCZAK M., JĘDRYSIAK J.: Free vibrations of transversally graded plate band,
Electr. J. Polish Agric. Univ., 13, 4, 2010.
[4] KAŹMIERCZAK M., JĘDRYSIAK J.: Tolerance modelling of vibrations of thin functionally
graded plates, Thin Walled Struct., 49, 2011, 1295-1303.
[5] KAŹMIERCZAK M., JĘDRYSIAK J., WIROWSKI A.: Free vibrations of thin plates with
transversally graded structure, Civ. Env. Eng. Rep., 5, 2010, 137-152.
[6] OSTROWSKI P., MICHALAK B.: Non-stationary heat transfer in a hollow cylinder with
functionally graded material properties, J. Theor. Appl. Mech., 49, 2011, 385-397.
[7] SURESH S., MORTENSEN A.: Fundamentals of functionally graded materials, Cambridge,
The University Press 1998.
[8] WOŹNIAK CZ., ET AL. [eds]: Mathematical modelling and analysis in continuum mechanics
of microstructured media, Gliwice, Wyd. Politechniki Śląskiej 2010.
[9] WOŹNIAK CZ., MICHALAK B., JĘDRYSIAK J. [eds]: Thermomechnics of microheterogeneous
solids and structures, Łódź, Wyd. Politechniki Łódzkiej 2008.
Effects of Damping Mechanisms in Forced Longitudinal Vibration of a Bar Connected
to a Viscoelastic Halfspace
Thanh Chung Pham, Jörg Wauer, Wolfgang Seemann (KIT) Schedule
This is one of our continuous researches about effects of damping mechanisms in free and forced
vibrations of some structural members, such as bars and beams [1]. The interactive transmission
of a signal from a cylindrical bar to an attached halfspace is presented in this study. The damping
and stiffness properties of the resonating environment are simultaneously taken into account. Finally,
it brings forward the substitution of an equivalent viscoelastic spring or impedance for the
foundation, as well as the identification of the clamping parameters. It is required to consider

Section 4: Structural mechanics 105
wave propagation effects by applying the theory of continuum mechanics, and numerical method
with integral transforms and approximation. The results of our previous study of the vibration of
a substitution system [1] as well some related studies, such as Saito and coworkers’ researches [2,
3], are utilized and related to ones in this paper.
Keywords: structural member, bar, beam, damping, stiffness, mechanisms, boundary condition,
identification, clamping parameter, halfspace, dynamic interaction, interactive transmission,
viscoelastic, longitudinal, axial, vibration, oscillation, substitution system, foundation, wave propagation,
integral transform.
[1] T. C. Pham, J. Wauer, W. Seemann, Effects of Damping Mechanisms in Free and Forced
Vibrations of Some Structural Members, Proc. Appl. Math. Mech., WILEY-VCH Verlag,
2011, 11, 259-260.
[2] H. Saito and S. Chonan, Forced longitudinal vibration of an elastic circular rod on an elastic
half-space, The Journal of the Acoustical Society of America 59(4), 861-865 (1976).
[3] H. Saito and H. Wada, Forced vibrations of a mass connected to an elastic half-space by an
elastic rod or a spring, Journal of Sound and Vibration 50(4), 519-532 (1977).
Simplified assessment of high-speed train induced bridge vibrations considering shear
effects
Patrick Salcher, Christoph Adam (Universität Innsbruck) Schedule
An improved response spectrum methodology for fast and yet accurate assessment of the dynamic
peak response of simple railway bridges is presented. The derived response spectra are based on
the Timoshenko beam theory in an effort to include the effect of shear deformation, which is of
importance, if the considered bridge is a truss structure. In contrast to the Bernoulli-Euler theory,
the ratio of two sequent natural frequencies depends on the bridge parameters when Timoshenko
theory is used. Thus, for the considered study the modal peak responses of the bridge such as
acceleration, displacement, and bending moment are derived separately. Then, the peak response
is found by statistical combination of the individual modal responses applying different rules. In
the underlying numerical analyses a sequence of moving single forces of constant speed simulate
the effect of passing trains. These loads are adjusted to real European high-speed trains and to the
train load models of Eurocode I. The presented response spectra are based on non-dimensional
characteristic bridge and train parameters. The proposed methodology is assessed and meaningful
examples are discussed.
S4.7: Material behavior II Thu, 16:00–18:00
Chair: Kai Willner S2|02–C120
Elastic limit analysis of a thick-walled cylindrical panel subject to radial heating
Eray Arslan (Inonu University, Turkey), Werner Mack (TU Wien) Schedule
In analogy to the theory of wide curved beams, first the basic equations for a thick-walled cylindrical
panel with rectangular cross-section under plane strain condition are given. The sides of
the panel parallel to the cylinder axis are presupposed to be guided in such a way that a displacement
in circumferential direction may occur and the curvature of the middle surface remains
constant. Then, both for homogeneous heating and for the occurrence of a temperature gradient

106 Section 4: Structural mechanics
independent of the circumferential coordinate, as it will occur e.g. by heating of the outer surface,
couples act on those sides. These couples give rise to a stress state corresponding to pure bending
conditions, and yielding may occur. Hence, in the present contribution, the limits for elastic behavior
in dependence on the heating conditions and on the thickness of the panel are investigated.
Moreover, thermal softening and therefore a reduced yield stress are taken into account, and both
von Mises and Trescas yield criterion are considered. For the latter, an example for the partially
plastic state after the onset of plastic flow is given, too.
A Finite Element formulation for static droplets in contact with rough surfaces
Muhammad Osman, Roger A. Sauer (RWTH Aachen) Schedule
The shapes of two dimentional static droplets in contact with rough surfaces are computed using
the Young-Laplace equation. The problem is modeled within a continuum mechanical framework,
and solved using the Finite Element method. Three constraints are introduced in a polar coordinates
based model. A constraint for the droplet volume is enforced using the Lagrange multiplier
method. Surface contact constraint is enforced by the penalty and the Augumented Lagrange
multiplier method. At the three phase contact line, the contact angle is prescribed as a penalty
constraint, allowing for capturing local contact at the individual asperities of the rough surface.
A two level structured rough surface is constructed by superposition of exponential functions.
The entire formulation is also expressed in cartesian basis for consistency and robustness. The
numerical model is verified against analytical solutions of special cases, and convergence has been
studied.
Micro - mechanical analysis of creep behavior in a multipass weld
Ivan Lvov (Universität Magdeburg) Schedule
A method of evaluating creep response of the multipass weld based on the micro-macro mechanics
approach is introduced. Multipass weld microstructure that consists from columnar, coarse and
fine grained zones is considered. Materials of these constituents assumed to be isotropic. Weld
metal properties of inelastic behavior have unknown type of symmetry and are described by the
following anisotropic creep constitutive model [1]:
〈 ˙ε〉 = 〈σ n 2〉[B]〈σ〉
To model the microstructure of the multipass weld metal the representative volume element
(RVE) is created for CAE Abaqus. Material properties of weld metal grain type zones are taken
from [2]. Numerical tests on uniform loading of the RVE are performed. Creep material properties
for equivalent weld material are found for welds with different number of passes. The symmetry
type of the creep material properties of multi-pass weld are evaluated for the equivalent weld
material. As an example of macro model analysis of the welding, the creep calculation of the
cylindrical shell with the welding under the uniform inner pressure is performed.
[1] Zolochevsky AA. About the influence of loading on the theory of creep in isotropic and anisotropic
materials / / J. Appl. mechanics and technical physics. - 1982, 4. - S. 140-144.
[2] Hyde T.H., Sun W. Creep failure behavior of a 9CrMoNbV weld metal with anisotropy under
a biaxial loading state“J. Strain Analysis Vol. 41 No. 5, 2006

Section 4: Structural mechanics 107
Influence of shotcrete composition on load-level estimation in NATM-tunnel shells:
Micromechanics-based sensitivity analyses
Christian Hellmich, Shafi Ullah, Bernhard Pichler, Stefan Scheiner (TU Wien) Schedule
Displacement measurement-based estimations of loads and utilization degrees in shotcrete tunnel
shells as part of the New Austrian Tunneling Method (NATM), have become standard tools
in tunnel practice; their quality, however, may crucially depend on the knowledge of the actual
shotcrete composition after spraying. To shed light on this issue, we here determine, based
on experimentally validated micromechanical representations of shotcrete, the hydration degreedependent
elastic, creep, and strength properties of different shotcretes, characterized by water
cement ratios (w/c) between 0.4 and 0.6, aggregate cement ratios (a/c) between 3.5 and 5, and
Youngs modulus of aggregates (Eagg) between 40 and 80 GPa. These properties are fed into a
structural shell model of the Sieberg tunnel, and this model is subjected to displacement fields
approximated from daily displacement measurements at five selected points along the shells inner
surface. Resulting stresses and forces in the tunnel shell allow for analyzing the influence of
shotcrete composition on load-level estimation in NATM tunnel shells: The magnitudes of circumferential
and longitudinal normal forces increase significantly with decreasing w/c, while a/c and
Eagg have the inverse and relatively minor effect. The utilization degree is virtually insensitive
to changes in w/c (especially at early ages), and only slightly decreases with decreasing a/c and
Eagg. The location of maximum loading is unaffected by the shotcrete composition underlying the
analysis. Conclusively, location and magnitude of maximum utilization degrees are very robust
estimates (not affected by limited knowledge on the shotcrete composition), whereas realistic estimation
of stresses and forces does require more accurate consideration of shotcrete composition.
S4.8: Stability and Eigenvalue Problems Thu, 16:00–18:00
Chair: Martin Schagerl S2|02–C205
Elastic stability of predeformed beams
Dominik Kern, Wolfgang Seemann (KIT) Schedule
As is well known, the load capacity of mechanical components is not only limited by the maximum
stresses but also by buckling failures. Beside the Euler cases, the lateral-torsional buckling is a
common failure mode, particularly for beams with a high ratio of the area moments of inertia. In
many applications, such as trusses, the predeformation may be neglected for the buckling analysis.
However, flexure hinges characteristically undergo large deformations in operation, thus the
predeformations must be taken into account. Mathematically, the predeformations are imperfections
changing the bifurcation paths. As consequence, the bifurcation point itself may not be a
precise indicator for the failure, since large failure displacements may occur at lower loads. Thus
alternative failure criteria are needed. As example the lateral-torsional buckling of a flexure hinge
(leaf spring type) is examined by energy methods. The crucial point is that the elastic energy
stored in the beam is formulated intrinsically, while the potential of external conservative loads
is formulated in a space-fixed coordinate system. Expressions derived from differential geometry
are compared with well-established approximations.
About the effect of elastic-plastic properties of the material on the stability of columns
under deterministic and stochastic parametric excitations
Vadim D. Potapov (Moscow State University of Means Communication) Schedule
In the message it is shown that at defined combinations of input data a linear elastic column
laying on a nonlinear elastic foundation under the action of the periodic deterministic parametric

force can perform a chaotic motion. If the material of the column is nonlinear, then the character
of its motion at the same input data is not changed principally. And if the material is elasticplastic
then the motion of the column remains unstable, but it strives to stationary process. It
is shown that an unstable motion of the elastic column at the deterministic treatment of the
problem can be done stable by the addition of a force in the form of a random stationary process.
(The stability for the deterministic problem is understood as the stability in Liapunov sense and
in the stochastic case as the almost sure stability, stability in the mean and stability in the mean
square.) In a case of a nonlinear elastic or elastic-plastic column at the same input data the similar
effect is not observed. If the column made from a nonlinear or elastic-plastic material is unstable
at deterministic treatment then it is unstable too at stochastic treatment of the problem.
Geometrically exact solutions of buckling columns with asymmetric boundary conditions
Gerhard Prechtl, Martin Schagerl, Kai-Uwe Schröder (Universität Linz) Schedule
For the symmetrically supported Euler buckling column with both ends hinged the classical stability
theory yields simple trigonometric functions as buckling modes, i.e. w(x) = A sin αx. The
eigenvalues α are just multiples of π. In comparison, the analysis of the asymmetrically supported
Euler buckling column with one end fixed and the other end hinged is more complicated: The buckling
modes are a combination of trigonometric functions in form of w(x) = A (sin αx − αx cos α).
The eigenvalues α follow from a transcendental equation.
Applying a geometrically exact theory to the aforementioned Euler buckling problems, a similar
relation in the complexity of the analyses will naturally arise. Using, e.g., the elastica model
the buckling modes of the symmetrically supported column are represented by elliptic integrals.
However, the determination of the buckling modes of the asymmetrically supported column turns
out to be much more complex and elaborate. This short communication presents a thorough
comparison of the symmetrically and asymmetrically supported buckling columns regarding their
analyses by means of classical stability theory and by a geometrically exact theory.
Comparative Study of Experimental and Simulated Buckled Shapes of Alternately
Loaded Plates
Russell Todres, Marcus Stoffel, Dieter Weichert (RWTH Aachen) Schedule
Experimental studies in a shock wave tube have shown that an initially plane, circular plate subjected
to uniform pressure and then alternately loaded to the same peak level deforms inelastically
and snaps-through at an ever increasing load until either a stable limit state is reached or the plate
fails. For the limit state, the final deformed profile is asymmetric. To determine whether such a
shape is optimal in terms of its resistance to instability, a symmetric spherical cap with height
corresponding to the limit state’s maximum out-of-plane displacement and base radius equal to
the radius of the flat plate is loaded once with the same uniform pressure as before. Simulations
and experiments are used to compare the snap-through pressure as well as the development of
plastic strains for this case with those for the limit state above.
Temperature and displacement fields in brake and clutch systems with thermoelastic
instabilities
Matthias Graf, Georg-Peter Ostermeyer (TU Braunschweig) Schedule
In brake and clutch systems kinetic energy is converted into thermal energy. Experiments show
that the corresponding temperature field can develop unstable periodic structures, which can be
parallel or normal to the sliding direction. The temperature field couples to the displacement

Section 4: Structural mechanics 109
field by thermal expansion. Local pressure maxima in the frictional plane and the corresponding
maxima in heat generated cause thermoelastic instabilities (TEI). They appear as so-called hot
bands or hot spots on the sliding bodies.
A model describing both effects covers layers of thermoelastic materials for all necessary
mechanical components of the system. The set of field equations of each layer can analytically
be solved by separation of constants. These solutions must fulfill the boundary conditions e.g. in
the sliding plane or between different layers in a layered material. A stability discussion yields
whether TEI appear or not.
To cover different TEI phenomena, an angle parameter allows the rotation of the two-dimensional
solution with respect to sliding plane. The observed temperature and displacement fields highly
depend on the structure of the sliding system. For example, existing models typically find hot
spots appearing in an antisymmetric pattern on both sliding faces on a brake disk. The model
under discussion shows that a symmetric solution is possible as well, when cooling channels in
the disk are taken into account.
On eigenvalue sensitivities of restricted eigenvalue problems
Nils Wagner (Intes GmbH) Schedule
Nowadays large finite element models consist of incompatible meshes for different parts of the
structure. Coupling is achieved by interpolation surfaces. The associated eigenvalue problem in
structural dynamics is given by
Kx = λMx, C T x = 0. (1)
We are interested in eigenvalue sensitivities
∂λ
∂C
with respect to these couplings. Some numerical examples are given.
(2)

110 Section 5: Nonlinear oscillations
Section 5: Nonlinear oscillations
Organizers: Dietrich Flockerzi (MPI Magdeburg), Edwin Kreuzer (TU Hamburg-Harburg)
S5.1: Nonlinear Oscillations I Tue, 13:30–15:30
Chair: Edwin Kreuzer, Dietrich Flockerzi S1|02–344
Self-excitation in decanter centrifuges - a simple mechanism
Eberhard Brommundt (TU Braunschweig) Schedule
Decanter centrifuges, used to separate liquid-solids slurry, can undergo self-excited rotational vibrations
(called ’chatter’ when severe). A model is developed to explain the excitation as result of
the dynamic interactions between the rotating bowl, the sedimented solids cake sliding inside it,
pushed by the slightly faster rotating conveyor screw. Including the drive, the multi-body system
has six degrees of freedom; Coulomb friction forces act between cake/bowl and cake/screw. The
effect of the turbulent slurry flow is accounted for by damping.
The stability of the stationary operation is studied by numerical solution of the variational
equation to the nonlinear equation of motion.
Self-excited vibrations and quenching by periodic forcing of nonlinear systems
Daniel Hochlenert, Utz von Wagner (TU Berlin) Schedule
In the linear case, the stability of the trivial solution of a dynamical system is independent of
a possibly acting external forcing. Therefore, it is impossible to influence self-excited vibrations,
indicated by an unstable trivial solution, by an appropriate forcing of the linear system. However,
in the nonlinear case and in the neighbourhood of a bifurcation point it is very well possible to
stabilize an unstable trivial solution by an external periodic forcing. This is often referred to as
quenching of self-excited vibrations.
The present talk deals with nonlinear self-excited systems under periodic forcing. Following
the concepts of normal form theory, the feasibility of quenching the self-excitation is investigated
with respect to the nonlinearities coupling the forcing with the states of system. It is analyzed
which nonlinearities are essential to allow for quenching self-excitation. The results are compared
with a direct numerical analysis of the nonlinear system.
An experimental method for the phase controlled frequency response measurement
of nonlinear vibration systems
Jörg Wallaschek, Sebastian Mojrzisch, Jan Bremer (Universität Hannover) Schedule
The experimental determination of the frequency response of nonlinear systems is difficult when
there exists more than one solution branch. Depending on the system at hand, various types of
”jump phenomena” can be observed and in the example of the well-known Duffing system, it is
not possible to experimentally determine the unstable solution branch if the system is excited by
a harmonic force.
In the present paper we investigate the Duffing system and we present a method which allows
to re-formulate the equation of motion of the system with force excitation in the form of an
equivalent self-excited system. Considering the phase between force and response as the input
variable, it is then possible to calculate the frequency of the system vibration for any given phase
shift. And in the same way the corresponding response amplitude can be determined.
An experimental set-up has been designed and built which was used to test the performance
of the method. Measurements of the backbone curve have been performed and will be discussed
on the background of the theoretical predictions.

Section 5: Nonlinear oscillations 111
Analysis of Chaotic Dynamics of Parametric Vibrations of Flexible Cylindrical Panels
and Plates by Using the Wavelet - Analysis
A.V. Krysko (Saratov State Technical University), U. Nackenhorst (Universität Hannover), I.V.
Papkova, V.A. Krysko (Saratov State Technical University) Schedule
In this contribution the mathematical model for the complex nonlinear vibrations of flexible cylindrical
panels and plates will be presented. Such kind of flexible panels and plates are the elements
of aircraft and ships constructions. The obtained strongly non-linear partial differential equations
are discretized in space by finite difference methods of different order, i.e. O(h 2 ), O(h 4 ), O(h 6 ).
The resulting system of ordinary differential equations in time is solved by a Runge-Kutta scheme
of fourth order.
The obtained solution is analyzed by methods of nonlinear dynamics. In order to study the
parametric vibrations of cylindrical plates and panels wavelet analysis has been applied. For these
studies on the chaotic dynamics of the parametric vibrations different types of wavelets have been
investigated, i.e. different types of Gaussian, the MHat (’Mexican hat’) wavelet and the Morlet
wavelet.
These studies guided us to investigate the optimal wavelet formulation for this kind of chaotic
parametric vibrations. In addition, with based on the wavelet analysis new phenomena of parametric
random vibrations of flexible cylindrical panels and plates have been identified. In particular,
a memory like phenomenon has been observed, when the system changes from one type vibrations
to another.
Determination of a stochastic friction coefficient depending on a randomly rough
surface
Nicole Gaus, Carsten Proppe (KIT) Schedule
Friction induced vibrations are a widely studied field. In these investigations the friction coefficient
is one of the most important parameters. Measurements show that the friction coefficient is
velocity dependent and underlies stochastic fluctuations.
The friction coefficient can be calculated using different analytical approaches which describe
friction causes such as adhesion and elastic deformation. The stochastic fluctuations of a friction
coefficient depend strongly on the roughness of the contacting surface. If the surface data is described
as a random field, the real contact area and the contact normal force can be calculated with
the Hertz contact formulation for contacting elastic bodies. The friction force can be calculated
with the Bowden-Tabor approach which suggests that the friction force is the force to shear apart
contacting asperities. The Bowden Tabor approach is a good model for adhesion which is often
the dominant part of friction in dry contact.
With these methods the stochastic properties of the friction coefficient can be calculated
depending on the stochastic surface data.
A Semi-Analytical Method of Solving the Fokker-Planck-Equation for High-Dimensional
Nonlinear Mechanical Systems
Wolfram Martens (TU Berlin) Schedule
Stochastic processes are a common way of describing systems that are subjected to random
influences. Technical systems may be excited by road roughness or wind gusts, for example,
as well as fluctuating system parameters, which can all be described by stochastic differential
equations.
In previous works by the author and others (see [1], for example) it has been demonstrated
how a Galerkin-method can be used to obtain global numerical solutions of the Fokker-Planck-
Equation (FPE) for nonlinear random dynamical systems. Computational efforts are reduced by

112 Section 5: Nonlinear oscillations
orthogonal polynomial expansion of approximate solutions so that probability density functions
(pdfs) for comparably high-dimensional problems have been computed successfully. Stationary
mechanical systems with dimensions up to d = 10 have been investigated, including polynomial
as well as non-smooth nonlinearities.
In general, increasing problem dimensions lead to immense numerical efforts in solving the
FPE, an issue commonly referred to as the ’curse of dimensionality’. In order for the presented
method to be feasible for general high-dimensional problems a covariance-based coordinate
transformation is applied. Special focus has been put on Gaussian approximate solutions as they
provide a number of analytical relations that can be exploited for efficient computation. However,
in the case of pdfs that are far from Gaussian it is also appropriate to use more sophisticated
approximate solutions.
This talk presents results for different nonlinear problems with polynomial nonlinearities as
well as a technical application with non-smooth damping elements. All results are compared with
numerical solutions from Monte Carlo simulations.
[1] W. Martens, U. von Wagner, V. Mehrmann, Calculation of high-dimensional probability density
functions of stochastically excited nonlinear mechanical systems, Nonlinear Dynamics
(13 July 2011), pp. 1-11. doi:10.1007/ s11071-011-0131-2
S5.2: Nonlinear Oscillations II Wed, 13:30–15:30
Chair: Dietrich Flockerzi, Edwin Kreuzer S1|03–104
Optimizing force time history for interaction between athlete and sports surface
Claudia Körner, Wolfgang Seemann (KIT) Schedule
The aim in high-performance sports activities is reaching the optimum between high efficiency
and low risk of injuries during workout. The goal of this contribution is to increase the understanding
of these two facts for an interaction between athletes and sports surfaces.
For several movements like landing, take-off or running the typical vertical ground reaction force
(VGRF) time history on a rigid ground is well known. In this paper, investigations for the
interaction of an athlete with a compliant ground (elastic, linear/nonlinear viscous-elastic) are
made. Therefore, the influence of the surface parameters on the force time history are analyzed
and finally optimized for typical movements. The optimization algorithm uses a cost function
which assumes that the work performed by a human body has to be minimal. In a second step,
the optimization criterions are specific key characteristics of the force time history such as peak
forces, time of peak forces, the first minimum and the time for the first minimum.
Hysteresis Effects in abrasive and frictional Contacts
Kristin M. de Payrebrune, Matthias Kröger (TU Freiberg) Schedule
Grinding is a very complex and high dynamical material removal process with stochastically distributed
grain engagements and strong varying local contact conditions. Over a long time only
macroscopic effects are analyzed and predicted by empirical relation. To understand the dynamical
behaviour also local effects must be considered.
Therefore the local contact conditions and especially the local friction coefficient are analyzed.
One detected effect is the dependency of the friction coefficient on the process forces and on
the gradient of the forces, so a hysteresis loop occurs for increasing and decreasing values. This
phenomenon is already studied for sliding objects in [1,2,3] but not for abrasion. With higher

Section 5: Nonlinear oscillations 113
force values the dependency on the force gradient decrease, whereas for low normal forces the
loop expand. With the force dependant friction coefficient local and dynamic effects are physically
interpretable. In contrast to this is the global friction coefficient over the entire force range
constant with which only quasi-static effects are describable.
[1] Kröger, M.; Lindner, M. Popp, K.; Modellierung instationärer Reibkräfte, PAMM, 2, 140-141,
2003
[2] Stelter, P. Nichtlineare Schwingungen reibungserregter Strukturen, Fortschritts Bericht VDI-
Reihe, 11, 1990
[3] Ruina, A.L.; Constitutive Relations for Frictional, in Mechanics of Geomaterials, ed. Bazart,
Z., Wiley, New York, 167-187, 1985
Influence of viscous damping on friction induced travelling waves
Alois Steindl (TU Wien) Schedule
We consider a simple model of a brake, a rigid shaft rotating in an elastic cylinder. Due to the
frictional contact between these bodies stick-slip travelling waves occur; also separation zones are
possible, if the pressure between the bodies is small. Numerical investigations show, that these
travelling waves are mostly unstable, which causes quasiperiodic and chaotic dynamics.
In this talk we investigate the influence of viscous damping on the existence, shape and
stability of the travelling wave solutions more closely. Preliminary calculations indicate, that
the smoothening effect may stabilize the travelling waves against the Hopf bifurcation, but it also
can destroy the travelling waves and force steady state solutions.
The presence of the damping terms also changes the structure of the differential equations for
the travelling waves by introducing a small leading coefficient. This singular perturbation also
has smoothening effects at the transitions between the different solution regimes.
Degenerate cases of stability loss of an elastic fluid-conveying tube
Richard Jurisits, Alois Steindl (TU Wien) Schedule
Motivated by the article [1], we consider a two-dimensional, slender elastic tube of length l being
clamped to the upper end and with a point mass m being fixed to its lower end. The centerline
of the tube is assumed to be inextensible, and the tube carries a fluid having a constant relative
velocity U relative to the tube tangent to the centerline. Two springs with constants c are fixed
to the tube at the position s = lξ (with 0 < ξ < 1) and exert forces only in horizontal direction.
A coefficient α describes the internal material damping of the tube, and the effect of gravity is
included.
We adopt the model equations for the tube system from previous works, see [2], [3]. The linearized
dimension-free governing equations, written in the standard form of a dynamical system read
w = (w1, w2) = (u, ˙u), λ = (ρ, Γ, α, ξ) , (1)
˙w = A(λ)w + g(w, λ) ,
�
0
A(λ) =
−C
�
1
,
−B
(2)
Cw1 = w ′′′′
1 + ρ 2 w ′′
1 − γ[(1 + Γ − s)w ′ 1] ′ , Bw2 = αw ′′′′
2 + 2 � βρw ′ 2 , (3)
and have to be supplemented by appropriate boundary and intermediate conditions. u and
˙u represent the horizontal dislocation and velocity, respectively, of a tube element. The nondimensionalized
parameters for U, m, α and ξ, forming the parameter vector λ, are considered

114 Section 5: Nonlinear oscillations
as distinguished parameters.
Performing a linear stability analysis of the straight downhanging equilibrium position of the
tube (u = 0, ˙u = 0) leads to a three-point boundary-value inverse eigenvalue problem of two
fourth-order ordinary differential equations, which can be solved numerically. The resulting stability
diagrams show that steady-state-Hopf and Hopf-Hopf (two flutter) bifurcation interactions
exist for certain parameter regimes. In this talk we focus on the possibility and the necessary
conditions leading to degenerate cases in which both interactions merge, resulting in a coupled
steady-state-Hopf-Hopf bifurcation.
[1] M. Ghayesh, M. Paidoussis, and Y. Modarres-Sadeghi, Three-dimensional dynamics of a
fluid-conveying cantilevered pipe fitted with an additional spring-Support and an end-mass,
JSV 330, p. 2869–2899 (2011).
[2] B. Albrecht, Dynamische Verzweigungen eines rotationssymmetrischen, flüssigkeitsdurchströmten
Schlauches mit einer punktförmigen Masse, diploma thesis, TU Wien (1997).
[3] M. Païdoussis, Fluid-structure interactions, Vols. 1 and 2, Academic Press (1998).
Trigger of coupled singularities: Nonlinear dynamics of mechanical systems with coupled
rotations about no intersecting axes or/and no ideal constraints
Katica (Stevanović) Hedrih (Serbian Academy of Sciences, Belgrade/University of Nis) Schedule
Starting of the numerous examples of mechanical system nonlinear dynamics with coupled rotations,
series of governing nonlinear differential equations are derived. We focused our attentions
to the system nonlinear dynamics with ideal as well as no ideal constraints with phase portrait
containing coupled singularities and homoclinic orbit in the form of number eight. By using special
example of heavy mass particle motion along ideal or no ideal rotating curvilinear rough line
about vertical or skew axis series of the coupled singularities are identified. A theorem of trigger
of coupled singularities and homoclinic orbit in the form of like number eight are presented.
Transformations of the phase portrait structure with appearance and disappearance of trigger of
coupled singularities with change of bifurcation parameters are presented. A example od phase
portrait of nonlinear dynamics of a heavy body coupled rotations about no intersecting axes is
analyzed. Abstractions of real engineering system nonlinear dynamics with coupled rotations into
models of a rigid body coupled rotations around nonintersecting axes in the gravitational field
show us numerous varieties of the homoclinic phase trajectories as well as different sets of the
tiger of coupled singularities. Also a series of the trigger of coupled singularities in the phase
portraits and with trigger of coupled half-one side singularities are identified in the heavy mass
particle oscillations/motion along rotating rough curvilinear line and no ideal constraints with
Amontons-Coulomb type friction. Governing differential double equation of a heavy are analyzed
and corresponding double equation of the phase trajectories are given. Linearizations of nonlinear
or double differential equations around singular points from trigger of coupled singularities are
used for analyzing stability or no stability of equilibrium positions or relative equilibrium positions
of the system.
Influence of gyroscopic effects on the nonlinear vibrations of high-speed rotors in
hydrodynamic bearings
Aydin Boyaci (KIT) Schedule
To improve the efficiency of turbomachines, the corresponding rotors are operated with very high
speeds. Thereby, high-speed rotors are often supported in hydrodynamic bearings which show se-

Section 5: Nonlinear oscillations 115
veral oil whirl/oil whip phenomena. Though the nonlinear vibrations of such rotors are very well
investigated, the influence of gyroscopic effects on the stability and bifurcation behavior of rotors
in hydrodynamic bearings is not fully understood. Therefore, a single-disk rotor in two identical
journal bearings is considered as a mechanical model. By applying a linear stability analysis, the
threshold speeds of the equilibrium position are determined. After the nonlinear rotor bearing
system loses its stability of the equilibrium position, the stability and bifurcations are analyzed
by using numerical continuation methods. In conclusion, the effect of the inertia moments and
the position of the disk is discussed on the nonlinear dynamics of the single-disk rotor in hydrodynamic
bearings.
S5.3: Nonlinear Oscillations III Wed, 16:00–18:00
Chair: Edwin Kreuzer, Dietrich Flockerzi S1|03–104
Liapunov Functions and Carleman Linearization
Heffel, E., Hagedorn, P. (TU Darmstadt) Schedule
In order to accurately predict the behavior of a nonlinear system, it is important to determine
the domains of attraction of its stationary solutions. This is in general a difficult problem which
can not be solved analytically. A common approach to estimate the domains of attraction of stationary
solutions of autonomous or non-autonomous systems is via Liapunov functions. Defining
an adequate Liapunov function is in general not easy, due to the lack of a systematic approach
for its construction, at least in the non-autonomous case. If the nonlinearities in the system dynamics
are sufficiently smooth, Carleman linearization can be used, not only to study the system
dynamics but also to define appropriate Liapunov functions. The basic idea is to expand the
non-autonomous nonlinear system into a higher dimensional autonomous and linear one, with a
higher order error term, by treating nonlinearities as additional state variables. Neglecting the
error term in a first instance, permits the systematic construction of Liapunov functions for the
new, linear system. These Liapunov functions can then be used to estimate the domains of attraction,
with the error term now being considered. This approach is demonstrated with simple
examples. At least in these examples the method works surprisingly well. Of course the method
can be used not only to study domains of attraction but also to examine stability regions in the
parameter domain.
Intermittent Control of Co-existing Attractors
Yang Liu, Marian Wiercigroch, James Ing (University of Aberdeen) Schedule
In the recent times, control of nonlinear dynamical systems has been among the most active fields
of research due to its diverse applications in engineering. Most of the existing work has been
focused on controlling chaos including stabilizing unstable periodic orbit, exploiting chaos‘ characteristics
for its control, and synchronizing two identical or different chaotic systems. However,
little attention has been paid to control of systems that exhibit multistability or co-existence of
several stable attractors for a given set of parameters, despite the fact that they are observed
abundantly in different fields of science, e.g. [1].
This paper proposes a new control method for a class of non-autonomous dynamical systems
that naturally exhibit co-existing stable attractors. As it is known, in some papers on controlling
co-existing attractors, e.g. [2], the control objective was achieved by the crisis of basins of attraction.
However, destroying co-existing attractors is extremely difficult for some complex dynamical
systems, e.g. [3], since any small perturbations of the system parameters can induce the emergence
of new complicated basins of attraction. It is therefore we propose a method of intermittent

116 Section 5: Nonlinear oscillations
control here without changing the original basins of attraction of the system. The central idea
is based on understanding of the system‘s basins of attraction where the control action is being
switched on only in the vicinity of the crossings of the actual and the desired trajectories. This
paper also focuses on appropriate selection of the control force, which is triggered when a certain
criterion is satisfied.
The method we proposed is applied to a well-known Duffing oscillator and an impact oscillator.
Both numerical and experimental results reveal that the proposed method is effective, and
therefore it can be applied to a broad range of continuous and discontinuous systems. For practical
purposes, the constrained intermittent control is considered, and is applied to the two example
systems in simulation and experiment. Further discussion is made for the forcing amplitude of
intermittent control and the duration of control action.
[1] J. Ing, E. Pavlovskaia, M. Wiercigroch, S. Banerjee, Experimental Study of Impact Oscillator
with One-sided Elastic Constraint, Phil. Trans. R. Soc. A 366 (2008), 679 – 704.
[2] O. Olusola, U. Vincent, A. Njah, Synchronization, Multistability and Basin Crisis in Coupled
Pendula, J. Sound and Vibration 329 (2010), 443 – 456.
[3] E. Pavlovskaia, J. Ing, M. Wiercigroch, S. Banerjee, Complex Dynamics of Bilinear Oscillator
Close to Grazing, Int. J. Bifurcation and Chaos 20 (2010), 3801 – 3817.
Algorithms for the solution of parameter dependent quadratic eigenvalue problems
Urs Miller (Universität Stuttgart), Lothar Gaul Schedule
The solution of mechanical problems often leads to quadratic eigenvalue problems (λ 2 M(p) +
λP(p) + Q(p))x = 0 with complex eigenvectors, especially if damping or gyroscopic effects are to
be considered. The system matrices are considered as dependent on a parameter p in this work.
Usually, the quadratic eigenvalue problem is solved by transformation to a standard eigenvalue
problem, where the dimension of the matrices doubles. Because this leads to an increase of memory
consumption, alternative algorithms for the direct solution of quadratic eigenvalue problems are
presented and compared.
For the parameter dependent problem, it is convenient to use a predictor corrector method.
This is compared to the solution with quadratic versions of the Rayleigh quotient iteration and
the Jacobi Davidson algorithm.
The algorithms are tested by some examples from dynamical systems with and without gyroscopic
effects.
Methology of reduced order modeling (ROMing) applying Proper Orthogonal Decomposition
(POD) of boiling water reactor (BWR) fuel assemblies (FAs) applied to
introductory examples
D. P. Prill, M. Stockmaier, A. G. Class (KIT), F. Wehle (AREVA Erlangen) Schedule
For high power low flow operating conditions associated with unfavorable power distribution
BWR operation requires attention with respect to density wave oscillations. The main drivers of
these phenomena are the multiple thermal hydraulic interactions between power, flow rate, and
density, reinforced by the neutronics feedback.
Admissible reactor operation conditions maintain a certain distance to the stability limit given
by linear theory. Evaluation of non-linear states requires time-consuming numerical integration
or experimental data but this depends on the specific transients considered. Non-linear stability
analysis aims at accelerating simulations and provides assessment of the whole parameter space.

Section 5: Nonlinear oscillations 117
In our transient analysis, the physical behavior of the system is approximated by a reduced
order model (ROM) that respects stability relevant characteristics. Proper orthogonal decomposition
(POD), i.e a spectral method based on experimental or computational fluid dynamics
(CFD) data, is capable of detecting oscillating states of the physical system. Moreover, POD provides
a well-defined truncation criterion for the minimum number of modes. A Galerkin method
employing POD modes as ansatz functions yields a non-linear ROM.
In the talk the chosen strategy is firstly applied to toy examples, i.e. the Korteweg de-Vries
(KdV) equation, and secondly to simplified reactor physics [1].
[1] T. Ortega-Gomez, Stability Analysis of the High Performance Light Water Reactor, Forschungszentrum
Karlsruhe, FZKA 7432, 2009, Germany
http://bibliothek.fzk.de/zb/berichte/FZKA7432.pdf
Symmetry and self-excited vibrations
Gottfried Spelsberg-Korspeter (TU Darmstadt) Schedule
Self-excited vibrations can be wanted or unwanted depending on where they occur. For the excitation
mechanism of flutter it can be shown that the excitation mechanism is directly related
to symmetries of the structure. This knowledge can either be used to avoid self-excitation but
can also be used to initiate self-excitation. The avoidance of self-excited vibrations is for example
beneficial to brakes and paper calenders whereas the initiation can be useful for example in
energy harvesting. Here self-excitation is a very desireable mechanism since it does hardly depend
on the frequency of the underlying structure. The current paper aims at showing the underlying
mechanisms and to exploit potential applications.
Rotor Stator Interaction with Many Degrees of Freedom
Oliver Alber (TU Darmstadt) Schedule
If an unbalanced rotor touches non-rotating parts (e. g. the housing) its dynamics becomes nonlinear.
As a result synchronous as well as asynchronous motions are possible. Asynchronous motion
patterns, especially in the case of a backward whirl motion, may exhibit large deflections of rotor
and stator in combination with large contact forces that might lead to severe damage of the
whole system. Earlier studies on the resulting dynamics of these systems focus predominantly
on a one-mass flexible rotor (Jeffcott rotor) which is in contact with a stator with one degree of
freedom only. For this case both analytical descriptions of the resulting synchronous motion and
their stability as well as approximate solutions or parameter studies for asynchronous motion are
available. However, in systems of practical interest typically not only a single resonance frequency
of the rotor stator system is relevant but many resonance frequencies of both rotor and stator
may contribute significantly. Thus, the question arises to which extent these previous results can
be extended to systems with many degrees of freedom. It is a main purpose of this contribution
to address this issue.
In particular, in this contribution the dynamics of a system consisting of a Multi-Disk Rotor
is investigated which is in contact with a system of flexibly mounted rigid stator rings. Both rotor
and stator are affected by external viscous damping. The contact areas between rotor and stator
are cylindrical surfaces with a clearance and account for dry friction between them. The dynamics
of the whole system is explored numerically in parameter regimes of practical interest.

118 Section 5: Nonlinear oscillations
S5.4: Nonlinear Oscillations IV Thu, 13:30–15:30
Chair: Dietrich Flockerzi, Edwin Kreuzer S1|03–107
Nonlinear vibration analysis of general supersonic composite laminated plates
Ardeshir Guran (Institute of Strutronics, Canada) Schedule
The nonlinear aeroelastic behavior of a three-dimensional general laminated composite plate at
high supersonic Mach numbers is investigated. The von-Karman’s large deflection plate theory is
assumed for structural modelling and the linear piston theory is used for aerodynamic modeling.
The effects of in-plane force, static pressure differential, fiber orientation and aerodynamic damping
on flutter behavior of the plates are considered. The numerical results obtained from the
integration of the governing nonlinear differential equations of the system were compared with
those obtained by ANSYS.
Finite oscillations of a channel with a flexible wall conveying viscous flow
Karolina Bach, Hartmut Hetzler, Wolfgang Seemann (KIT) Schedule
The interaction between a flexible structure and flowing fluid can cause flow-induced vibrations
and the steady state may loose stability by divergence or flutter, thus leading to undesirable
dynamic behaviour.
As a model for fluid-structure-interaction a planar and infinitely long channel is studied. The
flow is bounded by a rigid and a flexible wall. The latter is modelled as a one-parametric, nonpermeable
continuum on an elastic foundation, which exhibits bending and extensional stiffness.
It can be shown that for thin channels the coupling effects are strong and therefore the focus of
this contribution is to investigate the behaviour of a channel, where the structural displacements
are large compared to the gap width. Due to this large amplitudes a linear description of the
interface between fluid and structure will not be sufficient anymore and the relation between the
Eulerian description of the fluid and the Lagrangian description of the structure must be taken
into account: eventually, this yields nonlinear boundary conditions.
Furthermore in narrow gaps the viscosity of the fluid cannot be ignored. Hence the effect of viscosity
will also be considered within this contribution. In order to allow for analytical results and
keep the focus on the effects due to large displacements, a simplified fluid model is adopted: it is
assumed that the fluid is viscous, incompressible and that inertia terms may be neglected, thus
linear equations apply.
A perturbation analysis is utilized to determine the stability of the steady state as well as the
post-critical behaviour of the coupled problem.
How weathering influences the vibration behavior of oil paintings
Kerstin Kracht, Utz von Wagner (TU Berlin) Schedule
Oil paintings undergo vibrations due to multiple reasons. During transports high excitation levels
are reached. But also during exposition there is excitation by trespassing public or external traffic
load. Consequences may be damages in these art treasures. The presentation describes final results
of extensive experiments undertaken with a number of test dummies prepared by a docent of old
painting techniques. These test dummies were weathered over two years at a research institution
for paint and varnish at Magdeburg. There were alternating periods of weathering and measurements.
In the measurement periods the dummies were investigated for their dynamical behavior
using different excitations (harmonic, broad-band) and dynamic responses were measured using
special laser equipment newly adapted for measurements on the surface of painted canvas. Due
to chemical processes stiffness and density of the layers vary with corresponding influence on cha-

Section 5: Nonlinear oscillations 119
racteristic frequencies. Also varying occurrence of nonlinearities could be observed. The presented
work should finally lead to condition monitoring of oil paintings and techniques for the prevention
of artworks from vibrations.
On forced longitudinal vibrations of an axially moving yarn
Andreas Franze, Bernd W. Zastrau (TU Dresden) Schedule
During the manufacturing process of textiles, yarns are transported between rollers. Because of
the relative motion of yarn and roller the boundary conditions can not be assigned to fixed material
particles. Therefore this system is an example for media in motion with non-material boundary
conditions.
The equation of motion for an arbitrary time-varying transport velocity of the yarn is derived
from the balance equations. After linearisation of the system equations the analytical solution is
analysed and discussed.
Sudden Instabilities and Barring in Paper Machinery
Steffen Wiendl, Gottfried Spelsberg-Korspeter (TU Darmstadt) Schedule
The manufacturing of high quality paper is still a challenge to the engineers working in the construction
of paper machinery. Due to increasing production speeds and increasing width of the
nips vibration problems are harder to suppress. This work is concerned with vibration problems
arising in the process of paper calendering where in one of the last production steps the surface
of the paper is rened in huge calenders. In modern paper calenders two types of self-excited vibrations
are observed. Sometimes the rollers get into sudden instabilities which may damage the
whole production line if it is not shut of immediately. The second phenomenon is barring which is
a corrugation of the roller surfaces which develops on a smaller time scale. In this paper models
are developed to model the vibrational behavior of paper calenders with detailed focus on the
nip and the wear of the rollers. The models can build the basis for constructive measures against
squeal.
Zur Interaktion von Sägedraht und Ingot
M. Lorenz, A. Ams (TU Freiberg) Schedule
Es wird ein mechanisches Modell zur Beschreibung des bewegten Sägedrahtes unter Einwirkung
des Siliziumblocks (Ingot) vorgestellt. Mit dem Prinzip von Hamilton wird, unter der Voraussetzung
nichtlinearer Verformungskinematik sowie unter Berücksichtigung der Dehn- und Biegesteifigkeit
des Drahtes, das Variationsproblem und die Bewegungsgleichungen hergeleitet. Die
Wirkung des Ingot auf den bewegten Draht wird als Folgelast modelliert. Zudem werden die
mechanischen Eigenschaften von Ingot und Bettung in Abhängigkeit von Schnitttiefe und Schnittanzahl
bzw. Drahtposition mittels FEM bestimmt und in das Modell integriert. Ausgehend vom
Variationsproblem wird mit einem gemischten Ritz-Ansatz die stationäre Lage des Drahtes für
verschiedene Einflussparameter berechnet und Stabilitätsuntersuchungen durchgeführt.

120 Section 6: Material modelling in solid mechanics
Section 6: Material modelling in solid mechanics
Organizers: Daniel Balzani (Universität Duisburg-Essen), Wolfgang Dreyer (WIAS Berlin)
S6.1: Microstructures in Elasto-Plasticity I Tue, 13:30–15:30
Chair: Thorsten Bartel S1|01–A03
A model for martensitic microstructure, its geometry and interface effects
Mehdi Goodarzi, Klaus Hackl (Universität Bochum) Schedule
Martensitic materials demonstrate a characteristic microstructure in the form of parallel layers of
compatible phases. This is the consequence of a symmetry-breaking phase transformation which
can be well understood within a continuum mechanical framework by investigating energetically
favorable configurations of phase mixtures. We present a micromechanical model built upon this
approach that reflects numerous attributes of the microstructure.
In this model, a specific class of laminate geometries is constructed based on coherence condition
allowing for curved twin interfaces as well as three-dimensional aggregates. Proper forms of
surface energies are then proposed based on scaling arguments and crystallographic considerations.
We afterwards look into energy minimizing geometries within the class of morphologies that
are considered. The results are notably compliant to the observed scale properties, size effects
and accommodation patterns in the microstructure of martensite.
A Formulation of Finite Gradient Crystal Plasticity with Systematic Separation of
Long- and Short-Range States
S. Mauthe, F. Hildebrand, C. Miehe (Universität Stuttgart) Schedule
With the ongoing trend of miniaturization and nanotechnology, the predictive modeling of size
effects play an increasingly important role in metal plasticity. These size effects mainly stem
from geometrically necessary dislocations whose description requires gradient-extended theories
of crystal plasticity. However, a key challenge of the formulation and numerical implementation of
gradient crystal plasticity is the complexity within full multislip scenarios, in particular in context
of rate-independent settings.
In order to partially overcome this difficulty, we suggest a new viscous regularized formulation
of rate-independent crystal plasticity, that exploits in a systematic manner the long- and
short-range nature of the involved variables. To this end, we outline a multifield scenario, where
the macro-deformation and the plastic slips on crystallographic systems are the primary fields.
Related to these primary fields, we define as the long-range state the deformation gradient, the
plastic slips and their gradients. We then introduce as the short-range plastic state the plastic
deformation map, the dislocation density tensor and scalar hardening parameters associated with
the slip systems. It is then shown that the evolution of the short range state is fully determined
by the evolution of the long-range state. This separation into long- and short-range states
is systematically exploited in the algorithmic treatment by a new update structure, where the
short-range variables play the role of a local history base.
The model problem under consideration accounts in a canonical format for basic effects related
to statistically stored and geometrically necessary dislocation flow, yielding micro-force balances
including non-convex cross-hardening, kinematic hardening and size effects. Further key ingredients
of the proposed algorithmic formulation are geometrically exact updates of the short-range
state and a destinct regularization of the rate-independent dissipation function that preserves the
range of the elastic domain.
The formulation is shown to be fully variational in nature, goverend by rate-type continuous

Section 6: Material modelling in solid mechanics 121
and incremental algorithmic variational principles. We demonstrate the modeling capabilities and
algorithmic performance by means of representative numerical examples for multislip scenarios
in fcc single crystals.
Numerical Implementation of a Three-Dimensional Continuum Dislocation Microplasticity
Theory
Stephan Wulfinghoff, Thomas Böhlke (KIT) Schedule
The modelling of the mechanical behaviour of micro-devices can not be established by classical
continuum mechanical plasticity models without internal length scale. Depending on the system
size, ab-initio simulations or Discrete Dislocation Dynamics serve as mature tools to predict the
mechanical response of very small systems. Anyhow, the gap between these discrete and classical
continuum mechanical methods is not yet filled. Besides phenomenological gradient plasticity
models, dislocation density based approaches have emerged which account explicitly for dislocation
transport and line length increase. The presentation is based on the kinematical continuum
mechanical dislocation framework of Hochrainer et al. [1] which can be considered as a generalization
of Nye’s theory [3]. The theory transfers the kinematics of three-dimensional systems of
discrete dislocations to a continuum mechanical representation in terms of continuously distributed
dislocations. An averaged version of the theory by Hochrainer et al. [2] (see also Sandfeld et
al. [4]) leads to a significant reduction of the computational simulation effords and will mainly
be addressed. The kinematical dislocation theory is coupled to a crystal plasticity framework.
The presentation will focus on the numerical implementation of the theory, especially on promising
schemes for the numerical coupling of the set of PDEs. Finite Element simulation results
demonstrate the performance of the implementation in three-dimensional applications.
[1] T. Hochrainer, M. Zaiser and P. Gumbsch, A three-dimensional continuum theory of dislocations:
kinematics and mean field formulation. Philosophical Magazine 87 (2007), 1261–1282.
[2] T. Hochrainer, M. Zaiser and P. Gumbsch, Dislocation transport and line length increase in
averaged descriptions of dislocations. arXiv:1010.2884v1
[3] J. F. Nye, Some geometrical relations in dislocated crystals. Acta Metallurgica 1 (1953),
153–162.
[4] S. Sandfeld, T. Hochrainer, M. Zaiser and P. Gumbsch, Continuum modeling of dislocation
plasticity: Theory, numerical implementation, and validation by discrete dislocation
simulations. J. Mater. Res. 26 (2011), 623–632.
Rigorous derivation of a dissipation for laminate microstructures
Sebastian Heinz (WIAS Berlin) Schedule
We study models for finite plasticity in the framework of rate-independent evolutionary systems.
The corresponding incremental minimization problems, in general, admit no solutions due to
the creation of microstructure, see [1]. We focus on the case where the microstructure is made of
simple laminates only. We show in a mathematical rigorous way how the incremental minimization
problem can be relaxed and identify the relaxed dissipation as the one introduced in [2].
[1] C. Carstensen, K. Hackl, A. Mielke. Non-convex potentials and microstructures in finite-strain
plasticity, Proc. Royal Soc. London, Ser. A 458 (2002), 299 – 317.

122 Section 6: Material modelling in solid mechanics
[2] K. Hackl, D. M. Kochmann. Relaxed potentials and evolution equations for inelastic microstructures.
In B. Daya Reddy, editor, IUTAM Symposium on Theoretical, Computational
and Modelling Aspects of Inelastic Media, pages 27 – 39. Springer-Verlag, 2008.
Thermodynamically and variationally consistent modeling of distortional hardening:
application to magnesium
Baodong Shi (Helmholtz-Zentrum Geesthacht), Jörn Mosler (Helmholtz-Zentrum Geesthacht, TU
Dortmund) Schedule
To capture the complex elastoplastic response of many materials, classical isotropic and kinematic
hardening alone are often not sufficient. Typical phenomena which cannot be predicted by the
aforementioned hardening models include, among others, cross hardening or more generally, the
distortion of the yield function. However, such phenomena do play an important role in several
applications in particular, for non-radial loading paths. Thus, they usually cannot be ignored. In
the present contribution, a novel macroscopic model capturing all such effects is proposed. In contrast
to most of the existing models in the literature, it is strictly derived from thermodynamical
arguments. Furthermore, it is the first macroscopic model including distortional hardening which
is also variationally consistent. More explicitly, all state variables follow naturally from energy
minimization within advocated framework.
A viscosity-limit approach to the evolution of microstructures in finite plasticity
Christina Günther, Klaus Hackl (Universität Bochum) Schedule
Material microstructures in finite single-slip crystal plasticity occur and evolve due to deformation.
Their formation is not arbitrary, they tend to form structured spatial patterns. This hints at a
universal underlying mechanism, in the same manner as the minimization of the global energy governs
the behavior of purely elastic materials. For non-quasiconvex potentials, the minimizers are
small scale fluctuations, related to probability distributions of the deformation gradients, which
can be found by the relaxation of the potential.
As in the approach of D.Kochmann and K.Hackl, we use a variational framework, focusing on the
Lagrange functional. For the treatment of the laminates, the potentials have to be adapted. The
new approach rests on the introduction of a small smooth transition zone between the laminates
in order to avoid a global minimization. This makes the evolution equations more handable for
numerical calculations. We present explicit time-evolution equations for the volume fractions and
the internal variables. We outline a numerical scheme and show some examples.
S6.2: Polymers and Elastomers I Tue, 13:30–15:30
Chair: Mikhail Itskov, Vladimir Kolupaev S1|01–A1
Constitutive modelling of chemical ageing
Alexander Lion, Michael Johlitz (Universität der Bundeswehr München) Schedule
In order to model chemical ageing of rubber a three-dimensional theory is proposed. The fundamentals
of this approach are different decompositions of the deformation gradient in combination
with an additive split of the Helmholtz free energy into three parts. Its first part belongs to the
volumetric material behaviour. The second part is a temperature-dependent hyperelasticity model
which depends on an additional internal variable to consider the long-term degradation of the
primary rubber network. The third contribution is a functional of the deformation history and a
further internal variable; it describes the creation of a new network which remains free of stress

Section 6: Material modelling in solid mechanics 123
when the deformation is constant in time. The constitutive relations for the stress tensor and the
internal variables are deduced using the Clausius-Duhem inequality. In order to sketch the main
properties of the model, expressions in closed form are derived with respect to continuous and
intermittent relaxation tests as well as for the compression set test. Under the assumption of near
incompressible material behaviour, the theory can also represent ageing-induced changes in volume
and their effect on the stress relaxation. The simulations are in accordance with experimental
data from literature.
[1] A. Lion, M. Johlitz, On the representation of chemical ageing of rubber in continuum mechanics,
International Journal of Solids and Structures, under review.
Multi-phase modeling of shape memory polymers
Nico Hempel, Markus Böl (TU Braunschweig) Schedule
Shape memory polymers are a highly versatile class of so-called smart materials. They are able to
store a certain state of deformation and remember another one by means of an external stimulus
such as light or temperature. Usually, the physical mechanism responsible for this behavior is a
temperature-dependent phase transition between an “active”, entropy-elastic phase and a “frozen”,
energy-elastic phase. As polymers are usually capable of experiencing large deformations, models
are required which are able to represent both the phase transitions and states of large deformation.
In the present work, we propose a model based on the idea of the multiplicative decomposition
of the deformation gradient. Evolution equations for the several deformation components are
presented that provide for the storage of the entropy-elastic strain and its recovery during the
transition between the frozen phase and the active phase. First characteristic shape memory cycles
will be presented as a last point.
On response functions in linear thermoelastic models of shape memory polymers
Aycan Özlem Aydin, Rasa Kazakevičiute-Makovska , Holger Steeb (Universität Bochum) Schedule
There are two basic classes of constitutive models for thermoresponsive Shape Memory Polymers
(SMPs), rheological and thermoelastic models. In this work, we present a detailed analysis of
linear thermoelastic models. The first model within this class has been proposed by Liu et al. [1]
and in the following years numerous modifications of that model have been presented (cf. e.g. [2]).
All these models have a common mathematical structure with three basic response functions.
Different models developed within this concept follow from the general theory by specifications
of the relevant response functions. The general mathematical form of the response functions
is discussed and an experimental methodology determining of response functions directly from
experimental data is presented. Representative examples illustrate the quality and the efficiency
of the proposed methodology. It is shown that a reliable evaluation of thermoelastic models for
SMPs requires a comparison with data for all four steps of the termomechanical cycle, both under
strain- and stress controlled conditions.
[1] Y. Liu, K. Gall, M. L. Dunn, A. R. Greenberg, J. Diani, Thermomechanics of shape memory
polymers: Uniaxial experiments and constitutive modeling, Int. J. Plasticity, vol. 22, pp.
279-313, 2006.
[2] R. Kazakevičiute-Makovska, H. Steeb, A. Özlem Aydın, On the evolution law for the frozen
fraction in the linear theories of shape memory polymers, Arch. App. Mech., in press, 2011.

124 Section 6: Material modelling in solid mechanics
Modeling the finite strain deformation and initial anisotropy of amorphous thermoplastic
polymers
Philipp Hempel, Thomas Seelig (KIT) Schedule
The present work deals with modeling the temperature dependent finite strain deformation behavior
of amorphous thermoplastic polymers incorporating the effect of an initial anisotropy. The
anisotropy prevails in form of a frozen-in pre-orientation of molecular chains and results from preceding
manufacturing processes (e.g. injection molding) at elevated temperatures and subsequent
rapid cooling. The initial molecular orientation affects the mechanical response in terms of flow
strength and hardening.
The standard finite strain kinematics with a multiplicative split of the deformation gradient into
an elastic and plastic part is modified by introducing a network deformation gradient which comprises
the actual plastic deformation and the initial (processing induced) pre-deformation [1],[2].
As a computational example, an injection molded plate is investigated which displays nonuniform
shrinkage and buckling during heating due to the action of the frozen-in network stress. The
spatial distribution of molecular pre-orientation, and hence initial anisotropy, in the FE model is
estimated from optical birefringence.
[1] E.M. Arruda, M.C. Boyce, Evolution of plastic anisotropy in amorphous polymers during
finite straining, International Journal of Plasticity (1993), 6 –697.
[2] M.C. Boyce, D.M. Parks, A.S. Argon, Plastic flow in oriented glassy polymers, International
Journal of Plasticity (1998), 6 – 593.
Modeling of induced anisotropy at large deformations for polymers
Ismail Caylak, Rolf Mahnken (Universität Paderborn) Schedule
In this presentation we develop a model to describe the induced plasticity of polymers at large
deformations. Polymers such as stretch films exhibit a pronounced strength in the loading direction.
The undeformed state of the films is isotropic, whereas after the uni-axial loading the
material becomes anisotropic. In order to consider this induced ansiotropy during the stretch
process, a spectral decomposition of the inelastic Cauchy-Green tensor is done. Therefore, the
yield function can be formulated as a function of the anisotropic tensor, where again the anisotropic
tensor is a function of the maximum eigenvalue. A backward Euler scheme is used for
updating the evolution equations, and the algorithmic tangent operator is derived. The numerical
implementation of the resulting set of constitutive equations is used in a finite element program
and for parameter identification.
S6.3: Microstructures in Elasto-Plasticity II Tue, 16:00–18:00
Chair: Dennis Kochmann, Sebastian Heinz S1|01–A03
Microstructure development in a Cosserat continuum as a consequence of energy
relaxation
Muhammad Sabeel Khan, Klaus Hackl (Universität Bochum) Schedule
A rate-independent inelastic material model for a Cosserat continuum is presented. The free energy
of the material is enriched with an interaction potential taking into account the intergranular

Section 6: Material modelling in solid mechanics 125
kinematics at the continuum scale. As a result the total energy becomes non-convex, thus giving
rise to the development of microstructure. To guarantee the existence of minimizers an exact
quasi-convex envelope of the corresponding energy functional is derived. As a result microstructure
occurs in both the displacement and micro-rotation field. The corresponding relaxed energy
is then used for finding the minimizers of the two field minimization problem corresponding to a
Cosserat continuum. Finite element formulation and numerical simulations are presented. Analytical
and numerical results are discussed.
About the Microstructural Effects of Polycrystalline Materials and their Macroscopic
Representation at Finite Deformation
Eva Lehmann, Stefan Loehnert, Peter Wriggers (Universität Hannover) Schedule
In the sheet bulk metal forming field, the strict geometrical requirements of the workpieces result
in a need of a precise prediction of the material behaviour. The simulation of such forming processes
requires a valid material model, performing well for a huge variety of different geometrical
characteristics and finite deformation.
Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically
observable plastic deformation is traced back to dislocations within considered slip
systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level.
A finite crystal plasticity model is used to model polycrystalline materials in representative
volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation
gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the
elastic contribution. In order to circumvent singularities stemming from the linear dependency
of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the
plastic slips and slip resistances.
The model is validated with experimental microstructural data under deformation. The validation
on the macroscopic scale is performed through the reproduction of the experimentally
calculated initial yield surface. Additionally, homogenised stress-strain curves from the microstructure
build the outcome for a suitable effective material model. Through optimisation techniques,
effective material parameters can be determined and compared to results from real forming processes.
A rheological model for arbitrary symmetric distortion of the yield surface
A.V. Shutov, J. Ihlemann (TU Chemnitz) Schedule
A new rheological model is presented, which provides insight into phenomenological modelling of
combined nonlinear kinematic and distortional hardening. The model is constructed by coupling
idealized two-dimensional rheological elements like Hooke-body, Newton-body, and modified St.
Venant element [1,2]. The symmetric distortion of the yield surface and its orientation depending
on the recent loading path are captured by the rheological model in a vivid way. We emphasize the
flexibility of the proposed approach since it can be used to capture any smooth convex saturated
form of the yield surface observed experimentally, if the yield surface is symmetric with respect to
the recent loading direction. In particular, an arbitrary sharpening of the saturated yield locus in
the loading direction combined with a flattening on the opposite side can be taken into account
[2]. Moreover, the yield locus evolves smoothly and its convexity is ensured at each hardening
stage.
The rheological model serves as a guideline for construction of new constitutive relations. The
kinematic assumptions, the ansatz for the free energy and for the yield function are motivated by
the rheological model. Additionally to kinematic and distortional hardening, a nonlinear isotropic
hardening is introduced as well. Normality flow rule is considered, and a rigorous proof of ther-

126 Section 6: Material modelling in solid mechanics
modynamic consistency is provided. Finally, the predictive capabilities of the resulting material
model are verified using the experimental data for a very high work hardening annealed aluminum
alloy 1100 Al.
[1] A.V. Shutov, S. Panhans, R. Kreißig, A phenomenological model of finite strain viscoplasticity
with distortional hardening, ZAMM, 8, 653 - 680.
[2] A.V. Shutov, J. Ihlemann, A viscoplasticity model with an enhanced control of the yield
surface distortion, Submitted to International Journal of Plasticity.
Towards the simulation of Internal Traverse Grinding – from mesoscale modelling to
process simulations
Raphael Holtermann (TU Dortmund), Andreas Menzel (TU Dortmund / Lund University) Schedule
The present work aims at the modelling and simulation of Internal Traverse Grinding of hardened
100Cr6/AISI 52100 using electro plated cBN grinding wheels. We focus on the thermomechanical
behaviour resulting from the interaction of tool and workpiece in the process zone on a mesoscale.
Based on topology analyses of the grinding wheel surface, two-dimensional single- and multigrain
representative numerical experiments are performed to investigate the resulting loaddisplacement-behaviour
as well as the specific heat generation due to friction and plastic dissipation.
A thermoelastic-viscoplastic constitutive model is used to capture thermal softening of the
material taken into account. Based on previous work [1,2], an adaptive remeshing scheme which
uses a combination of error estimation and indicator methods, is applied to overcome mesh dependence.
In consequence, the formulation allows to resolve the complex deformation patterns
and to predict a realistic thermomechanical state of the resulting workpiece surface [3].
As a future goal, we aim at coupling the above cutting zone model to a process scale simulation
to model the thermomechanical behaviour of the entire three-dimensional workpiece.
[1] C. Hortig and B. Svendsen, Simulation of chip formation during high-speed cutting, J. Mat.
Processing Technology 186, 66–76 (2007)
[2] C. Hortig and B. Svendsen, Adaptive modeling and simulation of shear banding and high
speed cutting, Proc. 10th ESAFORM Conference on Material Forming CP907, 721–726
(2007)
[3] D. Biermann, A. Menzel, T. Bartel, F. Höhne, R. Holtermann, R. Ostwald, B. Sieben, M.
Tiffe, A. Zabel, Experimental and computational investigation of machining processes for
functionally graded materials, Procedia Engineering, accepted for publication, 2011
Multiscale crystal plasticity based on continuum theory of dislocation mechanics: an
extension to ductile fracture.
Mubeen Shahid, Klaus Hackl (Universität Bochum) Schedule
The presentation focuses on the modelling of phenomena associated with plastic deformations
in crystalline materials. The plastic deformation in crystalline materials strongly depends on
aggregate behaviour of dislocations. However there is no universal constitutive frame-work which

Section 6: Material modelling in solid mechanics 127
directly relates all the attributes of dislocations at microscale to the macroscale deformations,
both qualitatively and quantitatively.
First the macroscale constitutive model based on the continuum theory of dislocations [1,2]
is discussed. The plastic deformation and crack growth during ductile fracture mutually effect
each other, where dislocations’ movement shape the crack growth, and the latter effects the
dislocations density [3]. We discuss the numerical implementation of the proposed crystal viscoelastoplasticity
model coupled with modern dislocation measures [1,2] and present an example
where the mechanisms of crystal plasticity are linked to the ductile fracture. The results focus
the effect of severe plastic deformation on dislocations evolution and crack growth behaviour,
following the approach of Cherepanov [3].
[1] T. Hochrainer, M. Zaiser, P. Gumbsch, A three-dimensional continuum theory of dislocation
systems: kinematics and mean-field formulation, Philosophical Magazine, 87:8-9 (2007),
1261-1282.
[2] S. Sandfeld, T. Hochrainer, P. Gumbsch, M. Zaiser, Numerical implementation of a 3D
continuum theory of dislocation: dynamics and application to micro-bending, Philosophical
Magazine, 90:27-28 (2010), 3697-3728.
[3] G.P. Cherepanov et al., Dislocation generation and crack growth under monotonic loading,
J. Appl. Phys., 78(10) (1995), 6249-6264.
Multiscale modelling and simulation of micro machining of titan
Richard Lohkamp, Ralf Müller (TU Kaiserslautern) Schedule
The topology of micro machined surfaces depends strongly on the underlying heterogeneous microstructure
of the material. The crystal structure influences the deformation and separation
characteristics. In the case of α-titanium the deformation is dictated by the hcp crystal structure
with its specific slip systems. In the crystal plastic deformation it is essential to take self and latent
hardening into account. Furthermore to capture the rate dependent behavior a visco-plastic
evolution law is used. This setting serves as a framework for more complex constitutive laws, such
as the one given in [1].
As a first attempt to model the cutting process, the fracture mechanisms in a crystalline αtitanium
are analysed within the concept of configurational forces. To this end the theory of
configurational forces is presented for a standard dissipative medium and is specialized to the
crystal plasticity setting. The numerical implementation of the material law and the configurational
forces is done in a consistent way within the finite element method. The application of
configurational forces in the crystal plasticity setting is discussed and demonstrated by illustrative
examples.
S6.4: Polymers and Elastomers II Tue, 16:00–18:00
Chair: Alexander Lion, Joachim Schmitt S1|01–A1
How to approximate the inverse Langevin function?
Mikhail Itskov, Roozbeh Dargazany, Karl Hörnes (RWTH Aachen) Schedule
The inverse Langevin function directly results from the non-Gaussian theory of rubber elasticity
as the chain force and represents an indispensable ingredient of full-network rubber elasticity models.
However, the inverse Langevin function cannot be represented in a closed-form and requires

128 Section 6: Material modelling in solid mechanics
an approximation as for example a Padé approximation. The Padé approximations can be given
in a relatively simple form and are able to describe the asymptotic behavior of the inverse Langevin
function in the vicinity of the maximum chain extensibility. Far away from the asymptotic
area the approximation error can be, however, relatively large. In the present contribution we
compare various Padé approximants with the Taylor power series representation of the inverse
Langevin function. To this end, a simple recursive procedure calculating power series coefficients
of the inverse function is proposed. The procedure can be applied to any function which can be
expanded into Taylor series. Within the convergence radius the resulting series of the inversed
Langevin function demonstrates better agreement with the analytical solution than the Padé approximations.
Phenomenological modeling of a polymeric composite
Sebastian Borsch, Albrecht Bertram (Universität Magdeburg) Schedule
A composite material consisting of a polymeric matrix material and metallic filler particles is
modeled in a phenomenological way. The isotropic viscoplastic constitutive model is formulated
within the theory of finite deformations. The flow rule is a superposition of two terms. This
approach enables us to simulate the strong backflow behavior during unloading, which can be
observed in various polymeric materials. A quasi-static finite-element simulation has been performed
to compare the model with cyclic tension tests as well as a relaxation test.
Modelling of nanoindentation of polymers with effects of surface roughness and parameters
identification
Zhaoyu Chen, Stefan Diebels (Universität des Saarlandes) Schedule
Since the nanoindentation testing technique can measure the properties of extremely small volumes
with sub-m and sub-N resolution from the continuously sensed force-displacement curves,
it also became one of the primary testing techniques for polymeric materials and biological tissues.
The analysis of individual indentation tests using the conventionally applied Oliver & Pharr
method has limitations to capture the hyperelastic and rate-dependent properties of polymers.
Therefore, an inverse method with respect to the experimental testing, based on finite element
simulation and numerical optimisation has been used and evolved. However, nanoindentation is
composed of various error contributions, e. g. friction, adhesion, surface roughness and indentation
process associated factors. These contributions forming the systematic errors between the
numerical model and the experiments will often lead to large errors in the parameters identification.
Therefore, basic investigations and quantification of these influences are indispensable to
characterise the materials accurately from nanoindentation based on the inverse method.
In the present contribution, the characterisation of polymers through nanoindentation with effects
of the surface roughness based on inverse method will be investigated numerically. The boundary
value problems of nanoindentation of polymers are modelled with the FE code ABAQUS R○ .
In contrast to the traditional inverse method, virtual experimental data calculated by numerical
simulations with chosen parameters replace the real experimental measurements. Such a procedure
is called parameter re-identification. In this sense, the finite element code ABAQUS R○ is used as
our virtual laboratory. The model parameters are identified using an evolution strategy based on
the concept of numerical optimisation. The surface roughness effects are investigated numerically
based on the approach utilizing the phenomenological concepts. The surface roughness is chosen
to have a simple representation considering only one-level of roughness profile described by a
sine function. The influence of the surface roughness is quantified associated to the sine curve

Section 6: Material modelling in solid mechanics 129
parameters as well as to the indentation parameters. Moreover, the real surface topography is
characterised using multi-level of protuberance-on-protuberance profiles. The effects of the surface
roughness are investigated with respect to the identified model parameters using a surface
topography with one-level or multi-level profiles approximated by a sine function. The results are
expected to offer a deep insight into characterising the real surface roughness numerically.
Material force computation for the thermo-mechanical response of dynamically loaded
elastomers
Ronny Behnke, Michael Kaliske (TU Dresden) Schedule
Elastomers are widely used in our today’s life. The material is characterized by large deformability
upon failure, elastic and time dependent as well as non-time dependent effects which can
be also a function of temperature. In addition, cyclically loaded components show heat built-up
which is due to dissipation. As a result, the temperature evolution of an elastomeric component
can strongly influence the material properties and durability characteristics. Representing best
the real thermo-mechanical behaviour of an elastomeric component in its design process is one
motivation for the use of sophisticated, coupled material approaches within numerical simulations.
In order to assess the durability characteristics, for example regarding crack propagation, the
material forces (configurational forces) are one possible approach to be applied. In the present
contribution, the implementation of material forces for a thermo-mechanically coupled material
model including a continuum mechanical damage (CMD) approach is demonstrated in the context
of the Finite Element Method (FEM). Special emphasis is given to material forces resulting
from internal variables (viscosity and damage variables), temperature field evolution and dynamic
loading. Using an example of an elastomeric component, for which the material model parameters
have been previously identified by a uniaxial extension test, material forces are evaluated quantitatively.
The influence of each contribution (internal variables, temperature field and dynamics)
is illustrated and compared to the overall material force response.
Single and multiscale aspects of the modeling of curing polymers
Alexander Bartels ∗ , Sandra Klinge ∗ , Klaus Hackl ∗ , Paul Steinmann ∗∗ (Universität Bochum, Universität
Erlangen-Nürnberg) Schedule
Within this presentation, the focus is placed on the simulation of the isochoric behavior of polymers
during the curing process. To this end, a model based on the assumption for the free
energy in the form of a convolution integral is applied. Since this allows the implementation of
the time dependent material parameters, the free energy is interpreted as the total-accumulated
energy. Different from this, the strain energy is related to the current state of deformation and
used to define the temporary stiffness. In order to avoid volume locking effects typical for isochoric
materials, the free energy is furthermore split into a volumetric and a deviatoric part. A
multifield description depending on the displacements, volume change and hydrostatic pressure
is introduced as well. The model is implemented within a single- and multiscale FE program
and used to simulate the behavior of homogeneous and microheterogeneous polymers. The main
property of the multiscale concept used here is that the modeling of a heterogeneous body is
performed by simultaneously solving two boundary value problems: one related to the behavior
of the macroscopic body and the other one dealing with the analysis of the representative volume
element.
Influence of nano-particle interactions on the mechanical behavior of colloidal structures
in polymeric solutions
Roozbeh Dargazany, Ngoc Khiêm Vu , Mikhail Itskov (RWTH Aachen) Schedule

130 Section 6: Material modelling in solid mechanics
Colloidal structures inside solutions are usually considered as rigid bodies or linear springs. However,
recent experimental results show a strongly nonlinear mechanical response of large clusters.
In this contribution, the nonlinear elastic behavior of the colloidal structures inside polymeric
solutions is studied. So far, the influences of initial length and fractal dimension on the elastic response
of colloidal structures have mostly been considered by scaling theory. Here, we additionally
take into account a deformation induced evolution of the aggregate structure which is mainly influenced
by inter-particle interactions. To this end, central and lateral (non-central) inter-particle
forces are considered separately. Next, the directional stiffness of the colloidal structure is evaluated
by using the concept of a backbone chain. The backbone chain is a unique path between two
ends of the colloidal structure that carries the main portion of load. The mechanical response of
the backbone chain depends on aggregate geometry, deformation history and moreover, on the
nature and the strength of the inter-particle interactions. The aggregate geometry is described by
means of the angular averaging concept. The so-obtained model can further be generalized for all
types of colloidal structures with central and lateral inter-particle forces.
S6.5: Phase Transformations I Wed, 13:30–15:30
Chair: Markus Lazar, Wolfgang Dreyer S1|01–A03
A thermodynamically consistent framework for martensitic phase transformations
interacting with plasticity
Thorsten Bartel, Andreas Menzel (TU Dortmund) Schedule
We propose constitutive relations for martensitic phase transformations at large strains which
captures the interactions between phase transformations, plasticity and the local heating of the
material due to the inelastic processes. For the kinematics of finite deformations we make use
of logarithmic Hencky-strains. The total strain is additively decomposed into elastic, plastic and
transformation related parts, where the latter quantities are motivated by crystallographic considerations.
The thermodynamically consistent framework is based on a representative macroscopic
energy density and an inelastic potential in terms of a dual dissipation functional. With these
quantities at hand, thermodynamical driving forces as well as rate-independent evolution equations
are derived in a canonical way. In this regard, the proposed model states an alternative to the
models described in [1,2]. Referring to [3], the local heating of the material is realised by a consistently
derived temperature evolution equation capturing the effect of self heating. The solution
of the obtained local system of equations is challenging and demands a sophisticated algorithmic
treatment. To this end, we present a scheme which avoids cumbersome and time-consuming active
set searches by the use of Fischer-Burmeister NCP functions and furthermore prevents the
occurence of redundant equations by a specific condensation strategy. The numerical examples
emphasize the capabilities of the proposed model which is, among other aspects, exemplified by
a transformation induced anisotropy. Furthermore, special attention is paid to the simulation of
the complex material behaviour of, e.g., TRIP-steels.
[1] T. Bartel, A. Menzel, B. Svendsen, Thermodynamic and relaxation-based modeling of the
interaction between martensitic phase transformations and plasticity, J. Mech. Phys. Sol.
Vol. 59, 1004-1019, 2011,
[2] R. Ostwald, T. Bartel, A. Menzel, A one-dimensional computational model for the interaction
of phase-transformations and plasticity, Int. Journal of Structural Changes in Solids Vol. 3,
63-82, 2011,
[3] J. C. Simo, C. Miehe, Associative coupled thermoplasticity at finite strains: Formulation,

Section 6: Material modelling in solid mechanics 131
numerical analysis and implementation, Comp. Meth. Appl. Mech. Engrg. Vol. 98, 41-104,
1992
Deformation induced martensite transformation in a cold-worked forming process of
austenitic stainless steel
Tim Dally, Kerstin Weinberg (Universität Siegen) Schedule
Within the last years the goal of industrial manufacturing processes - such as tube forming - has
shifted towards an optimization of technological as well as mechanical properties of the manufactured
structures. For example, during the forming procedure of sheets made of austenitic stainless
steel X5CrNi18-10, the content of strain-induced martensite needs to be controlled. In order to
achieve optimal structural properties of the manufactured tube with respect to very high-cycle
fatigue (VHCF), a martensite ratio of approximately 25% needs to be obtained.
On the basis of experimental investigations our contribution deals with the numerical simulation
of the forming process with special consideration of the martensite ratio c as a function of
temperature and deformation field:
c = c(T, ε p ).
In particular, we study the interaction of processing temperature, friction, plastic deformation
and stress state during forming. We will further present different approaches of modelling the
martensite evolution as well as the extension of an existing martensite model on polyaxial states
of stress and compare experimental results and numerical simulations for the modified model.
Additionally a facility to calculate the hardening due to martensitic phase transformation will be
presented.
Finally, we will propose a strategy to control the martensite evolution during the tube-forming
process that enables us to achieve the optimal c mentioned above.
Micromechanical modeling of bainitic phase transformation
A. Schneidt, R. Mahnken (Universität Paderborn), T. Antretter (Montanuniversität Leoben)
Schedule
We develop a micromechanical material model for phase transformation from austenite to bainite
for a polycrystalline low alloys steel. In this material (e.g. 51CrV4) the phase changes from
austenite to perlite-ferrite, bainite or martensite, respectively. This work is concerned with phase
transformation between austenite and n-bainite variants in different orientated grains. Characteristic
of bainite are the combination of time-dependent transformation kinetics and lattice shearing
in the microstructure. These effects are considered on the microscale and by means of homogenisation
scale in the polycrystalline macroscale with stochastically orientated grains. Furthermore, the
numerical implementation of our model with a Newton projection algorithm into a finite-element
program is presented, based on the algorithm in [1].
[1] R. Mahnken and S. Wilmanns, A projected Newton algorithm for simulation of multivariant
textured polycrystalline shape memory alloys. Computational Materials Science 50,
25352548, 2011.

132 Section 6: Material modelling in solid mechanics
Effects of heat treatment on phase transformation in powder metallurgical multifunctional
coating
Reza Kebriaei, Jan Frischkorn, Stefanie Reese (RWTH Aachen) Schedule
Heat treatment is an indispensable part of the manufacturing of metallic products, especially in
powder coating process. It provides an efficient way to manipulate the properties of the metal as
e.g. hardness, yield stress and tensile stress by controlling the rate of diffusion and the rate of
cooling within the microstructure.
The process-integrated powder coating by radial axial rolling of rings is a new hybrid production
technique which is introduced in [1]. It takes advantage of the high temperatures and high
forces of the ring rolling process not only to increase the rings diameter, but also to integrate
the application and compaction of powder metallurgical multi-functional coatings to the solid
substrate rings within the same process [2]. The applied temperatures in hot rolling are within
the range of austenitizing temperatures for the investigated steels. Therefore, controlled cooling
can be conducted directly from process heat subsequent to the deformation process.
The talk is concerned with the finite element (FE) simulation of the process-integrated powder
coating by radial axial rolling of rings and the integration of heat treatment of the rolled ring
into the subsequent cooling process. Finally parameter studies are performed to analyse the
temperature profile and phase transformation in the rings cross-section.
[1] J. Frischkorn, S. Reese, Modelling and Simulation of Process-integrated Powder Coating by
Radial Axial Rolling of Rings, Archive of Applied Mechanics 81 (2011)
[2] R. Kebriaei, J. Frischkorn, S. Reese, Influence of Geometric Parameters on Residual Porosity
in Process-integrated Powder Coating by Radial Axial Rolling of Rings, Steel Research
International 163 (2011)
Simulation of phase-transformations based on numerical minimization of intersecting
Gibbs energy potentials
Richard Ostwald, Thorsten Bartel (TU Dortmund), Andreas Menzel (U Dortmund / Lund University)
Schedule
We present a novel approach for the simulation of solid to solid phase-transformations in polycrystalline
materials. To facilitate the utilization of a non-affine micro-sphere formulation with
volumetric-deviatoric split, we introduce Helmholtz free energy functions depending on volumetric
and deviatoric strain measures for the underlying scalar-valued phase-transformation model.
As an extension of affine micro-sphere models [3], the non-affine micro-sphere formulation with
volumetric-deviatoric split allows to capture different Young’s moduli and Poisson’s ratios on the
macro-scale [1]. As a consequence, the temperature-dependent free energy assigned to each individual
phase takes the form of an elliptic paraboloid in volumetric-deviatoric strain space, where
the energy landscape of the overall material is obtained from the contributions of the individual
constituents.
For the evolution of volume fractions, we use an approach based on statistical physics—taking
into account actual Gibbs energy barriers and transformation probabilities [2]. The computation
of individual energy barriers between the phases considered is enabled by numerical minimization
of parametric intersection curves of elliptic Gibbs energy paraboloids. The framework provided
facilitates to take into account an arbitrary number of solid phases of the underlying material,
though we restrict ourselves to the simulation of three phases, namely an austenitic parent phase
and a martensitic tension and compression phase. It is shown that the model presented nicely

Section 6: Material modelling in solid mechanics 133
reflects the temperature-dependent effects of pseudo-elasticity and pseudo-plasticity, and thus
captures experimentally observed behaviour at different temperatures.
[1] I. Carol and Z. Bažant, Damage and plasticity in microplane theory, Int. J. Sol. Struct. 34,
3807–3835 (1997)
[2] S. Govindjee and G.J. Hall, A computational model for shape memory alloys, Int. J. Sol.
Struct. 37, 735–760 (2000)
[3] R. Ostwald, T. Bartel and A. Menzel, A computational micro-sphere model applied to the
simulation of phase-transformations, J. Appl. Math. Mech. 90(7-8), 605–622 (2010)
S6.6: Elasticity, Viscoelasticity, -plasticity I Wed, 13:30–15:30
Chair: Merab Svanadze, Daniel Balzani S1|01–A1
Thermoviscoplasticity deduced from enhanced rheological models
Christoph Bröcker, Anton Matzenmiller (Universität Kassel) Schedule
In the concept of rheological models, basic elements like springs (ideal elastic), dashpots (ideal
viscous) or friction elements (ideal plastic) are assembed to networks for representing complex
material behaviour [1]. In case of viscoelastic material models, the phenomenological constitutive
equations are usually deduced directly from a rheological network. However, in the case of elastoplasticity,
the rheological models are often used only to visualise the fundamental structure of
the related material model.
In the presentation, a new ideal body is defined for isotropic hardening besides minor modifications
of some well–known basic elements from the literature [2, 3]. Hence, a rheological model of
thermoviscoplasticity may be assembled with linear isotropic and kinematic hardening and nonlinear
strain rate sensitivity. The related constitutive equations including the yield function and the
flow rule are directly deduced from the kinematics and the stress equilibrium of the rheological
network and results in a well–known model. By evaluating the dissipation inequality, the heat
conduction equation is obtained with the dissipative power term, driven by plastic deformations.
Moreover, nonlinear isotropic and kinematic hardening as well as an improved description
of energy storage and dissipation are accomplished by introducing several additional dissipative
strain elements into the viscoplastic arrangement of the rheological model [see also 4], which
corresponds to a generalization of an ideal body already used in [2, 3]. Again, the constitutive
equations may be deduced from the rheological network, its kinematics, and the stress equilibrium.
For that purpose, however, the dissipation inequality has to be utilized.
[1] M. Reiner, Rheologie in elementarer Darstellung, Carl Hanser Verlag, 1969.
[2] A. Krawietz, Materialtheorie, Springer, 1986.
[3] A. Lion, Constitutive modelling in finite thermoviscoplasticity: a physical approach based on
nonlinear rheological models, Int. J. Plast. 16 (2000), 469–494.
[4] A. Matzenmiller, C. Bröcker, Modelling and simulation of coupled thermoplastic and thermoviscous
structuring and forming processes, In: Maier et al. (eds.): Functionally graded
materials in industrial mass production, Verlag Wissenschaftliche Skripten, Auerbach, 2009,
235–250.

134 Section 6: Material modelling in solid mechanics
Steady vibrations problems in the theory of viscoelasticity for Kelvin-Voigt materials
with voids
Maia M. Svanadze (Universität Göttingen) Schedule
Viscoelastic materials play an important role in many branches of engineering, technology and
biomechanics. The modern theories of viscoelasticity and thermoviscoelasticity for materials with
microstructure have been a subject of intensive study in recent years. Recently, the theory of
thermoviscoelastic materials with voids is constructed by Iesan (2011).
In this paper the linear theory of viscoelasticity for Kelvin-Voigt materials with voids is considered
and the basic internal and external boundary value problems of steady vibrations are investigated.
The formulae of integral representations of regular vectors are obtained. The single-layer,
double-layer and volume potentials are constructed and their basic properties are established.
The uniqueness and existence of regular solutions of the boundary value problems are proved by
means of the potential method.
Modelling of predeformation- and frequency-dependent material behavior of filled
rubber under large predeformations superimposed with harmonic deformations of
small amplitudes
D. Wollscheid, A. Lion (Universität der Bundeswehr München) Schedule
Viscoelastic materials show a frequency- and predeformation-dependent behavior under loadings
that consist of large predeformations with superimposed harmonic deformations of small amplitudes.
In order to consider this materialbehavior, some static and dynamic experiments are
developed. Based on Haupt & Lion [1] and Lion, Retka & Rendek [2] we introduce a recently
developed constitutive approach of finite viscoelasticity in the frequency domain that is able to
describe the frequency- and predeformation-dependent materialbehavior with respect to storageand
loss-modulus. The constitutive equations are evaluated in the frequency domain and geometrically
linearized in the neighbourhood of the predeformation. Furthermore a formulation for
incompressible material behavior is introduced and the corresponding dynamic modulus tensors
are derived. Besides constitutive modelling and experiments, parameter identification and some
numerical simulations are presented.
[1] P. Haupt, A. Lion, On finite linear viscoelasticity of incompressible isotropic materials, Acta
Mechanica 159 (2002), 87 – 124.
[2] A. Lion, J.Retka, M.Rendek On the calculation of predeformation-dependent dynamic modulus
tensors in finite nonlinear viscoelasticity, Mechanics Research Communications 36
(2009), 653 – 658.
A multi-scale modelling approach for bituminous asphalt
Thorsten Schüler, Ralf Jänicke, Holger Steeb (Universität Bochum) Schedule
Bituminous asphalt is a standard material e.g. in road constructions. However, the term asphalt
involves an extremly broad class of complex multi-scale and multi-phase materials. Typically,
asphalt consists of a mineral filler (e.g. crushed rock), a bituminous binding agent (possibly including
further additive compounds) and pores. The various constituents are to be adapted for
the particular application.

Section 6: Material modelling in solid mechanics 135
Nowadays, requirements on noise reduction of road constructions become more and more important.
In our ongoing research activities, we focus on the solid-borne acoustic properties of the
asphalt cover layer, i.e. the top layer of the entire asphalt-construction. In order to predict the
macro-scale effective material properties of asphalt we apply a numerical homogenisation scheme
based on volume averaging techniques. The main advandtage of this numerical approach is, that
the effective material properties can be determined in knowledge of the micro-scale properties.
Hence, the first step towards an overall model for bituminous asphalt is the quantification of
the micro-scale mechanical properties. Against the background of solid-borne acoustical properties
we restrict ourselves to a geometrically linear description involving only small deformations
on both, macro- and micro-scale. Doing so, the linear-elastic properties of the stiff, granular filler
can be adopted from relevant literature. The viscoelastic behaviour of the bituminous phase is
characterized by rheological experiments (dynamic shear rheometer with plate-plate geometry).
The numerical implementation on the micro-scale is realized using a generalized Zener model (3d).
Making use of the numerical homogenization approach, the effective viscoelastic properties on
the macro-scale are investigated within transient experiments (relaxation/creep test). In particular
we are interested in the particular relaxation mechanisms and the related characteristic frequencies
to be observed on the macro-scale. The influence of micro-scale boundary conditions will be
taken into account. In order to study the interaction between micro-constituents as well as their
geometrical morphology on the one hand and the effective viscoelastic properties on the other,
we introduce artificially produced periodic unit cells based on simplified geometries with varying
volume and surface fractions of the mineral filler.
Jumps of the critical tracking loadings for viscoelastic beams with vanisihing internal
viscosity
S.A.Agafonov (Moscow State Technical University), D.V.Georgievskii (Moscow State University)
Schedule
Transverse vibrations of a viscoelastic beam under action of a tracking loading are considered.
The constitutive relation represents the following non-linear connection of stress σ(t), strain ε(t)
and strain rate ˙ε(t):
σ = Eε +
where E is the Young modulus, k (n)
i
N�
n�
n=1 i=1
k (n)
i ε2(n−i) ˙ε 2i−1 , N ≥ 1
> 0 are the coefficients of internal viscosity.
Analytical and numerical investigation of dynamic stability in case N = 3, k (1)
1 = 0, k (2)
1 = 0,
k (1)
2 = 0 shows that if k (3)
α → 0 (k (3)
β
= 0, k(3)
γ = 0; (α, β, γ) may be some permutation of (1, 2, 3))
then three critical values of tracking loading corresponding to each nonzero coefficient of viscosity
k (3)
α less than the value for elastic system by a finite quantity.
Numerical modeling of a non-linear viscous flow in order to determine how parameters
in constitutive relations influence the entropy production
Wolfgang H. Müller, B. Emek Abali (TU Berlin) Schedule
Some rheological materials like melting polymers, cosmetic creams, ketchup, toothpaste can be
modeled as non-Newtonian fluids by using a non-linear constitutive relation. Flow of this kind
of amorphous matter can be considered as a thermodynamic process, and a solution of pressure,
velocity and temperature fields describe it fully. Since flow processes are generally irreversible,
entropy is produced leading to dissipation in the system. This energy loss can be measured

136 Section 6: Material modelling in solid mechanics
indirectly in a cone/plate viscometer which is used to determine viscosity of a Bingham fluid.
While dissipation is a measurable quantity we want to be able to calculate it. Thus the goal of
this work is to explain how to calculate entropy production using balance equations in a spatial
frame.
Starting from balance of mass, linear momentum, internal energy and employing method
of weighted residuals, we get a non-linear coupled set of partial differential equations in space
and time. A space discretization in finite elements method and a time discretization in finite
difference method leads to an approximation after a successful linearization. We achieve to solve
the problem without any stabilization or usage of specific type of elements and show here the
entropy production and its variation subject to material parameters for the sake of a better
intuitive understanding of dissipation. This may lead to an inverse problem where the calculated
dissipation is measured and material parameters are determined out of it, which is left to future
research.
S6.7: Phase Transformations II Wed, 16:00–18:00
Chair: Wolfgang Dreyer S1|01–A03
Nonsingular Dislocation Loops in Gradient Elasticity
Markus Lazar (TU Darmstadt) Schedule
This work studies the fundamental problem of nonsingular dislocations in the framework of the
theory of gradient elasticity. A general theory of nonsingular dislocations is developed for linearly
elastic, infinitely extended, homogeneous, isotropic media. Using gradient elasticity, we give the
nonsingular fields produced by arbitrary dislocation loops. We present the ‘modified’ Mura, Peach-
Koehler and Burgers formulae in the framework of gradient elasticity theory. These formulae are
given in terms of an elementary function, which regularizes the classical expressions, obtained
from the Green tensor of generalized Navier equations. Using the mathematical method of Green’s
functions and the Fourier transform, we found exact, analytical and nonsingular solutions. The
obtained dislocation fields are nonsingular due to the regularization of the classical singular fields.
On a paradox within the phase field modeling of storage systems and its resolution
Clemens Guhlke, Wolfgang Dreyer (WIAS Berlin) Schedule
We study two import storage problems: The storage of lithium in an electrode of a lithium-ion
battery and the storage of hydrogen in hydrides.
When foreign atoms are reversibly stored in a crystal, there may be a regime where two coexisting
phases with low and high concentration of the stored atoms occur. Furthermore hysteretic
behavior can be observed, i.e. the processesof loading and unloading follow different paths.
We apply a viscous Cahn-Hilliard model with mechanical coupling to calculate the voltagecharge
diagram of the battery, respectively the pressure-charge diagram of a hydrogen system.
The diagrams exhibit phase transition and hysteresis. However, we show that the model can only
describe the observed phenomena for fast but nor for slow loading.
We relate the reason for failure to the microstructure of modern storage systems. In fact these
consist of an ensemble of nano-sized interconnected storage particle. Each particle is described by
a non-monotone chemical potential function but on the time scale of slow loading of the ensemble,
the coexisting phases are unstable within an individual particle and cannot be observed on the
time scale of the loading.
In the slow loading regime, the occurence of two coexisting phases phases is a many-particle
effect of the ensemble. The nucleation and evolution of the phases is embodied by a nonlocal

Section 6: Material modelling in solid mechanics 137
conservation law of Fokker-Planck type.
Numerical Simulation of Coarsening in Metallic Alloys
Uli Sack, Carsten Gräser, Ralf Kornhuber (FU Berlin) Schedule
Phase separation phenomena in alloys, such as spinodal decomposition and Ostwald ripening
can be described by phasefield models of Cahn-Hilliard-type. Realistic models based on thermodynamically
correct logarithmic free energies contain highly nonlinear and singular terms as
well as drastically varying length scales (cf. [1]). We present a globally convergent nonsmooth
Schur-Newton Multigrid method for vector-valued Cahn-Hilliard-type equations ([2, 3]) and a
numerical study of coarsening in a binary eutectic AgCu alloy taking into account elastic effects.
Vector-valued Cahn-Hilliard computations open the perspective to multicomponent simulations.
[1] W. Dreyer, W.H. Müller, F. Duderstadt and T. Böhme, “Higher Gradient Theory of Mixtures”,
WIAS-Preprint No 1286 (2008)
[2] C. Gräser and R. Kornhuber, “Nonsmooth Newton Methods for Set-valued Saddle Point
Problems”, SIAM J. Numer. Anal. (2009) 47 (2)
[3] C. Gräser, R. Kornhuber, “Schur-Newton Multigrid Methods for Vector-Valued Cahn–Hilliard
Equations”, in prep
A Phase Field Model for Martensitc Transformations
Regina Schmitt, Ralf Müller, Charlotte Kuhn (TU Kaiserslautern) Schedule
Considering the microscopic level of steel, there are different structures with different mechanical
properties. Under mechanical deformation the metastable austenitic face-centered cubic phase
transforms into the tetragonal martensitic phase at which transformation induced eigenstrain
arises. On the other hand, the mircostructure affects the macroscopic mechanical behavior of
the specimen. In order to take the complex interactions into account, a phase field model for
martensitic transformation is developed. Within the phase field approach, an order parameter
is introduced to indicate different material phases. Its time derivative is assumed to follow the
time-dependent Ginzburg-Landau equation. The coupled field equations are solved using finite
elements together with an implicit time integration scheme. With the aid of this model, the effects
of the elastic strain minimization on the formation of microstructure can be studied so that the
evolution of the martensitic phase is predictable. The applicability of the model is illustrated
through different numerical examples.
Investigation of the strain localization behavior with application of the phase transition
approach
M. Ievdokymov, H. Altenbach, V.A. Eremeyev (Universität Magdeburg) Schedule
Metal foams found recently many applications in civil, airspace and mechanical engineering. In
particular, foams have a good energy absorption property. This property relates to the phenomenon
of localization of strains in foams under loading. In porous materials the localization of
strains leads to change of mass density of material and appearance of areas with low and high
densities separated by sharp interface. This behavior is similar to the phase transitions in solids
with sharp interfaces.
In this paper we use the methods of modelling of phase transitions in solids to the description of
strain localization in foams. We assume that the foam consist of two phases with different densities

138 Section 6: Material modelling in solid mechanics
and mechanical properties. The results of modelling of one- and two-dimensional problems are
discussed. The calculations are performed by Abaqus and script language Python.
S6.8: Elasticity, Viscoelasticity, -plasticity II Wed, 16:00–18:00
Chair: Ismail Caylak S1|01–A1
A New Continuum Approach to the Coupling of Shear Yielding and Crazing with
Fracture in Glassy Polymers
Lisa Schänzel, Christian Miehe (Universität Stuttgart) Schedule
Over the past decades, considerable effort was made to develop constitutive models that account
for finite viscoplasticity and failure in glassy polymers. Recently, we developed a new model
of ductile thermoviscoplasticity of glassy polymers in the logarithmic strain space [1]. However,
depending on thermal and loading rate conditions to which the material is subjected, the response
might change from ductile to brittle. This brittle response is characterized by inelastically deformed
zones, so-called crazes, having the thickness of micrometers and spanning at some fractions of
a millimeter [2]. The crazing is associated with considerable dilatational plasticity, containing a
dense array of fibrils interspersed with elongated voids. The shear yielding and crazing are not
completely independent excluding each other. In this lecture, we outline an extension of the ductile
plasticity model [1] towards the description of (i) volumetric directional plasticity effect due to
crazing and (ii) the modeling of the local failure due to fracture. To this end, the first extension
accounts for a (i) dilatational plastic deformation mechanism in the direction of the maximum
principle tensile stress. The ultimate amount of this volumetric plastic craze strain is bounded
by a limiting value, where failure occurs. Then, in a second step, the (ii) modeling of subsequent
failure mechanisms is realized by the introduction of a fracture phase field, characterizing via an
auxiliary variable the crack topology. Here, we adopt structures of a recently developed continuum
phase field model of fracture in brittle solids [3], and modify it for a fracture driving term related
to the volumetric plastic deformation of the crazes. We demonstrate the performance of proposed
formulation by means of representative boundary value problems.
[1] Miehe, C.; Mendez, J.; Göktepe, S.; Schänzel, L. [2011]: Coupled thermoviscoplasticity of
glassy polymers in the logarithmic strain space based on the free volume theory. International
Journal of Solids and Structures, 48: 1799–1817.
[2] Kramer, E. J.[1983]:Microscopic and Molecular Fundamentals of Crazing. Advances in Polymer
Science, 52/53: 1–56.
[3] Miehe, C; Hofacker, M.; Welschinger, F. [2010]: A phase field model for rate-independent
crack propagation: Robust algorithmic implementation based on operator splits. Computer
Methods in Applied Mechanics and Engineering, 199: 2765-2778.
Anisotropic finite strain hyperelasticity based on the multiplicative decomposition of
the deformation gradient
Raad Al-Kinani, Kaveh Talebam, Stefan Hartmann (TU Clausthal) Schedule
Frequently, the case of finite strain anisotropy, particularly, the case of transversal isotropy, is
applied to biological applications or to model fiber-reinforced composite materials. In this article
the multiplicative decomposition of the deformation gradient into one part constrained in the direction
of the axis of anisotropy and one part describing the remaining deformation is proposed.

Section 6: Material modelling in solid mechanics 139
Accordingly, a form of additively decomposed strain-energy function is proposed. This leads to a
clear assignment of deformation and stress states in the direction of anisotropy and the remaining
part. The decomposition of the case of transversal isotropy is explained. The behavior of the
model is investigated at different simple analytical examples, such as uniaxial tension along and
perpendicular to the axis of anisotropy, and simple shear. In addition, the model is also studied for
the case of a thick-walled tube under internal pressure, where a second order ordinary differential
equation (two-point boundary-value problem) is obtained.
Experimental characterization of the viscoelastic behaviour of discontinuous glass
fibre reinforced thermoplastics
B. Brylka, T. Böhlke (KIT) Schedule
In automotive applications short and long glass fibre reinforced thermoplastics are commonly used
for non-structural parts. Due the versatile possibilities of manufacturing, forming, joining and
recycling, thermoplastic matrix based composites are increasingly used also for semi-structural
parts. Thermoplastics like e.g. polypropylene show a high temperature and strain-rate dependency,
especially in the temperature and strain-rate ranges which are relevant for automotive
applications. Additionally, the non-linear influence of the viscoelastic behaviour of the matrix
material on the effective material behaviour of the composite is of high interest.
The dynamic mechanical analysis (DMA) technique is an effective method to investigate the
elastic and viscoelastic stiffness response of materials under cyclic loading. After a short introduction
into the DMA technique, experimental results for a polypropylene and polypropylene based
composite material will be presented. The composite under consideration is an discontinuous glass
fibre reinforced polypropylene. In the manufacturing process, which is commonly compression or
injection moulding, the flow of the mould induces an heterogeneous and anisotropic distribution
of fibre orientations. Therefore, the effective properties as well as the temperature and strain-rate
dependency has been investigated taking into account an anisotropic material behaviour. The
comparison of the elastic and viscoelastic material response of the matrix and the composite will
be discussed in detail. Additionally, a parameter identification for common viscoelastic material
models will be presented.
[1] Middendorf, P.: Viskoelastisches Verhalten von Polymersystemen, Fortschritt-Berichte VDI,
Reihe 5, VDI Verlag (2002).
[2] Deng, S., Hou, M., Ye, L.: Temperature-dependent elastic moduli of epoxies measured by
DMA and their correlations to mechanical testing data, Polym. Test., 26, 803-813 (2007).
[3] Schledjewski, R., Karger-Kocsis, J.: Dynamic mechanical analysis of glass mat-reinforced
polypropylene (GMT-PP), J. Thermoplast. Compos., 7, 270-277 (1994).
A solid-shell finite element for fibre reinforced composites
J.-W. Simon, B. Stier, S. Reese (RWTH Aachen) Schedule
Fibre reinforced composites are typically characterized by high Young’s modulus at low density,
which makes them very attractive for lightweight constructions. The fibre composites considered
here consist of several layers, each of which is composed of a woven fabric embedded in a matrix
material. This structure makes the constitutive behavior of fibre composites anisotropic. Moreover,
it is generally highly nonlinear, and the materials’ response in tension and compression can

140 Section 6: Material modelling in solid mechanics
differ significantly. In order to describe this rather complex behavior, we use a modification of
a micromechanically motivated model proposed by Reese [1]. Therein, an anisotropic model has
been presented for the hyperelastic material behavior of membranes reinforced with roven-woven
fibres, which is particularly suitable for the present fibre reinforced composites.
The use of a fully three-dimensional material model strongly suggests using solid elements.
On the other hand, fibre composites are mostly applied in thin shell-like structures, where shell
elements should usually be preferred. Therefore, we use a solid-shell element presented by Schwarze
and Reese [2] which combines the advantages of both solid elements and shell elements at the
same time. This element allows for displaying realistically the three-dimensional geometry while
still providing the suitable shape for thin structures.
In addition, the present solid-shell formulation utilizes a reduced integration scheme within the
shell plane using one integration point, whereas a full integration is used in thickness direction.
Thus, an arbitrary number of integration points can be chosen over the shell thickness. Thereby,
different fibre orientations of the layers can be taken into account easily, since the material
parameters can be defined for each integration point separately.
Moreover, the proposed solid-shell formulation removes all potential locking phenomena. In
particular, volumetric locking in case of (nearly) incompressible materials as well as Poisson
thickness locking in bending problems of shell-like structures are eliminated by use of the enhanced
assumed strain (EAS) concept. In addition, to cure the transverse shear locking which is present
in standard eight-node hexahedral elements, the assumed natural strain (ANS) method is applied.
[1] S. Reese. A micromechanically motivated material model for the thermo-viscoelastic material
behaviour of rubber-like polymers, Int J Plast, 19, 909–940, 2003.
[2] M. Schwarze, S. Reese. A reduced integration solid-shell finite element based on the EAS and
the ANS concept - large deformation problems, Int J Numer Methods Engng, 85, 289–329,
2011.
On consistent tangent operator derivation and comparative study of rubber-like material
models at finite strains
Mokarram Hossain, Paul Steinmann (Universität Erlangen-Nürnberg) Schedule
The overall micro-structure of rubber-like materials can be idealized by chain-like macromolecules
which are connected to each other at certain points via entanglements or cross-links. Such
special structure leads to a completely random three-dimensional network [2,3]. To model the
mechanical behaviour of such randomly-oriented micro-structure, several phenomenological and
micro-mechanically motivated network models for nearly incompressible hyperelastic polymeric
materials have been proposed in the literature. To implement these models for polymeric material
(undoubtedly with widespread engineering applications) in finite element method, one would
require two important ingredients, e.g. the stress tensor and the consistent fourth-order tangent
operator where the latter is the result of linearization of the former.
In this contribution, an extensive overview on several hyperelastic rubber-like material models
has been presented. Special focus is given particularly to derive the accurate stress tensors and
tangent operators which yield quadratic convergence when the governing nonlinear equations for
a boundary value problem are solved by the Newton-like iterative schemes. A simple but efficient
algorithm will be demonstrated to testify the correctness of the tangent operator locally of a
particular model without going into details of the finite element implementation [1].

Section 6: Material modelling in solid mechanics 141
[1] Steinmann P, Hossain M, Possart G (2011), Hyperelastic models for rubber-like materials:
Consistent tangent operators and suitability for Treloar’s data. Archive of Applied Mechanics,
In review (2011)
[2] Boyce MC, Arruda EM (2000), Constitutive models of rubber elasticity: a review. Rubber
Chemistry and Technology, 73: 504-523, 2000
[3] Marckmann G, Verron E (2006), Comparison of hyperelastic models for rubber-like materials.
Rubber Chemistry and Technology, 79 (2006) 835-858
Accelerating constitutive modeling by automatic tangent generation
Steffen Rothe, Stefan Hartmann (TU Clausthal) Schedule
Nowadays models become more and more complex. Within the framework of finite elements a
material, i.e. consistent, tangent is required for the overall Newton-like method. Obtaining these
derivatives is time consuming and error-prone which contradicts to the goal of changing the model
during the developing process. On the one hand the calculation by hand can be very expensive
and on the other hand also the implementation has to be done with high diligence. Therefore, a
fast and safe way of consistent tangent generation will be presented with the help of automatic
differentiation (AD) techniques.
Analytical tangents have the advantage that they are exact. However during the constitutive
modeling process a change of the model is natural. Thus, the effort is very high to calculate
the derivative after every modification. Numerical tangents computed by finite differences are
easy to compute, but can lead to a significant slowdown or even to a failure of the simulation
due to numerical errors. Tangents generated by OpenAD have no round-off errors and are easily
computed by the help of automatic differentiation.
These three methods (analytical, numerical and automatic differentiation) for tangent generation
will be analyzed concerning the simulation time and applicability for a number of different
constitutive models.
S6.9: Microheterogeneous Materials Thu, 13:30–15:30
Chair: Johannes Schnepp, Eleni Agiasofitou S1|01–A03
The boundary value problems of the full coupled theory of poroelasticity for materials
with double porosity
Merab Svanadze (Ilia State University, Tbilisi) Schedule
Porous materials play an important role in many branches of engineering, e.g., the petroleum industry,
chemical engineering, geomechanics, and, in recent years, biomechanics. The construction
and the intensive investigation of the theories of continua with microstructures arise by the wide
use of porous materials into engineering and technology.
The general 3D theory of poroelasticity for materials with single porosity was formulated by
Biot (1941). The double porosity model was first proposed by Barenblatt and coauthors (1960).
The quasi-static theory of poroelasticity for materials with double porosity in the framework of
mixture theory was presented by Aifantis and his co-workers (1982).
In this paper the full coupled theory of poroelasticity for materials with double porosity is
presented. This theory unifies the earlier proposed quasi-static model of Aifantis of consolidation
with double porosity. The boundary value problems (BVPs) of the steady vibrations are investigated.
The fundamental solution of system of equations of steady vibrations is constructed. The

142 Section 6: Material modelling in solid mechanics
basic properties of plane waves and the radiation conditions for regular vector are established. The
uniqueness theorems of the internal and external BVPs of steady vibrations are proved. The basic
properties of elastopotentials are established. The representation of general solution of equations
of steady vibrations is obtained. The existence of regular solution of the BVPs by means of the
boundary integral method and the theory of singular integral equations are proved.
Application of an anisotropic growth and remodelling formulation to computational
topology optimisation
Tobias Waffenschmidt (TU Dortmund), Andreas Menzel (TU Dortmund / Lund University) Schedule
A classical topology optimisation problem consists of a problem-specific objective function which
has to be minimised in consideration of particular constraints with respect to design and state
variables. In this contribution we present a conceptually different approach for the optimisation or
rather improvement of the topology of a structure which is not based on a classical optimisation
technique. Instead, we establish a constitutive micro-sphere-framework in combination with an
energy-driven anisotropic microstructural growth formulation, which was originally proposed for
the simulation of adaptation and remodelling phenomena in hard biological tissues such as bones.
The key aspect of this contribution is to investigate this anisotropic growth formulation with
a special emphasis on its topology-optimising characteristics or rather topology-improving properties.
To this end, several illustrative three-dimensional benchmark-type boundary value problems
are discussed and compared qualitatively with the results obtained by classic topologyoptimisation
strategies. The simulation results capture the densification effects and clearly identify
the main load bearing regions. It turns out, that even though making use of this conceptually
different growth formulation as compared to the procedures used in the more classic topologyoptimisation
context, we identify qualitatively very similar topologies. Moreover, in contrast to
common topology optimisation strategies, which mostly aim to optimise merely the structure,
i.e. size, shape or topology, our formulation also contains the optimisation or improvement of the
material itself, whichapart from the structural improvementresults in the generation of problemspecific
local material anisotropy and textured evolution.
Amplification damping properties of multiphase composites with spherical and fibers
inclusions
Sergey Lurie (Institute of Applied Mechanics, RAS), Natalia Tuchkova (Dorodnicyn Computing
Centre, RAS), Juri Soliaev (Institute of Applied Mechanics, RAS) Schedule
We consider composite materials reinforced with spherical and fibrous inclusions coated with a
layer of lossy viscoelastic material. For the coating layers, typical viscoelastic properties of a polymer
at and well above the glass transition region are assumed. It is shown that the remarkable loss
amplification mechanism is also operative in such particulate-morphology materials. The aim of
our study is to determine the effective loss modulus composites, which formally defines the rate
of energy dissipation per unit volume. We use a combination of modeling and numerical tools
to study composite materials consisting of a matrix filled with spherical and fibrous inclusions
coated with a layer of lossy viscoelastic material.
The method of the four phases is used to describe the damping properties of composites
filled with multiphase spherical inclusions and monolayer with multiphase fibrous inclusions. The
constituent phases are supposed to be isotropic. Using the Eshelby method the effective moduli
are determined self-consistently, by requiring that the average strain in the composite inclusion
is the same as the macroscopic strain imposed at infinity. The analytical solution of this problem
were received. The effective dynamic modulus and loss modulus were found using a viscoelastic

Section 6: Material modelling in solid mechanics 143
analogy.
It is shown[1] that the analytical give very similar, practically indistinguishable predictions
from the numerical solutions which were received using finite element method. Hence, when
studying such systems one can rely on the predictions of the four-phase sphere model, which
are much easier to achieve than the finite element ones. a polymer at and well above the glass
transition region are assumed. It is shown that by optimizing the thickness of the layers, one can
achieve multiphase materials with effective loss characteristics significantly exceeding those of the
individual materials constituents. It was found that for the considered composites have place the
additional peak damping properties, which is realized for very small thicknesses of the viscoelastic
phase. This peak is still about a factor 20 or so compared to the loss modulus of the pure matrix.
We demonstrated that by introducing thin layers of a viscoelastic material, one can significantly
increase the loss characteristics of discrete morphology multiphase materials. The layered fibers
composites are also considered. It is shown that for such materials may be implemented at the
same time as high elastic properties, and abnormally high damping properties.
[1] A.A.Gusev , S.A. Lurie, Loss amplification effect in multiphase materials with viscoelastic
interfaces. Macromolecules (2009) 42,14, 5372 – 5377.
Modeling of composite structural elements made from aramid fiber using the method
of features objects
Michał Majzner, Andrzej Baier (Silesian University of Technology) Schedule
The use of modern materials such as composite materials, enabling the production of new or modifying
existing design solutions, improve their technical characteristics, while use in the process
of design and engineering and manufacturing, will allow the modification of endurance, physical
and chemical properties to match the features and functionality that are comply with. In research
studies, it is proposed to systematize and formalize elementary objects in the context of modeling
and fabrication of objects created on the basis of structural fiber composites. Application of features
objects methods was shows on an example of modeling the structural element, in the form
of an existing manufactured from steel, which was modified and converted with aramid fiber. It
was necessary to carry out research in the form of numerical analysis, examining the strength of
the modified object.
On the fibres shape effect for non-linear and unidirectional stationary heat conduction
in two-phase hollow cylinder with radially graded material properties
Piotr Ostrowski (Technical University of Lodz) Schedule
The main aim of this paper is to consider unidirectional and stationary heat conduction in the
infnite two-phase hollow cylinder with temperature dependent material properties. The deterministic
microstructure of this composite is periodic (for a fixed radius) along the angular axis
and has slowly varying effective properties in the radial direction. Therefore, we deal here with
a special case of functionally graded materials, FGM, c.f. Suresh, Mortensen (1998). One of the
components is called fibre, which is arranged in considered hollow cylinder with circular pattern.
The physical phenomenon of the heat transfer is described by well known Fourier’s equation
c ˙ θ − ∇(K∇θ) = 0, (1)
which contains temperature dependent (in this case), highly oscillating and discontinuous coefficients
of K = K(θ) - heat conduction tensor, and c = c(θ) - specific heat. To this macroscopic
model the tolerance averaging approximation will be used, cf. Wozniak, Wierzbicki (2000). The

144 Section 6: Material modelling in solid mechanics
general approach to the description of longitudinally graded stratified media can be found in
[Wozniak, Michalak, Jedrysiak 2008]. The fibres width function g = g(r) of radius r will be examined
and its effects on the temperature field. The averaged differential equation has smooth
and slowly varying coefficients, hence in some special cases, for boundary value problem, analytical
solution can be obtained. In other cases, numerical methods have to be used. This model
takes into account the effect of microstructure size on the overall heat transfer behaviour.
[1] S. SURESH, A. MORTENSEN, Fundamentals of functionally graded materials, Cambridge,
The University Press, 1998.
[2] Cz. WOZNIAK, B. MICHALAK, J. JEDRYSIAK (eds), Thermomechanics of micro-heterogeneous
solids and structures. Tolerance averaging approach, Wydawnictwo Politechniki Lodzkiej,
Lodz, 2008.
S6.10: Elasticity, Viscoelasticity, -plasticity III Thu, 13:30–15:30
Chair: Daniel Balzani S1|01–A1
Network evolution model: thermodynamics consistency, parameter identification and
finite element implementation
Vu Ngoc Khiêm, Roozbeh Dargazany, Mikhail Itskov (RWTH Aachen) Schedule
In this contribution, the previously proposed network evolution model [1] for carbon black filled
elastomers is further studied. First, we show that the model does not contradict the second law of
thermodynamics and is thus thermodynamically consistent. On the basis of new experimental data
the influence of filler concentration on the material parameters is further examined. Accordingly,
this influence concerns only three material parameters and is approximated by phenomenological
relations. These relations enable one to simulate rubbers based on the same compound with
various filler concentrations. Finally, the model is implemented to the FE-Software ABAQUS and
illustrated by a number of numerical examples. The examples demonstrate good agreement with
experimental results with respect to the Mullins-Effect, permanent set and induced anisotropy.
[1] R. Dargazany and M. Itskov, A network evolution model for the anisotropic Mullins effect
in carbon black filled rubbers, International Journal of Solids and Structures 46 (2009),
2967–2977.
Shakedown analysis of periodic composites with kinematic hardening material model
Min Chen, A. Hachemi, D. Weichert (RWTH Aachen) Schedule
Lower-bound limit and shakedown analysis of periodic composites with the consideration of kinematic
hardening are investigated on the representative volume element. With the combination of
homogenization theory, the homogenized macroscopic admissible loading domains are evaluated.
Furthermore, the strengths of periodic composites of elastic-perfectly plastic, unlimited and linear
limited kinematic hardening material models are calculated and compared in this paper.
Theory of mixture based material modeling - An inelastic material model for a 12%chromium
steel
Andreas Kutschke, Konstantin Naumenko, Holm Altenbach (Universität Magdeburg) Schedule

Section 6: Material modelling in solid mechanics 145
Components composed of advanced heat resistant steels face a complex loading of mechanical and
thermal stresses under cyclic and long-term conditions. Additionally, a failure of these components
usually has serious outcome, because of the extreme working conditions. From this follows the
need of a reliable material model for the construction process.
Classical technical guidelines are historically grown and the experience of engineers contributed
to their development, but it turns out that these classical guidelines face their limit of use. Recently
more sophisticated material models are developed to reach the real limit of the materials and to
predict their behavior with more accuracy.
Starting with the theoretical concept of Prandtl, who introduced the idea of a hardening
substance in a material, and the investigations of Mughrabi, who established a composite model
for chromium steels, the advanced steels are treated as a composition of at least two continua, in
the sense of the theory of mixture.
Therefore the general balance equations for a mixture will be presented. The example of a
12% chromium steel will be used to illustrate this approach and to derive a material model for
a mixture of two constituents. It will be shown that the model predicts tension-, compression-,
cyclic-creep, uniaxial monotonic tension und low-cycle-fatigue loading in a satisfying manner in
comparison with experimental results.
Zur Abtragssimulation beim Strömungsschleifen (AFM)
Joachim Schmitt, Stefan Diebels (Universität des Saarlandes) Schedule
Im Zuge konkurrenzfähiger Produktionsverfahren werden seit einigen Jahren schwer zugängliche
Kanten im Inneren von komplex aufgebauten Fertigungsteilen (wie beispielsweise die Gehäuse von
Einspritzanlagen) mittels des Strömungsschleifens (Abrasive flow machining - AFM) verrundet
bzw. oberflächenvergütet. Dazu wird eine mit Schleifpartikeln versetzte Silikonpaste mehrfach
durch das Bauteil gepresst. Das viskose Verhalten der Paste ist dabei für die effektive Wirkung
dieses Verfahrens sehr wichtig. Beim Überströmen von Kanten steigt die Schergeschwindigkeit und
damit auch die Viskosität je nach Materialmodell überproportional an. Die so geänderten Druckund
Geschwindigkeitsverhältnisse an der Bauteiloberfläche verändern auch den Materialabtrag
durch die Schleifpaste.
Im Rahmen dieser Studie werden zunächst die viskosen Eigenschaften der Paste anhand von
Experimenten untersucht und die Modellparameter bestimmt. Im zweiten Teil wird die Paste
hinsichtlich ihrer abrasiven Eigenschaften vorgestellt und eine Abschätzung des Materialabriebs
vorgenommen. Ein daraus gebildetes einfaches Abtragsmodell wird mittels einer FEM-Simulation
an elementaren Bauteilgeometrien umgesetzt und qualitativ überprüft.
Material parameter identification using model reduction to uniaxial tensile tests
Stephan Krämer, Steffen Rothe, Stefan Hartmann (TU Clausthal) Schedule
Uniaxial tensile tests are commonly used for material parameter identification. It is also common
to use one-dimensional formulations of a constitutive model to identify the corresponding
material constants, although these material parameters are not necessarily identical to the material
parameters in the three-dimensional material model. We present an easy way to reduce a
three-dimensional material routine to the case of uniaxial tension and to use the reduced form
to derive material parameters using common trust-region algorithms. With this approach one
is able to use the full three-dimensional model for parameter identification. Instead of using a
full finite element software, one is able to use the material driver routine, which leads to a more
straight forward calculation of material parameters. In this respect, it is shown that the classical
structure of stress algorithms and consistent tangent operators are necessary within the three-

146 Section 6: Material modelling in solid mechanics
to one-dimensional problem reduction. This procedure is also extendable to further homogeneous
stress- and strain-states.
Systematic representation of the yield criteria for isotropic materials
Vladimir A. Kolupaev (DKI Darmstadt), Holm Altenbach (Universität Magdeburg) Schedule
The theory of plasticity operates with different flow criteria of incompressible material behavior.
These criteria have hexagonal symmetry in the π-plane and do not distinguish between tension
and compression (non-SD-effect). Many tasks in the engineering practice are treated on the basis
of these criteria and the flow rule.
Selection of an appropriate criterion for a specific material is challenging. The models of Tresca
and Schmidt-Ishlinsky, representing two regular hexagons in the π-plane, define accordingly the
lower and the upper limit of convexity. The criteria of Sokolovskij and Ishlinsky-Ivlev describe
the regular dodecagons in the π-plane and have only geometrical meaning. In difference to these
four criteria, the model of von Mises has no singular corners and delivers unique results by the
strain rates calculation.
The evaluation of the measurements shows that the material behavior differs from the idealized
models. The models proposed by Drucker, Dodd-Naruse, Edelman-Drucker and Hershey aim to
better adapt the flow surface. These models are the functions of one parameter. They have no
claims on the generality and are used only for the approximation of the measurements.
Three models with one parameter are known as generalized models: Unified Yield Criterion
(UYC) of Yu, Bi-Cubic Model (BCM), and Multiplicative Ansatz (MA) [1]. These models include
the models of Tresca and Schmidt-Ishlinsky. They allow approximating of existing measurements
better than other models.
This work compares the flow criteria. For this aim their geometries in the π-plane will be
considered in polar coordinates R and ϕ. The radii of the surface at the angles of ϕ = 15 and
30 ◦ are related to the radius at ϕ = 0 ◦ : h = R(15 ◦ )/R(0 ◦ ), k = R(30 ◦ )/R(0 ◦ ). On the basis of
these two relations, well-known criteria will be systematized and shown in the h − k–diagram.
New criteria will be introduced. The convexity limits for them will be stated.
From the h−k–diagram, it is clear that UYC and MA set left and right boundary of convexity.
Thus, the extreme solutions for parts can be found. The two models UYC and MA are the
functions of the parameter k. The linear combination of UYC and MA provides a universal model
with two parameters k and ξ ∈ [0, 1] describing all convex surfaces of incompressible material
behavior of hexagonal symmetry in the π-plane.
The proposed consideration of the flow criteria simplifies the selection of the model and is
suitable for didactic purposes. All known and new flow criteria can be described by universal
model, and thus can be omitted.
[1] Kolupaev, V. A., Altenbach, H.: Considerations on the unified strength theory due to Mao-
Hong Yu, Forschung im Ingenieurwesen 74(3), (2010).
S6.11: Special Methods in Material Modeling Thu, 16:00–18:00
Chair: Bernhard Eidel, Markus Scholle S1|01–A03
Modeling of Carbon Nanotubes by Molecular Mechanics
Oliver Eberhardt, Thomas Wallmersperger (TU Dresden) Schedule
Carbon Nanotubes (CNTs) are structures in the nanoscale consisting of carbon atoms which are
arranged in a hexagonal lattice. Hence, they can be imagined as a plane sheet of graphene rolled

Section 6: Material modelling in solid mechanics 147
into a seamless tube. By doing so we obtain a so called Single Wall Carbon Nanotube (SWCNT).
Besides Single Wall Carbon Nanotubes also Double Wall Carbon Nanotubes (DWCNT) and, in
general, Multi Wall Carbon Nanotubes (MWCNT) exist. Their high stiffness and active deformation
of approx. 1 % at applied low electric voltages (approx. 1 V) make the Carbon Nanotubes a
very promising material for applications e.g. in new classes of composites and actuators/sensors.
In this research the approach to model Carbon Nanotubes is made by using molecular mechanics.
The aim of these efforts is to determine the mechanical properties, for example the Young’s
modulus. The Molecular Mechanics method originates in the investigation of the properties of
big molecules which due to their size cannot be handled by quantum mechanical methods. In
Molecular Mechanics the behavior of the covalent bonds in a Single Wall Carbon Nanotube is
represented by a set of potentials. Here every single potential expression describes a corresponding
bond deformation. As a result of the description of the bonds by potentials, the force acting
between the atoms can be calculated as the derivatives of the potentials with respect to their
corresponding displacement variable. Hence, the Carbon Nanotube is modeled by point masses
representing the carbon atoms and a set of springs or beam elements representing the bonds. Regarding
Multi Wall Carbon Nanotubes this model can be extended by adding the van-der-Waals
interactions, described by another potential.
During the process of modeling and also during the evaluation of the results we have to rise
several challenges. Since the Molecular Mechanics method is a so called semi-empiric method we
have to choose between different sets of potentials. Some of these potentials - leading to linear
or nonlinear behavior of the interaction forces between the atoms - are investigated regarding
their advantages and disadvantages. In order to illustrate this we compare the (theoretical) results
available in literature with our numerical results, which we obtain by using the model to
conduct a virtual tensile test. The dependance of the Young’s modulus on type and diameter of
the Carbon Nanotubes is discussed.
Dislocation Dynamics in Quasicrystals
Eleni Agiasofitou, Markus Lazar (TU Darmstadt), Helmut Kirchner (Leibniz Institut für neue
Materialien, Saarbrücken) Schedule
In this work, we present a theoretical framework of dislocation dynamics in quasicrystals [1] according
to the continuum theory of dislocations. Quasicrystals have been discovered by Shechtman
et al [2] in 1982 opening a new interdisciplinary research field. A comprehensive presentation of
the current state of the art of this research field, focused on the mathematical theory of elasticity,
can be found in the recently published book of Fan [3].
We start presenting the fundamental theory of moving dislocations in quasicrystals giving
the dislocation density tensors and introducing the dislocation current tensors for the phonon
and phason fields, including the Bianchi identities. In the literature, there exist different versions
of generalized linear elasticity theory of quasicrystals. The difference of these versions lies in the
dynamics of phonon and phason fields. In the present work, we deal with the elastodynamic as well
as the elasto-hydrodynamic model of quasicrystals. According to the first model, the equations of
motion are of wave-type for both phonons and phasons while according to the second model the
equations of motion for the phonons are equations of wave-type and for the phasons are equations
of diffusion-type. Therefore, we give the equations of motion for the incompatible elastodynamics
as well as for the incompatible elasto-hydrodynamics of quasicrystals.
We continue with the derivation of the balance law of pseudomomentum thereby obtaining
the generalized forms of the Eshelby stress tensor, the pseudomomentum vector, the dynamical
Peach-Koehler force density and the Cherepanov force density for quasicrystals. Moreover, we
deduce the balance law of energy that gives rise to the generalized forms of the field intensity

148 Section 6: Material modelling in solid mechanics
vector and the elastic power density of quasicrystals. The above balance laws are produced for
both models. The differences between the two models and their consequences are revealed. The
influences of the phason fields as well as of the dynamical terms are also discussed.
[1] E. Agiasofitou, M. Lazar and H. Kirchner, Generalized dynamics of moving dislocations in
quasicrystals, J. Phys.: Condens. Matter 22 (2010), 495401 (8pp).
[2] D. Shechtman, I. Blech, D. Gratias and J. W. Cahn, Metallic phase with long-range orientational
order and no translational symmetry, Phys. Rev. Lett. 53 (1984), 1951 – 1953.
[3] T. Fan, Mathematical Theory of Elasticity of Quasicrystals and its Applications, Science
Press Beijing and Springer-Verlag Berlin, 2011.
On inverse form finding based on an ALE formulation
Sandrine Germain, Paul Steinmann (Universität Erlangen-Nürnberg) Schedule
A challenge in the design of functional parts in forming processes is the determination of the
initial, undeformed shape such that under a given load a part will obtain the desired deformed
shape. Two numerical methods might be used to solve this problem, which is inverse to the
standard kinematic analysis in which the undeformed shape is known and the deformed shape
unknown.
The first method deals with the formulation of an inverse mechanical problem, where the
spatial (deformed) configuration and the mechanical loads are given. Hence the objective is to
find the inverse deformation map that determines the (undeformed) material configuration.
The second method deals with shape optimization that predicts the initial shape in the sense
of an inverse problem via successive iterations of the direct problem. In [1] a nodes-based shape
optimization approach for elastoplastic materials based on logarithmic strains is presented. An
update of the reference configuration is considered in order to avoid mesh distortions, which often
occur in nodes-based optimization problems. The principal drawback is the high computational
costs. An alternative is an Arbitrary-Lagrangian-Eulerian (ALE) formulation [2,3], which is neither
purely Lagrangian (the nodes are not attached to the material) nor purely Eulerian (the nodes
are not fixed in space). The nodes are free to move in space independently of the material.
In this contribution we review the ALE formulation [2,3] for anisotropic hyperelastic materials
and its application in shape optimization. Several examples illustrate the ALE approach in
hyperelasticity. Results and computational costs are compared with the ones obtained with the
approach in [1].
This work is supported by the German Research Foundation (DFG) within the Collaborative
Research Centre SFB Transregio 73.
[1] S. Germain and P. Steinmann. Towards form finding methods for a sheet-bulk-metal (DC04),
15th ESAFORM, Key Engineering Materials submitted (2012).
[2] E. Kuhl et al., An ALE formulation based on spatial and material settings of continuum
mechanics. Part 1: Generic hyperelastic formulation, Comput. Methods Appl. Mech. Engrg.
193 (2004), 4207 – 4222.
[3] H. Askes et al., An ALE formulation based on spatial and material settings of continuum
mechanics. Part 2: Classification and applications, Comput. Methods Appl. Mech. Engrg.
193 (2004), 4223 – 4245.

Section 6: Material modelling in solid mechanics 149
On the direct connection of rheological elements in nonlinear continuum mechanics
Ralf Landgraf, Jörn Ihlemann (TU Chemnitz) Schedule
The direct connection of rheological elements is a widely used concept to develop material models
for one-dimensional deformation processes at small strains. This concept is based on the decomposition
of the total strain into several subparts and the formulation of single material laws for
idealized phenomena (e.g. nonlinear elastic behaviour and viscous or plastic yielding). Several
of those elements are then assembled to one complex material model. This can be achieved by
enforcing the equilibrium of stresses on the connecting points between rheological elements.
Within the scope of nonlinear continuum mechanics there also exists the concept of rheological
elements. The kinematics is described by the deformation gradient which gets multiplicatively
decomposed into several sub deformation gradients. For the definition of the material behaviour,
a common approach is to formulate a free energy function as a sum of sub free energy functions
attributed to the defined sub deformation gradients. By the evaluation of the Clausius-Duheminequality
and under consideration of constitutive assumptions a system of equations describing
a thermodynamically consistent material behaviour can be derived. Depending on particular definitions,
those materials can include a mixture of elastic, viscous and plastic material behaviour.
An alternative approach has been presented by Ihlemann (2006). It is based on the additive
decomposition of the stress power density and leads to a system of equations for the derivation
of the stress equilibrium on defined intermediate configurations as well as the derivation of the
total stresses. Special attention has to be given to the definition of accurate stress measures on
the intermediate configurations. By this approach, a formal procedure for the direct connection of
single elements at large deformation processes can be obtained. The procedure itself is independent
of the concrete material behaviour.
The concept of direct connection of rheological elements in nonlinear continuum mechanics
and some examples for its application will be presented. Furthermore, a numerical strategy for
the direct implementation of this concept will be demonstrated.
[1] J. Ihlemann (2006), Beobachterkonzepte und Darstellungsformen der nichtlinearen Kontinuumsmechanik,
Habilitation, Universität Hannover
A stochastic model for the direct and the inverse problem of adhesive materials
N. Nörenberg, R. Mahnken (Universität Paderborn) Schedule
This work deals with the generation of artificial data [1] based on experimental data for adhesive
materials and the application of this data to the inverse and the direct problem. In reality there are
only a very limited number of experimental data available. Therefore, the prediction of material
behaviour is difficult and a statistical analysis with a stochastic proved thesis is nearly impossible.
In order to increase the number of tests a method of stochastic simulation based on time series
analysis [2] is applied. With artificial data an arbitrary number of data is available and the
process of the parameter identification can be statistically analysed. Additionally, two examples
are shown, which adapt the analysed material parameter to the direct problem. The stochastic
finite element method [3] is used to take into account the distribution and deviation of the fracture
strain.
[1] S. Schwan, Identifikation der Parameter inelastischer Werkstoffmodelle: Statistische Analyse
und Versuchsplanung. Diss. Shaker, 2000.

150 Section 6: Material modelling in solid mechanics
[2] P. J. Brockwell and R. A. Davis, Time series: theory and methods. Springer, 2009
[3] I. Babuška, R. Tempone and G. E. Zouraris, Galerkin finite element approximations of stochastic
elliptic partial differential equations. SIAM Journal on Numerical Analysis 42(2)
(2005), 800 – 825
Analysis of nanoindentation experiments by means of rheological models
Holger Worrack, Wolfgang H. Müller (TU Berlin) Schedule
The nanoindentation technique, which is similar to the instrumented indentation hardness according
to MARTENS, is established in the field of material characterization at small dimensions.
It is daily practice to analyze nanoindentation data with an almost classical formula based on
the publications by Oliver and Pharr and Fischer-Cripps. In this formula the gradient at the
beginning of the unloading curve is used to determine Youngs modulus of the tested material,
which is one of the material parameters of interest.
The procedure works well for elastic time-independent plastic material behavior, for example
copper and the calibration material fused silica, even at higher test temperatures. However, low
melting solder materials are susceptible to creep behavior, especially at the higher indentation
temperatures where the homologous temperature is > 0.5. As a result of the creep effects the
beginning of the unloading curve often shows a bulge. This discrepancy from the ideal unloading
curve complicates the correct determination of the unloading stiffness and finally yields to
incorrect results for Youngs modulus.
For this reason, additional analysis procedures are required to determine the material parameters
more precisely. In this paper the authors want to give an introduction to an enhanced
analysis of nanoindentation data based on rheological models, which are often used to describe
the time-dependence of material response. Two examples of such models are the MAXWELL- and
the KELVIN-body. In these models springs and dashpots connected in series and/or in parallel are
used to describe the time-dependent material response. The viscous parameters, determined from
the recorded data during the nanoindentation experiment, can be used to identify the mechanical
material parameters. The authors present miscellaneous viscoeleastic and viscoplastic rheological
models in connection with the corresponding equations which are used to extract the material
properties from the recorded data. Results of the analysis are presented and discussed in context
with the results from the classical Oliver and Pharr procedure and with the material parameters
published in the literature. Finally, the models are assessed by their applicability of modeling the
time-dependent material response of low melting solder materials.
S6.12: Special Material Behavior Thu, 16:00–18:00
Chair: Lurie Sergey, Jaan-Willem Simon S1|01–A1
Carbon Fibre Prepregs: Simulation of a Thermo-Mechanical-Chemical Coupled Problem
F. Hankeln, R. Mahnken (Universität Paderborn) Schedule
In automotive industry research is done to replace high strength steel by combinations of steel
and carbon-fibre prepregs (pre-impregnated fibres). It is planned to form both steel and uncured
prepregs in one step followed by the curing process under pressure in the forming die [1]. The
ability to simulate the mechanical behaviour during forming and curing would allow more economical
processes. The simulation of prepregs must regard highly anisotropic, viscoelastic and
thermal- chemical properties. For this the model is split into an anisotropic elastic part, which

Section 6: Material modelling in solid mechanics 151
represents the fibre fraction and an isotropic, viscoelastic part, representing the matrix. This part
also contains curing, causing a dependency on time and temperature. During deep-drawing large
deformations are occurring, so a large strain model regarding anisotropy[2], viscoelasticity [3]
and curing [4] has been developed. Also experiments were made to validate this model. Current
progress is the identification of material parameters.
[1] Homberg, W., Dau, J., Damerow, U. Combined Forming of Steel Blanks with Local CFRP
Reinforcement, in: G. Hirt, A. E. Tekkaya (Eds.), steel research int., Special Edition: Proceedings
of the 10th International Conference on Technology of Plasticity, Wiley-VCH,
Weinheim, 2011, pp. 441-446
[2] Menzel, A., Modelling and Computation of Geometrically Nonlinear Anisotropic Inelasticity,
Dissertation, University of Kaiserlautern, 2002
[3] Tschoegl, N.W. The Phenomenologial Theory of Linear Viscoelastic Behaviour, Springer
Verlag, 1989
[4] Lion, A. and Höfer, P., On the phenomenological representation of curing phenomena in
continuum mechanics, Arch. Mech. 59, 2007
On the axially compressed multiple walled carbon nanotubes
Ligia Munteanu (Institute of Solid Mechanics of Romanian Academy) Schedule
A new approach is proposed in this paper, which combines elements of Toupin-Mindlin strain
gradient theory and the Molecular Mechanics to include the inlayer van der Waals atomistic
interactions for axially compressed multiple walled carbon nanotubes. The neighboring walls of
a multiwalled nanotube are coupled through van der Waals interactions, and the shell buckling
would initiate in the outermost shell, when nanotubes are short. The load-unloaded-displacement
curve, the critical buckling and the appropriate values for elastic moduli are obtained. The theoretical
results obtained show a good agreement with the experimental data reported by Waters,
Gudury, Jouzi and Xu (2005). The size dependence of the hardness with respect to the depth
and the radius of the indenter is also investigated. Results show a peculiar size influence on the
hardness, which is explained via the shear resistance between the neighboring walls during the
buckling of the multiwalled nanotubes. The present method can be further extended to investigate
the stress-strain relations and the fracture behaviors of S/MWCNT
From vortices to dislocations: How fluid mechanics can inspire solid mechanics
Markus Scholle (Hochschule Heilbronn) Schedule
Although it is known for nearly a century that production and movement of dislocations are the
elementary processes responsible for the plastic deformation of a solid body, all attempts to derive
a continuum theory of plasticity from the discrete micro–theory of dislocations did not succeed
in universally valid field equations like e.g. Navier–Stokes equations in fluid dynamics.
In this paper an approach is presented based on an analogy between dislocations and vortex
lines in fluid flow. Since the dynamics of the latter ones is well understood in terms of the Navier–
Stokes equations, it is near at hand to make use of this analogy in order to establish a kind of
’Navier–Stokes equations for the distorsion tensor’.
Starting from Clebsch’s variational formulation for inviscid flow, a relation beween the symmetries
of the Lagrangian and the balance of vorticity resulting from it is shown giving rise for
the construction of another Lagrangian from which the respective dislocation balance results.

152 Section 6: Material modelling in solid mechanics
The present state of the theory is discussed.
On the connection of dissipation and deviatoric stress in the continuum theory of
defects
Johannes Schnepp (RWTH Aachen) Schedule
Continuous distributions of defects (e. g. dislocations) can be described as differential geometric
properties of the material manifold. Material forces and the Eshelby tensor are also quantities
in this three-dimensional material space. The relation to defects has been treated often in the
literature and various theories for the dynamics of defects have been proposed.
Moving defects lead to differential geometric quantities changing with time. This has motivated
some authors to augment the three space-like coordinates in the material space by a time-like
coordinate. In this way one gets a four-dimensional material space-time manifold, analogous to
the four-dimensional physical space-time in the theory of relativity. A connection of a time-like
material coordinate to temperature can be found in the literature on relativistic elasticity. These
ideas will be brought together in this contribution and some implications will be developed.
A time-like vector field in the material space-time can be associated with temperature and
heat flux. Together with the three lattice vectors a tetrad field is defined and this field determines
the differential geometric properties of the material manifold. If a variational formulation
for a hyper-elastic solid is adopted, the derivatives of the Lagrangian density with respect to the
components of the tetrad can be arranged in a four-dimensional second-order tensor. This tensor
unifies the information about the three-dimensional Eshelby tensor (material momentum current),
the entropy current, and the entropy density. The time-like component of the divergence of this
tensor is the entropy production. Besides the entropy production due to heat transfer the theory
yields entropy production due to defect movement which is proportional to deviatoric stress.
Stress Reduction Factor of Ceramic Plate to Thermal Shock
Weiguo Li, Tianbao Cheng (College of Resources and Environmental Science, Chongqing), Daining
Fang (Peking University) Schedule
In this work, through introducing the analytical solution to transient conduction problem for the
thin rectangular plate with convection into the thermal stress field model of the elastic plate, the
stress reduction factor which is useful in determining the thermal stresses in the ceramic plate
subjected to thermal shock was presented in the dimensionless form. The properties and appropriate
conditions of the stress reduction factor were analyzed. Then the definitions, origins and
limitations of the first and second thermal stress fracture resistance parameters which characterize
the thermal shock resistance of brittle ceramics were discussed. Because of the demands in
the calculation of thermal stress, a new stress reduction factor was defined and compared with
the previous one. For the given Biot number, the previous stress reduction factor first increases
and then reaches a maximum value, and afterwards decreases as the Fourier number increases.
However, the new stress reduction factor decreases as the Fourier number increases. The new
factor is more convenient for calculating the thermal stress in the plate subjected to thermal
shock. The presented results are useful for the calculating of the thermal stress and choosing of
the appropriate thermal stress fracture resistance parameter when the ceramic plate is subjected
to thermal shock.
Modeling Deformation Twinning in FeMn Alloys
Shyamal Roy, Rainer Glüge, Albrecht Bertram (Universität Magdeburg) Schedule
Multiple twinning [1] in single crystals is modeled by studying the response at each material
point in order to understand micro-structural evolution and mechanical properties of FeMn

Section 6: Material modelling in solid mechanics 153
(TWIP steel). Here the minimum elastic strain energy approach is used. It is well known that the
elastic strain energy of an individual material is convex. Since twinning leads to isomorphic structures,
the elastic strain energy of a twin material is convex too and hence, forms a non-convex
energy landscape. A smooth strain energy landscape is constructed to avoid the discontinuity
at the transition point from parent to twin material. A controlled viscous relaxation scheme is
incorporated since the boundary value problem of the non-convex energy function is ill posed [2].
Dealing with multiple energy wells is numerically very challenging. The solution is not deterministic
as any twin configuration can be activated from the parent configuration, which is unknown
initially. Therefore, to have a complete energy landscape in hand at the beginning is impossible.
The material response is instantaneously calculated depending on which twin configuration is
activated. However, the minimum strain energy approach faces its limitation because of elastic
strain energy invariance, which occurs due to the crystallographic equivalence of possible twin
configurations. Having identified the preferred twin configuration, the secondary and, hence, the
multiple twinning are modeled.
[1] Christian J. W., Mahajan S., Deformation Twinning, Prog Mat Sci, 39, 1-157 (1995)
[2] Carstensen C., Ten Remarks on Non-convex Minimization for Phase Transition Simulations,
Comp Meth App Mech Eng, 194, 169-193 (2005)

154 Section 7: Coupled problems
Section 7: Coupled problems
Organizers: Marc Kamlah (KIT), Bernd Markert (Universität Stuttgart)
S7.1: Porous Media Problems Tue, 13:30–15:30
Chair: Bernd Markert S1|03–223
Investigations of wave induced fluid flow in heterogeneously and partially-saturated
porous media
Christian Becker, Holger Steeb (Universität Bochum) Schedule
Wave induced fluid flow in partially-saturated porous media is a multiscale phenomenon. First
evidence of this was gained by the fact that damping mechanisms that were forecast by models
based on a macroscopic poroelastic approach differed from the results of conducted experiments.
Based on the macroscopic models several enhancements were provided that allowed for the incorporation
of flows occuring on the microscopic (squirt flow, cf.[1]) and mesoscopic scale (mesoscopic
loss, cf.[2-3])
In our contribution the physical phenomena of wave induced fluid flow processes are revisited
briefly. Furthermore a thermodynamically sound three-phase model, developed in the framework
of the Theory of Porous Media, suitable for the numerical analysis of partially-saturated porous
media is presented. Representative elementary volumes (REVs) with layerwise-varying saturation
and no-flux boundary condition on all boundaries are numerically investigated. Layers of varying
saturation are oriented perpendicular to the flow direction. This setup will induce interlayer flow
and is hence responsible for the mesoscopic loss.
To identify and quantify mesoscopic loss mechanisms on the effective damping behaviour,
relaxation- and creep-like one-dimensional numerical analyses are performed and discussed.
[1] R. O’Connell, B. Budiansky, Seismic velocities in dry and saturated cracked solids, J. Geophys.
Res. 79 (1974), 5412–5426.
[2] J. E. White, Computed seismic speeds and attenuation in rocks with partial gas saturation,
Geophysics 40 (1975), 224–232.
[3] J. E. White, N. G. Mikhaylova, F. M. Lyakhovitskiy, Low-frequency seismic waves in fluid
saturated layered rocks, Izvestija Academy of Sciences USSR, Phys. Solid Earth 11 (1975),
654–659.
Simulation of Freezing and Thawing Processes with Capillary Effects in fluid filled
porous media
Wolfgang Moritz Blossfeld, Joachim Bluhm (Universität Duisburg-Essen), Tim Ricken (TU Dortmund)
Schedule
In many branches of engineering, e.g. soil constructions, material science and geotechnics, freezing
and thawing processes of fluid filled porous media play an important role. The coupled
fluid-ice-solid behavior is strongly influenced by phase transition, heat and mass transport as
well as interactions of fluid-solid/ice pressure depending on the entropy of fusion, see [1], and is
accompanied by a volume expansion. The volume increases in space and time corresponds to the
moving freezing front inside the porous solid. In this contribution, within the framework of the
Theory of Porous Media (TPM) a macroscopic quadruple model consisting of the constituents
solid, liquid (freezable water), ice and gas will be presented. Particular attention is paid to the

Section 7: Coupled problems 155
description of the distribution of fluid pressure and solid stresses before, during and after the ice
formation in consideration of energetic and capillary effects. For the detection of energetic effects
regarding the characterization and the control of phase transition of water and ice, a physically
motivated evolution equation for the mass exchange based on the local balance of the heat flux
vector is used, see [2]. Furthermore, the porosity change of the porous materiel is considered, i.e.,
the variation of permeability during ice formation can be simulated. Numerical examples will be
presented to demonstrate the practical application of the model.
[1] O. Coussy, Poromechanics of freezing materials, Journal of the Mechanics and Physics of
Solids 53, (2005), 1689 – 1718.
[2] J. Bluhm, T. Ricken, W.M. Blossfeld, Ice-Formation in Porous Media, In Lecture Notes in
Applied and Computational Mechanics 59, F. Pfeiffer, P. Wriggers, Series Eds., Advances
in Extended and Multifield Theories for Continua, B. Markert, Ed., (2011), 219 p., [978-3-
642-22737-0].
Experimental evaluation of phase velocities and tortuosity in fluid-saturated porous
and high-porous media
Ibrahim Gueven, Patrick Kurzeja, Holger Steeb (Universität Bochum) Schedule
Quantification of sound and ultrasound in high porous media saturated with viscous fluids is
of great importance in many research areas with applications in engineering and medical technologies.
In particular, Quantitative UltraSound (QUS) became of great interest with respect
to osteoporosis diagnosis, cf. [2]. In order to improve predictive diagnosis tools, physical models
are required. The accuracy of such multiphase models, like Biot’s poroelasticity [1,2], depends on
various material parameters of the bulk phases but also parameters which take into account coupling
phenomena. One of those important coupling parameters is the tortuosity of Biot’s theory,
which is a geometrical and frequency-dependent quantity, cf. [1,2]. It accounts for the coupling
of the solid and the fluid, especially in the high frequency range where inertia coupling dominates.
In the present contribution, we present a novel method for the determination of the high frequency
tortuosity parameter, α∞. Therefore, time-domain measurements of ultrasonic signals are
performed with a transmission technique. Systems of sintered, monodisperse glassbeads (φ = 0.35)
and aluminium foam (φ = 0.95) in combination with different pore fluids will be under the scope
of the experimental investigations. Finally, the results are compared with analytical and numerical
pore-scale wave propagation tests.
[1] M. A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Lowfrequency
range, J. Acoust. Soc. Am., 28:168-178, II. Higher frequency range, J. Acoust.
Soc. Am., 28:179-191, 1956.
[2] H. Steeb, Ultrasound propagation in cancellous bone, Arch. Appl. Mech., 80:489-502, 2010.
Numerical homogenization approach of acoustic attenuation in poroelastic media
Ralf Jänicke, Holger Steeb (Universität Bochum) Schedule
Acoustic waves propagating through a poroelastic medium are well-known to undergo certain
attenuation mechanisms related to different length scales. Attenuation can be explained in particular
by local pressure gradients induced by the passing wave and, as a consequence, by the local

156 Section 7: Coupled problems
flow of the pore fluid relative to the skeleton. The critical frequency of attenuation is dictated by
the range of fluid flow. One may distinguish between local effects (e.g. squirt flow, i.e. fluid flow
in/between fractures) and meso scale effects (flow between patches of the poroelastic medium
with spatially varying elastic and/or hydraulic coefficients).
In the present contribution we apply a consistent (meanfield) homogenization approach to
predict macroscopic effective properties of a mesoscopic poroelastic medium applying relaxation/creep
tests. Whereas the heterogeneous meso scale is described using Biot’s theory of poroelasticity,
the homogeneous macro scale is treated as a viscoelastic solid medium. In particular,
we focus on the formulation of averaging rules relating meso- and macroscopic quantities and
we comment on the formulation of relaxed boundary conditions and its impact on the complex
viscous properties of the effective medium.
Finally, we present certain 2-Dim and 3-Dim numerical results obtained by an u-p implementation
in a Finite Element Code.
On the Flow Characteristics of a Geothermal Plant in a Heterogeneous Subsurface
David Koch, Wolfgang Ehlers (Universität Stuttgart) Schedule
Due to the scarcity of fossil fuel with a simultaneous rising in global energy demand, it is important
to develop the use of other energy sources. Geothermal energy holds great potential, which is
increasingly studied in recent years [1].
The modelling approach of the flow processes in a heterogeneous subsurface proceeds from the
Theory of Porous Media (TPM) including an elastically deformable solid, an incompressible fluid,
and a gaseous phase [2]. Starting from the gas-filled porous rock, the fluid phase ist introduced
by a borehole. By the rising pressure gradient, the fluid distributes, displaces the gas and escapes
through a second borehole.
To solve the initial-boundary-value problem, the governing primary variables of the strongly coupled
three-phase modell are spatially approximated by mixed finite elements, whereas for the
time-discretisation is carried out by an implicit Euler time-integration scheme. The goal of the
presented numerical simulations is to study the specific flow characteristics in a heterogenous
subsurface to find the most suitable geologic structures.
[1] R. DiPippo, Geothermal Power Plants: Principles, Applications, Case Studies and Environmental
Impact, Second Edition, Butterworth Heinemann, Oxford 2008.
[2] W. Ehlers, Challenges of porous media models in geo- and biomechanical engineering including
electro-chemically active polymers and gels, Int. J. Adv. Eng. Sci. Appl. Math. 1 (2009), 1
– 24.
Multiphase FEM Modelling of Infiltration Processes in Cohesionless Soils
Alexander Schaufler, Christian Becker, Holger Steeb (Universität Bochum) Schedule
It is well known, that the application of a macroscopical hydraulic gradient to a fluid-saturated
cohesionless soil causes seepage flow. Furthermore, the microstructure of the porous skeleton
dominates the physics of infiltration processes of complex fluids (fluid & fines) and thus the
evolution of the hydraulic and mechanical properties of the soil [1]. From a modelling point of
view, approaches taking into account the macro- and the micro-scale physics are yet not well
established. The transportation process of fines through the pore network strongly depends a)
on the mentioned hydraulic boundary conditions and b) on the microscopic topology of the pore

Section 7: Coupled problems 157
space.
The aim of this work is to develop a continuum multiphase model to describe infiltration processes
for cohesionless soils. For this purpose, a Representative Volume Element (RVE) is considered and
described by the continuum mixture theory extended by the concept of volume fractions (Theory
of Porous Media - TPM). The thermodynamically consistent TPM is a macroscopical multiphase
modelling approach, extended from classical single-phase continuum mechanics [2,3].
In the present context, we further extend the concept of volume fractions by certain distribution
functions of microscopical quantities. Initially, the fluidizable fraction of the soil is determined
from the Grain Size Distribution (GSD) curve [4]. Implementing this multi-scale approach into a
Finite Element code, the computational expense of the method is one of the key points.
The present contribution is focused on a critical study of that issue. On the one hand, different
methods for evaluating the GSD are compared. Finally, we discuss a specific approach which
could be used in multiphase FEM models. The resulting numerical model is applied to different
infiltration applications. One specific application of the proposed model is situated in mechanized
tunneling. In that case, the infiltration of grout in the surrounding soil leads to the evolution of
hydraulic properties of the soil and is finally responsible for deformations on the surface.
[1] Santamarina, J.C., Soils and Waves, John Wiley & Sons Ltd (2001).
[2] Steeb, H., Internal erosion in gas-flow weak conditions, AIP Conf. Series 1227 (2011), 115 –
134.
[3] Ehlers, W., & Bluhm, J., Foundations of multiphasic and porous materials. In Porous Media:
Theory, Experiments and Numerical Applications (2002), 3 – 86, Berlin: Springer.
[4] Steeb, H. & Scheuermann, A., Modelling internal erosion: A continuum- based model enriched
by microstructural information, J. Geotech. Geoenviron., under review (2011).
S7.2: Multifield Problems 1: Polymers Tue, 13:30–15:30
Chair: Marc Kamlah S1|03–226
Numerical Modeling of Dielectric Elastomer Actuators
Ralf Müller, Markus Klassen (TU Kaiserslautern) Schedule
In modern actuator design the dielectric elastomer is considered as a new actuation material. The
main advantage of this dielectric material is the possibility to achieve large deformations under
the influence of an electric field. The mechanical deformation is produced by the polarization of
the elastomer due to the influence of the electric field. Since the actuation range of dielectric
elastomer actuators (DEAs) is similar the the one of natural muscles, one of the interesting application
fields is the realization of artificial muscles. In the present work the fundamental concepts
for the numerical modeling of electromechanical coupled problems are introduced in first place.
After the introduction some concepts of the material modeling of the elastomer are discussed.
Here the neo-Hooke and the Yeoh model are taken into consideration. Furthermore the issue of
incompressibility is addressed. Based on these modeling concepts, a numerical study is performed
to investigate the influence of microstructural inhomogeneities in the elastomer structure. For this
purpose a capacitor structure consisting of a dielectric elastomer between two compliant electrodes
serves as a benchmark. With the help of inserting material inhomogeneities in the capacitor
structure the compression behavior is modified. As a final aspect the numerical modeling of the

158 Section 7: Coupled problems
dynamics of DEAs is presented. Here the focus lies on the study of the dynamic behavior of DEAs
under the influence of an oscillating electric field.
Inverse-motion-based form finding for electro-active polymers
Ralf Denzer (TU Dortmund), Andreas Menzel (TU Dortmund/Lund University) Schedule
Electroactive polymers (EAP) exhibit large mechanical deformation under an applied electrical
field. This electro-mechanical coupling is an attractive property for actuators, e.g., artificial
muscles for micro-robotics. In this presentation we focus on the theoretical and computational
aspects of computing the undeformed and load free configuration B0 for a given deformed configuration
Bt and given boundary conditions in the case of electro-active polymers. This is of practical
interest for the design of actuators or grippers. We first formulate the inverse motion problem
for coupled electro-mechanical problems and then show how a straight-forward Bubnov-Galerkin
discretization leads to an attractive simulation scheme to solve such inverse motion problems. We
discuss implementation issues of the proposed method and give some numerical results for model
problems.
A three-phase model for polymer curing including diffusive motion and agglomeration
of inclusions.
Bernd Lenhof, Stefan Diebels (Universität des Saarlandes) Schedule
The material properties of cured polymers with inclusions of different sizes depend strongly on
the location and the size of the inclusions. Hence, an appropriate curing model has to take into
account diffusive motion of the inclusions. A side effect of the relative motion of the inclusions
is potentially agglomeration of fines and, as an implication, separation of agglomerates. Obviously,
diffusion as well as agglomeration/separation are coupled to the curing state of the polymer.
In this contribution, only one type of inclusion-material is assumed, still, the moving inclusions
may agglomerate. A three-phase continuum model will be shown, where one phase represents the
curing polymer, while the remaining two phases represent the inclusion in the fine state and the
agglomerated state. With respect to the inclusion phases, the model contains not only the diffusion
terms, but also terms modelling phase exchange between the inclusion states. With respect
to the polymer phase, the model includes curing effects. Mixture theory is utilized to formulate
the pertinent time dependent balance equations and the FE-method is used to obtain numerical
solutions. As to the FE-software, the equations were implemented into the open-source library
deal.II.
Mechanical behavior of a pH-sensitive hydrogel ring used in a micro-optical device
Nicolas Zalachas (Clermont Université), Shengqiang Cai, Zhigang Suo (Harvard University), Yuri
Lapusta (Clermont Université) Schedule
A hydrogel is a polymer network that can absorb a large quantity of solvent and swell due to a
physical or chemical stimulus. Hydrogels are more and more used as smart materials in recent
micro-applications. This fact requires the development of adequate models and simulation tools
for their large deformation behavior. These models must also predict the onset of instabilities,
such as folding or creasing [1]. In this work, we study an interesting application of adaptive optical
microsystem [2] using a previously developed theory of inhomogeneous large deformation
of a pH-sensitive hydrogel [3]. The devices function is based on the swelling of a ring made of
a pH-sensitive hydrogel. The latter controls the focal length of the liquid microlens. Our aim is
to analyze major design parameters that affect the hydrogel ring behavior and the function of
the micro-optical device. The problem is solved numerically with the finite element commercial
software ABAQUS. Various modes of large deformation and the influence of the rings aspect ratio

Section 7: Coupled problems 159
on the behavior of the micro-device are investigated. Results show that, for relatively short rings,
a stable swelling takes place. Rings with a relatively big aspect ratio can have an unstable swelling
with the propagation of a creasing instability.
[1] W. Hong, X. H. Zhao, Z. G. Suo : Formation of creases on the surfaces of elastomers and
gels. Applied Physics Letters, 95, 111901 (2009).
[2] L. Dong, A. K. Agarwal, D. J. Beebe, H. R. Jiang : Adaptive liquid microlenses activated by
stimuli responsive hydrogels. Nature, 442, 551-554 (2006).
[3] R. Marcombe, S. Q. Cai, W. Hong, X. H. Zhao, Y. Lapusta and Z. G. Suo : A theory of
constrained swelling of a pH-sensitive hydrogel, Soft Matter, 6, 784-793 (2010).
Numerical Modeling and Simulations of Dielectric Elastomer Actuators for Thin
Structures
Sandro Zwecker, Sven Klinkel (TU Kaiserslautern) Schedule
The contribution is concerned with a finite element formulation that deals with thin structures
made from dielectric elastomer material. For that a special solid shell formulation, which uses
eight nodes per element and four degrees of freedom (three displacements and one for the electric
potential) per node, is presented. It is based on a Hu-Washizu mixed variational principle using
six independent fields: displacements, electric potential, strains, electric field, mechanical stresses,
and dielectric displacements. In recent years structures made from dielectric elastomers have
been investigated by many researchers. This interest is caused by the ability of such devices to
efficiently transform electric energy into mechanical work at inexpensive cost of production. The
efficiency increases with a higher area to thickness ratio, thus the need to accurately simulate thin
structures is well-founded. On the other hand a 3d description of the constitutive behaviour is necessary
to capture all nonlinear effects arising from the material. Thus a 3d constitutive law with
respect to the electro-mechanical coupling incorporated in a finite element solid shell formulation
is presented. Some examples demonstrate how it deals with finite strains and large deformations
of thin structures applying electrical loading conditions. The analysed devices respond with
elongation, bending, or buckling, depending on the mode of activation. The electrically induced
buckling can be utilized to obtain large deformations.
Modeling of healing processes in a polymer matrix
Joachim Bluhm, Jörg Schröder, Steffen Specht (Universität Duisburg-Essen) Schedule
Traditionally, engineers are focused to design new materials with increasing durability to ensure
a long lifetime cycle, but they can eventually fail. In contrast, natural materials, e.g. biological
tissues, are dealing with failures in a more efficient way: by self-healing. A material is called selfhealing
material, when it has the ability to recover its strength, stiffness and fracture toughness
after a crack has occurred. One approach to transfer self-healing ability to manufactured materials
is achieved by using a capsule-based healing system. Here, the encapsulated healing agent and
catalyst are embedded in the polymer matrix. If a crack tip brakes through a capsule, the healing
material flows out, polymerized by reaction with the catalyst and close the crack.
In this contribution, for the simulation of such a self healing system, a macroscopic multiphase
model based on the Theory of Porous Media (TPM) is presented. The healing process of the solid
matrix consisting of the phases solid, healing material (catalysts, liquid healing and solid healed
materials) and gas (cracks and damaged material). The modeling of healing is associated with

160 Section 7: Coupled problems
the formulation criteria regarding the onset of the healing process, i.e., the break open of the
capsules in connection with the subsequent motion of the liquid healing material and change of
the aggregate state from liquid healing to solid healed material. The transition from the liquid-like
healing material to the solid-like healed material will be captured by introducing mass exchange
between the mentioned constituents. For simplification of the model it will be assumed that the
motion of solid, healing agents and catalysts as well as the solidified healing-material at a pointed
moment are all equal. Numerical examples will be presented to demonstrate the applicability of
the model in view of the description of healing processes.
S7.3: Numerical Solution Methods Tue, 16:00–18:00
Chair: Bernd Markert S1|03–223
A flexible multi-physics coupling interface for partitioned solution approaches
S. Brändli, A. Düster (TU Hamburg-Harburg) Schedule
A common way of solving multi-physics problems is the use of a partitioned approach. To this end
specialised solvers are utilized for the different subproblems and linked via a common communication
interface. A partitioned approach to be developed should allow to solve different types of
coupled problems. These might be either volume coupled problems with different physical fields
in one domain or surface coupled problems with different physical fields in different domains.
Examples for these different types of coupled problems are thermoelasticity and fluid-structure
interaction (FSI). The use of a MPI-library allows for a fast data exchange, whereas special care
has to be taken to perform an accurate interpolation of the different fields. In addition one has
to ensure numerical stability and efficiency of the coupling algorithm. As a consequence an implicit
algorithm including relaxation-techniques, predictors and convergence criteria is developed
to solve different types of coupled problems.
In previous works, FSI problems were solved utilizing a p-FEM solver, which was coupled to a
Lattice Boltzmann Method (LBM) [1] and a Boundary Element Method (BEM) [2]. In [2] also a
FEM-RANSE coupling approach was presented. The interface used in [1,2] for the communication
between the simulation codes was strongly attached to the p-FEM solver. In order to be more
flexible to treat different types of coupled problems and to include different simulation codes,
a new coupling interface is designed, which is solver independent and offers the aforementioned
features.
The relaxation techniques to accelerate the convergence of the implicit iteration include standard
underrelaxation, Aitken underrelaxation and variants of the quasi Newton method. The
flexibility and performance of the proposed coupling approach will be demonstrated by different
examples ranging from thermo-mechanical problems to fluid-structure interaction. The emphasis
will be placed on fluid-structure interaction presenting several benchmark examples.
Keywords: FSI, fluid-structure interaction, coupled problems, partitioned approaches, convergence
acceleration
[1] Kollmannsberger S.; Geller S.; Düster A.; Tölke J.; Sorger C.; Krafczyk M.; Rank E.: Fixedgrid
fluid-structure interaction in two dimensions based on a partitioned Lattice Boltzmann
and p-FEM approach. IJNME 79, p. 817ff., 2009.
[2] Brändli S.; Abdel-Maksoud M.; Düster A.: A FEM-BEM approach for Fluid-Structure Interaction.
PAMM Vol. 11, 2011.

Section 7: Coupled problems 161
Stability Analysis of Decoupled Solution Strategies for Coupled Multi-field Problems
- A General Framework
Seyedmohammad Zinatbakhsh, Bernd Markert, Wolfgang Ehlers (Universität Stuttgart) Schedule
The mathematical modelling of coupled problems often results in systems of coupled partial
differential equations (PDE) in space and time, which are usually solved numerically following a
monolithic or decoupled solution algorithm.
Employing an implicit time integration, monolithic schemes result in unconditionally stable numerical
solutions independent of the machine accuracy and occurring errors. However, using a
monolithic solver, one considers the coupled problem as a whole, regardless of the specialised
solvers that may exist for different subsystems. This has motivated the development of various
decoupled solution strategies. However, decoupled integrators can be detrimental to the stability
of the solution and must always be accompanied by an exhaustive stability analysis.
The first goal of this contribution is to propose a feasible algorithm for the stability analysis of
this family of solutions. The algorithm is used to study the stability behaviour of selected volumetrically
and surface-coupled problems in d dimensions, d = {1, 2, 3}. As the first example,
two decoupled solution methods for the linear problem of thermo-elastodynamics as presented
in [1] are considered and the influence of implicit and explicit predictors on the stability of the
solution algorithm is demonstrated. The respective necessary stability condition for 1-d, 2-d and
3-d problems are established. It is shown that using an explicit predictor yields conditional stability
of the solution scheme. The coupled problem of porous media dynamics serves as the second
example. There, the independence of the obtained stability condition for the decoupled solution
scheme proposed in [2] from the permeability factor is investigated. In the last example, the importance
of the order of integration and its impact on the critical time-step size for the problem
of structure-structure interaction (SSI) is studied.
[1] F. Armero, J.C. Simo, A new unconditionally stable fractional step method for non-linear
coupled thermomechanical problems, Int. J. Numer. Meth. Eng. 35 (1992), 737 – 766.
[2] B. Markert, Y. Heider, W. Ehlers, Comparison of monolithic and splitting solution schemes
for dynamic porous media problems, Int. J. Numer. Meth. Eng. 82 (2010), 1341 – 1383.
Acceleration of partitioned coupling schemes for problems of thermoelasticity
P. Erbts, A. Düster (TU Hamburg-Harburg) Schedule
A partitioned coupling scheme for problems of thermoelasticity at small strains is presented
utilizing the p-version of the finite element method. The coupling between the mechanical and
thermal field is one of the most important multi-physics problem. Typically two different strategies
are used to find an accurate solution for both fields: Partitioned or staggered coupling schemes, in
which the mechanics and heat transfer is treated as a single field problem, or a monolithic solution
of the full problem. Monolithic formulations have the drawback of a non-symmetric system which
may lead to extremely large computational costs. Because partitioned schemes avoid this problem
and allow for numerical formulations which are more flexible, we consider a staggered coupling
algorithm which decouples the mechanical and the thermal field into partitioned symmetric subproblems.
In [1], [2] this algorithmic decoupling has been referred to as the isothermal operatorsplit
methodology.
Since a partitioned coupling algorithm requires fast data exchange, a flexible coupling interface has
been developed which is not restricted only to thermomechanical problems. In order to accelerate

162 Section 7: Coupled problems
the convergence of the algorithm, numerical relaxation methods have been implemented. Such
methods are well-known from other multi-physic problems, especially in fluid-structure-interaction
analysis they have been applied with great success. The influence of three different relaxation types
are analyzed: Static under-relaxation with constant relaxation coefficients, its dynamic variant
with a residual based relaxation coefficient and a Quasi Newton method.
The numerical solution of the thermal and mechanical part is computed by using a high order finite
element code. Several numerical simulations of quasi-static problems are presented investigating
the performance of accelerated coupling schemes.
Keywords
thermoelasticity, staggered coupling algorithm, convergence acceleration
[1] Miehe C. : Entropic thermoelasticity at finite strains: Aspects of the formulation and numercial
implementation. Computer Methods in Applied Mechanics and Engineering, 79:243-269,
1995.
[2] Simo, J.C.; Miehe, C. : Associative coupled thermoplasticity at finite strains: Formulations,
numerical analysis and implementation. Computer Methods in Applied Mechanics and Engineering,
98:41-104, 1992.
A Class of Fluid-Structure Interaction Solvers with a Nearly Incompressible Elasticity
Model
Huidong Yang (Johann Radon Institute for Computational and Applied Mathematics) Schedule
In this work, we present some numerical studies on two partitioned fluid-structure interaction solvers:
a preconditioned GMRES solver and a Newton based solver for a class of fluid-structure interaction
problems with a nearly incompressible elasticity model in a classical mixed (displacementpressure)
formulation. Both solvers are highly relying on the robust solvers for the structure and
the fluid sub-problems discretized by extended and stabilized finite element methods on hybrid
meshes, for which we use a special class of algebraic multigrid solvers.
A finite element contact implementation to investigate rubber friction with themomechanical
coupling effects
Thang Xuan Duong, Roger A. Sauer (RWTH Aachen) Schedule
The knowledge of friction when rubber-like material is in contact with a hard material is practically
important for the design and production of mechanical parts made of rubber, e.g., tires, wiper
blades, seals, etc. In theoretical studies, simple phenomenological friction models, like Coulomb’s
law are usually used to describe the friction behavior. However, for the mechanisms underlying
rubber friction, like mechanical surface interlocking, material hysteresis and adhesion, these
models may fail to predict the results. Thus, our aim is to use numerical experiments with the
structural approach to formulate friction models that can capture such phenomena of rubber
friction. In order to do this, coarse-graining techniques can be used to investigate the mechanisms
in detail and to determine their effective behaviors. For this purpose, we provide a framework to
characterize the influence of material hysteresis on rough surface friction. The work includes the
implementation of a model for 3D finite deformation viscoelastic materials used for rubber-like
materials proposed by S. Reese and S. Govindjee [1], which is valid not only for large deformations
but also large perturbation away from the thermodynamic equilibrium due to the nonlinearity
of the evolution equation. For the consideration of the thermo-mechanical coupling effects, the

Section 7: Coupled problems 163
thermo-viscoelasticity constitutive model by S. Reese and S. Govindjee [2] is used. The implementation
is then integrated into a suitable finite element formulation solving contact problems
of a viscoelastic body on rough surfaces. Energy dissipation across the body, which is important
to determine the internal friction of rubber during contact, are computed and visualized. Some
results of parametric studies are presented to show the impact of relaxation time, normal pressure
and the rough surface parameters on the frictional behavior of the rubber material.
[1] S. Reese and S. Govindjee, A theory of finite viscoelasticity and numerical aspects, International
Journal of Solids and Structures 35 (1998),3455-3482.
[2] S. Reese and S. Govindjee, Theoretical and numerical aspects in the thermo-viscoelastic material
behaviour of rubber-like polymers, Mechanics of Time-Dependent Materials 1 (1998),
357-396.
Approximate Galerkin method applied to an analysis of vibration of continuous mechanical
systems
Marek Płaczek (Silesian University of Technology) Schedule
Paper presents fundamental assumptions of the approximate Galerkin method application in order
to vibration analysis of continuous mechanical systems with different form of vibration and
different boundary conditions. Flexural vibration of beams, longitudinal vibration of rods and
torsional vibration of shafts with all possible ways of fixing were considered. Analyzed mechanical
systems were treated as subsystems of mechatronic systems with piezoelectric transducers. This
work was done as an introduction to the analysis of mechatronic systems with piezoelectric transducers
used as actuators or passive vibration dampers. It is impossible to use an exact Fourier
method in this case. This is the reason why the approximate Galerkin method was chosen and
analysis of its exactness was done as a first step of this work. Dynamic flexibilities of considered
mechanical systems were calculated twice, using exact and approximate methods. Obtained results
were juxtaposed and it was proved that in some cases the approximate method should be
corrected while in the other it is precise enough. A correction method was proposed and it was
assumed that the approximate method can be used in mechatronic systems analysis.
S7.4: Multifield Problems 2: Electromechanics Tue, 16:00–18:00
Chair: Marc Kamlah S1|03–226
Uncertainty Analysis for Piezoelectric Models
Tom Lahmer (Universität Weimar), Jürgen Ilg (Universität Erlangen-Nürnberg) Schedule
In the recent years many publications have appeared dealing with the characterization of all entries
in the material tensors for the description of the piezoelectric effect. The strategies proposed
differ in the methods used and in particular in the type of measurements evaluated. Also the
dependency of single parameters, e.g., on effects like temperature changes or large-signal loading
are under investigation.
Generally, the approaches are very ambitious, since all parameters shall be identified with highest
accuracy while using a limited number of specimens. In particular for less influential parameters
confidence intervals might be large.
It remains unclear, to which extend remaining uncertainties in the parameters influence the response
of the model and if these uncertainties are actually critical for the prognosis for which the
model is used for.

164 Section 7: Coupled problems
Therefore, we propose a variance based uncertainty analysis of piezoelectric models in order to
identify sources of uncertainty and to quantify every parameters influence to the model output.
By considering both, first order and total order effects, interactions between the parameters can
be assessed additionally.
Semi-analytical investigations of R-curve behavior in ferroelectric materials considering
different scales
Roman Gellmann, Andreas Ricoeur (Universität Kassel) Schedule
Due to the brittleness of ferroelectric materials fracture mechanical approaches are playing an essential
role in the modern research. The strength of these materials, in terms of the critical stress
intensity factors, is significantly determined by nonlinear ferroic effects arising on the mesoscopic
scale.
In the present work we study the effective fracture toughness of ferroelectrics by taking the mesoscopic
as well as the macroscopic level into account. On the macroscopic scale we apply an
extended theory of stresses at interfaces in dielectric solids [1]. Further, on the mesoscopic scale,
nonlinear effects are introduced by applying the small scale switching approximation, i.e. the effects
are limited to a small region around the crack tip. Finally, we discuss the effective fracture
toughness and crack resistance curves for different loading and poling conditions. The analysis
is done considering the full anisotropy and electromechanical coupling of the material by using
piezoelectric weight functions [2]. In contrast to previous approaches, the presented model also
takes the inverse switching (180 degree) into account yielding a contribution to the electric
displacement intensity factor.
[1] R. Gellmann, A. Ricoeur, Arch. Appl. Mech., 2011
[2] R. McMeeking, A. Ricoeur, Int. J. Solids Struct., 2003
A micromechanically motivated method to develop switching surfaces in ferroelectroelasticity
Sebastian Stark, Peter Neumeister, Herbert Balke (TU Dresden) Schedule
Macroscopic phenomenological models are widely used to predict the irreversible material behaviour
of polycristalline ferroelectroelastic ceramics under electromechanical loading conditions.
Usually, these models are based upon a thermodynamically consistent continuum mechanics framework
involving the choice of a switching surface, which separates the domains of reversible and
irreversible material behaviour. The switching surfaces proposed in the literature are typically
suitable to represent the material behaviour found in experiments for simple loading conditions,
such as bipolar electric cycling and uniaxial compression. However, their predictive capabilities
in the case of complex, electromechanical loadings are not satisfactory yet. Therefore, a better
understanding of the properties of switching surfaces is desirable. In this talk, a micromechanically
motivated method to develop switching surfaces is proposed and applied to predict the
shape of the initial switching surface of a virgin ceramic. The approach is based upon energetic
considerations leading to maximum dissipation. The results obtained are discussed with respect
to the electromechanical generalisation of the Tresca and von Mises yielding surfaces known
from metal plasticity. Furthermore, a comparison to experimental results is given, showing that
the presented approach is appropriate to describe the onset of switching under proportional electromechanical
loading.
On the released energy in nonlinear electro-elastostatics
Duc Khoi Vu, Paul Steinmann (Universität Erlangen-Nürnberg) Schedule

Section 7: Coupled problems 165
In this work the change of energy under a change of material configuration of an electro-sensitive
body subjected to electric stimulations is considered by taking into account the free space surrounding
the body. The free space can have a significant impact on the electric field and on the
deformation field inside a body made of materials with low electric permittivity like the so-called
electronic electroactive polymers (EEAPs). By using a stored energy density function for both
the material body and the free space, the formulas for the part of energy that is released from
the system material body - applied forces in response to a change in the material configuration
are formulated. These formulas are useful in the study of defects like crack propagation.
Dynamic response of dielectric elastomer actuators with the sandwich structure
Bai-Xiang Xu (TU Darmstadt), Anika Theis, Markus Klassen, Ralf Mueller (TU Kaiserslautern),
Dietmar Gross (TU Darmstadt) Schedule
As potential material for artificial muscles and haptic displays, dielectric elastomer provides large
deformations with lower cost and high efficiency. The material behaves nonlinearly in both the
geometry and the constitutive relation. The nonlinear modeling and simulation of the material
in the static case has received considerable investigation. However, the material is mostly expected
to perform under dynamic situations in applications with high frequencies, e.g. pumps and
loudspeakers. Therefore the modeling of the dynamic response of the dielectric elastomer is also
of importance.
In this work, a theoretical model is proposed to study the dynamic behavior of a dielectric
elastomer actuator with a standard sandwich structure. The nonlinear equation of motion can
be obtained through the Euler-Langrange equation or a variational analysis. Unlike in most of
the cases studied in the literature, the ordinary differential equation for the motion involves
additionally the first time derivative of the deformation, due to the exact formulation of the kinetic
energy in space. Numerical solutions for exemplary cases will be presented, i.e. the vibration under
a constant potential and the forced oscillation under harmonic excitation. In particular, resonance
phenomenon and damping effects are investigated. Results will be discussed in comparison with
those of the related topics in the literature.
S7.5: Phase Change and Interface Problems Wed, 13:30–15:30
Chair: Bernd Markert S1|03–226
Modeling and simulation of binary and ternary reactive systems
Kerstin Weinberg, Denis Anders (Universität Siegen) Schedule
For the production and design of functional materials reaction-diffusion systems gain more and
more importance.
In this contribution the spinodal decomposition in multicomponent systems subjected to chemical
reactions is studied. To this end, the classical Cahn-Hilliard phase field model is extended
by additional contributions accounting for chemical reactions. After a thorough derivation of the
reaction-diffusion model in a thermodynamically consistent way, numerical simulations of binary
and ternary chemically reactive phase separating systems are presented.
Finite element methods for solid-liquid phase transitions with free melt surface
Mischa Jahn, Andreas Luttmann, Alfred Schmidt (Universität Bremen), Jordi Paul (Universität
Erlangen) Schedule
The modelling and computation for a problem with solid-liquid phase transition and a free boundary
surface will be discussed. The main components of the used model are heat conduction, a
moving phase boundary, and its coupling with the Navier-Stokes equations.

166 Section 7: Coupled problems
We present FE methods using two different approaches for the phase boundary, namely a
sharp interface with moved mesh, and an energy conservation based approach with mushy-region
elements. By combining both methods in a proper way, we benefit from the advantages of the
respective approach.
The methods are applied to the accumulation of material by melting the tip of thin steel wires
using laser heating. The beneficial ratio of surface tension and gravity enables the generation of
functional parts in micro scale metallic components. Simulation and experimental results will be
presented.
Carbon-dioxide storage and phase transitions: towards an understanding of crack
development in the cap-rock layer
Kai Häberle, Wolfgang Ehlers (Universität Stuttgart) Schedule
Supercritical CO2 can be injected into deep saline aquifers to reduce the amount of CO2 in the
atmosphere and thus, lessen the impact on the global warming. Qualified reservoirs should be in a
sufficient depth to guarantee the thermodynamical environment for the supercritical state of CO2
and should be confined by an impermeable cap-rock layer. It is crucial to guarantee the safety
of the storage site. Therefore, deformation processes and crack development of the rock matrix
and the cap-rock layer, which might be induced by the high pressure injection of CO2, must be
investigated. If cracks occur, CO2 could migrate into shallower regions, where the temperature and
pressure cannot support the supercritical condition of the CO2 anymore. Thus, it is important to
describe the phase transition process between supercritical, liquid and gaseous CO2. The Theory
of Porous Media (TPM), see e. g. [1], provides a useful continuum-mechanical basis to describe
real natural systems in a thermodynamically consistent way. Hence, the TPM is applied to model
multiphasic flow of CO2 and water and include elasto-plastic solid deformations of the porous
matrix. The Peng-Robinson equation, e. g. [2], is implemented as a cubic equation of state to
describe the phase behaviour of CO2. However, the two-phase region cannot be represented by a
continuously differentiable function such as the Peng-Robinson equation and thus, the Antoine
equation provides additional information of the vapourisation curve. The extended Finite Element
Method (XFEM) will be used to account for the discontinuities arising from crack development
due to solid deformations [3]. Herein, special attention has to be paid to the matrix-fracture
interaction of the fluid phases. Numerical examples are performed to investigate the injection
of CO2 into a saline aquifer. These are computed with the FE program PANDAS, which allows
solutions of strongly coupled multiphasic problems in deformable porous media.
[1] W. Ehlers, Foundations of multiphasic and porous materials, in: W. Ehlers and J. Bluhm
(eds.), Porous Media: Theory, Experiments and Numerical Applications. Springer-Verlag,
Berlin 2002, pp. 3 – 86.
[2] B. Poling, J. Prausnitz, J. O’Connell, The properties of gases and liquids, McGraw-Hill. New
York 2001, 5th edn.
[3] N. Moës, J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing,
Int. J. Numer. Meth. Eng. 4 (1999), pp. 131 – 150.
Phase Transition in Methane Oxidation Layers - A Coupled FE Multiphase Description
Andrea Sindern, Tim Ricken (TU Dortmund), Renatus Widmann, Martin Denecke (Universität
Duisburg-Essen) Schedule

Section 7: Coupled problems 167
Worldwide, the most common sites of waste disposal are landfills. After solid waste is deposited in
a landfill, physical, chemical, and biological processes ensue and modify the waste. Due to these
reactions, landfill gas is produced inside the landfill body and effuses into the atmosphere at the
outer layer. These processes create environmentally harmful landfill pollutants (methane (CH4))
and carbon dioxide (CO2)). The impact of methane on the greenhouse effect is actually 21 - 23
times higher than that of carbon dioxide.
In order to estimate potential environmental risk, a second important phenomenon has to be
taken into account: the bacterial methane conversion in the porous cover layer which significantly
reduces the amount of methane emitted into the atmosphere. Subsequently, the metabolism of
different methanotrophic bacteria converts methane and oxygen into carbon dioxide, water, and
biomass.
To model this highly complex and coupled problem we used the well-known theory of porous media
to obtain a thermodynamically consistent description which in turn leads to a fully-coupled
finite element (FE) calculation concept. In this talk, the theoretical and numerical framework will
be presented in order to describe the coupled processes occurring during the phase transition by
bacterial activity in the methane oxidation layer. The model analyzes the relevant gas concentrations
of methane, carbon dioxide, oxygen, and nitrogen as well as the driving phenomena of
production, diffusion, and convection. Based on a model predicting gas production in landfills, see
[1,2], a multiphase continuum approach for landfill cover layers is presented. In order to validate
the model, we compare numerical simulations with experimental data.
Acknowledgement: This work was supported by the DFG (Grant No. RI 1202/3-1)
[1] Ricken, T. and Ustohalova, V.: Computational Materials Science, Vol. 32, pp. 498–508, (2005).
[2] Robeck, M. et al.: Waste Management, Vol. 31, pp. 663–669, (2011).
Macroscopic modelling of the selective beam melting process
D. Riedlbauer, J. Mergheim, A. McBride, P. Steinmann (Universität Erlangen-Nürnberg) Schedule
The selective beam melting process is used for the additive manufacturing of three-dimensional
components from particulate media. The component is formed by scanning the beam (electron
or laser) over successively deposited layers. The intense energy imparted by the beam causes
the particles to undergo an irreversible phase change from a powder to a melt and then to a
solid. The accuracy of the process is dependent upon numerous parameters (e.g. beam scan path,
rate of cooling). Computational modelling can assist the design procedure by providing a virtual
environment in which to test a huge range of parameters. The applicability of the model is in
turn dependent on its ability to capture the key physical processes such as: the dependence of the
material properties on the temperature, the coupling of thermal and mechanical processes, and
the phase changes which occur.
The objective here is to detail a thermodynamically consistent continuum model for thermoelasticity
to describe selective beam melting. The implementation of the model within the
open-source finite element library deal.ii [2] is also described. In particular, a comparison of the
fractional split method [1] and the monolithic approach is presented. In order to accurately describe
the boundary of the solid region, an adaptive finite element strategy is adopted.
The accuracy and efficiency of the model is demonstrated via a series of benchmark problems.
[1] Armero, F., Simo, J. C., 1992. A new unconditionally stable fractional step method for nonlinear
coupled thermomechanical problems. International Journal for Numerical Methods
In Engineering 35, 737–766.

168 Section 7: Coupled problems
[2] Bangerth, W., Hartmann, R., Kanschat, G., 2007. deal.II — a general purpose object oriented
finite element library. ACM Transactions on Mathematical Software 33 (4), 24.
S7.6: Multifield Problems 3: Magnetomechanics Wed, 16:00–18:00
Chair: Marc Kamlah S1|03–226
Numerical Aspects of Three-Dimensional MSMA Modeling
B. Kiefer, T. Bartel, A. Menzel (TU Dortmund) Schedule
Magnetic shape memory alloys (MSMA) exhibit a complex constitutive behavior that combines
the nonlinear, dissipative and thermomechanically-coupled features of classical shape memory
response with strong magneto-mechanical coupling. The magnetic shape memory effect is made
possible by the simultaneous occurrence of high magnetic anisotropy and high twin boundary
mobility that allows the field-induced reorientation of variants in the ferromagnetic martensite
phase.
Several constitutive models for MSMAs have been proposed in the literature. What is missing,
however, are numerical integration schemes for such models that capture the complex multidimensional
thermo-magneto-mechanical behavior of MSMAs and can be implemented into finite
element codes solving the coupled field equations. In this work, two main algorithmic versions of
the Kiefer & Lagoudas internal variable model for MSMAs [1] are presented. The more classical
approach is based on a predictor-corrector-type return mapping scheme. The second approach
employs so-called Fisher-Burmeister NCP functions to avoid the undesired necessity to evaluate
multiple sets of Karush-Kuhn-Tucker conditions (cf. [2], or [3] in the context of phase transformations).
Starting from the simplest form of the MSMA model in which only field-induced martensitic
variant reorientation is considered, the macroscopic phenomenological model is extended to include
the local magnetization rotation and magnetic domain wall motion mechanisms, through the
evolution of additional internal state variables. Special attention is paid to three-dimensional response
modeling, in which additional martensitic variants must be considered. Finally, FE-based
simulations of the coupled global response are discussed.
[1] B. Kiefer and D. C. Lagoudas, Modeling the Coupled Strain and Magnetization Response of
Magnetic Shape Memory Alloys under Magnetomechanical Loading, Journal of Intelligent
Material Systems and Structures Vol. 20, 143–170, 2009.
[2] A. Fischer, A Special Newton-Type Optimization Method, Optimization Vol. 24, 269–284,
1992.
[3] T. Bartel and K. Hackl, A Micromechanical Model for Martensitic Phase-Transformations in
Shape-Memory Alloys Based on Energy-Relaxation, Zeitschrift für Angewandte Mathematik
und Mechanik Vol. 89, 792–809, 2009.
XFEM-modelling of stationary magnetic and coupled magneto-mechanical boundary
value problems
J. Goldmann, C. Spieler, M. Kästner, V. Ulbricht (TU Dresden) Schedule
The goal of this work is to analyse a composite material with magnetically switchable stiffness
properties. To this end, the coupling between the magnetic and the mechanical field has to be

Section 7: Coupled problems 169
considered. This presentation features one step towards the long-time objective of predicting the
effective behavior of the composite using a homogenisation algorithm.
The magnetic problem here is reduced to magnetostatics, allowing for a weak coupling of
magnetic and mechanical fields, thus both boundary value problems may be solved separately.
At first the stationary magnetic field is computed in terms of the magnetic vector potential. The
existing jumps of the magnetic field quantities across material interfaces cause a non vanishing
force distribution at the interface. This traction at the interface is obtained by a total stress tensor
split into an electromagnetic and a mechanical part according to [1]. The calculated nodal forces
are then transferred to the structural pass.
The numerical solution of the coupled field problem is performed using the eXtended Finite
Element Method (XFEM). Over the past decade XFEM has been applied to a variety of mechanical
and non-mechanical problems involving weak and strong discontinuities [2]. Still magnetic
problems have not been considered in lots of publications. Therefor special attention will be paid
to the magnetic calculation and the coupling. To this end two demostration problems featuring
resulting concentrated loads as well as distributed loads will be presented. The numerical solutions
will be analysed using known analytical solutions. In this context different types of elements
will be compared.
[1] Eringen, A. C.; Maugin, G. A. Electrodynamics of continua, Springer, New York, 1990
[2] Fries, T.-P.; Belytschko, T. The extended/generalized finite element method: An overview of
the method and its applications, Int. J. Numer. Meth. Engng 84 (2010), 253–304
Effects of different crack-face boundary conditions on the dynamic intensity factors
in linear magnetoelectroelastic solids
Michael Wünsche, Chuanzeng Zhang (Universität Siegen) Schedule
Keywords: magnetoelectroelastic materials, non-linear crack-face boundary conditions, impact
loading, dynamic intensity factors
New multifield materials for the development of smart devices and structures are receiving
increasing attentions. Composite materials consisting of piezoelectric and piezomagnetic phases
with an additional magnetoelectric coupling effect offer advanced opportunities and may be used
for broadband sensing, actuating devices and many other smart devices and structures which are
required in engineering sciences. Static and dynamic crack analysis of magnetoelectroelastic solids
is of special importance because such solids are often very brittle and the corresponding results
have a direct relevance to the design and optimization of real structures. Since analytical solutions
are usually limited to very simple crack and loading configurations, numerical solution algorithms
have to be used in general cases. The boundary element method (BEM) has been shown to be very
attractive and efficient for solving dynamic crack problems in linear magnetoelectroelastic solids.
A critical issue in the numerical simulation of crack problems in linear magnetoelectroelastic solids
is a realistic description of the mechanical and electromagnetical crack-face boundary conditions.
The aim of this paper is the investigation of different electrical, magnetic and mechanical crackface
boundary conditions and their influences on the static and dynamic intensity factors in twodimensional
and linear magnetoelectroelastic solids subjected to different mechanical, electrical,
magnetic and combined loadings. Iterative algorithms are developed to handle the semi-permeable
electrical and magnetic crack-face boundary conditions. To solve the non-linear crack-face contact

170 Section 7: Coupled problems
problem when a physically unacceptable crack-face intersection occurs, an additional iterative
scheme is implemented. Numerical examples will be presented and discussed.
Geometrical Aspects in the Incremental Variational Formulation for Phase Field
Modeling in Micromagnetics
Gautam Ethiraj, Christian Miehe (Universität Stuttgart) Schedule
Magnetic materials have been finding increasingly wide areas of application in industry ranging
from magnetic cores of transformers, motors, inductors, generators to high density magnetic recording
devices. There is therefore an increased interest in the modeling of such materials that
have an inherent coupling between the magnetic and mechanical characteristics. In a previous
work we presented a phase field model within an incremental variational framework to describe
the formation and quasi-static evolution of magnetic domains. Such a model incorporates characteristic
size-effects that are observed and reported in literature. The associated time evolution
arising from this incremental potential is shown to be consistent with the Landau-Lifschitz equation,
containing the damping term of the Landau-Lifschitz-Gilbert equation to describe the time
evolution of the magnetization. A particular challenge in the modeling of such materials is the
algorithmic preservation of the geometric constraint on the magnetization director field, that remains
constant in magnitude. We presented a novel finite element formulation for the treatment
of the variational-based, symmetric three-field problem, considering the mechanical displacement,
the magnetization director, and the magnetic potential induced by the magnetization as the
primary fields where the geometric property of the magnetization director is exactly preserved
pointwise by nonlinear rotational updates at the nodes. In the current work however, we present an
alternative approach that involves a standard finite element solution followed by a projection step
for the magnetization vector. This method has provides significant advantages in terms of speed
and ease of implementation at the cost of some drawbacks. The current work therefore presents
comparative study of the the two methods by means of a spectrum of benchmark problems.
S7.7: Surface-Coupled Problems Thu, 13:30–15:30
Chair: Thomas-Peter Fries, Ralf Müller S1|03–226
Fluid-Structure-Interaction-Analysis concerning Damping Features of Viscous Fluids
Vilmar Fuchs, Olaf Wünsch (Universität Kassel) Schedule
Fluid-Structure-Interaction (FSI) concerning technological constructions on sea are becoming very
important in view of growing consumption of renewable energy sources. Sea constructions like
offshore wind farms are exposed to extreme weather conditions due to sea storms which cause
enormous loads by wind and waves. In the long term these exposures may lead to serious damage
of the load-bearing piles. On that account this work deals with the damping characteristics of
viscous liquids which are determined to protect the structure. We modeled a damping element
prototype consisting essentially of an elastic cover that is attached to the cylindrical mono pile
foundation at a height of waves. The chamber between the flexible structure and the mono pile
is filled with a viscous fluid. The damping element has been constructed as a test object in the
laboratory scale in a water channel. In order to measure the hydrodynamic loads on the test object,
we placed 16 piezoelectric sensors on the stagnation point of the mono pile. The experiments
of the interaction process of wave loads on the damping element are set up to determinate the
damping influence of fluids with different viscosity. Within the framework of FSI the impact of
breaking waves on a three-dimensional model of a damping element prototype corresponding to
[1] is simulated. In order to measure the influence of different liquid properties on the damping of

Section 7: Coupled problems 171
the impact, the calculations are set up using newtonian and non-newtonian fluids with varying
viscosity. The newtonian results are compared with experiments showing good agreements. For
the non-newtonian investigation verification is carried out with a CFD model.
[1] V. Fuchs, O. Wünsch, Numerical Simulation of Free Surface-Structure-Interaction with Multi-
Regional Mesh Deformation, accepted proceeding PAMM (2011).
Numerical simulations of dense fluid-particle flows using computational fluid (CFD)
dynamics and discrete element method (DEM)
N. Iqbal, C. Rauh, A. Delgado (Universität Erlangen-Nürnberg) Schedule
Particle loaded flows are of significant importance in various industrial applications including
chemicals, fertilizers and energy processes.With the increase of computational capacity, it has
become possible to simulate such flows with a reasonable complexity level such as flow pattern,
particle tracking and reaction kinematics as well. There are two basic approaches to model particleladen
flows: namely Eulerian-Eulerian (two-fluid models) and Eulerian-Lagrangian. In this work
the later that is also known as CFD-DEM approach is used. Fluid phase is modelled using
continuum approach considering transient, compressible and turbulent nature of the flow and
particles are modelled with Lagrangian approach. Generally in this approach for dilute complex
flows the particle tracking is simulated using Lagrangian approach and particle-particle interaction
is neglected. That is not appropriate in dense flows as the collision phenomena have prevailing
effects on the formation and evolution of heterogeneous structures. In current study, the particle
tracking as well as particle-particle interactions are taken into account. This model is capable of
simulating flows with a wide range of particulate void fractions. Momentum exchange between the
phases is modelled by combining the well-known Ergun’s equation and Wen and Yu relation. These
relations are used by several researchers [1,2]. Collision forces between particles are calculated
using soft sphere model (spring, slider and dashpot model).
The framework of OpenFOAM an open source CFD simulation code is used. In the current
study, fluidized bed simulation is considered. The coupled mass and momentum balance equations
are used to calculate the flow behavior, particle fluidization and bubble formation. The dimensions
of the simulation domain are similar to Link et al. (2005)but with different stiffness of particles.
The higher velocity of fluid relative to particles entering through a jet causes the particles to
fluidize. The particles behavior, fluidization, bubble formation and the velocity vectors of particles
show a good agreement with the literature. The results are compared with the two-fluid model
(TFM) that clearly shows that the DEM based model captures the heterogeneous structure in
more detail than the TFM. The quantitative comparison is planned in near future. Preliminary
work on simulations with heat transfer between the phases and chemical reactions is also done.
[1] Y. Tsuji, T. Kawaguchi and T. Tanaka: Discrete particle simulation of two-dimensional fluidized
bed. Powder Technology, 77 (1993) 79-87.
[2] J.M. Link, L.A. Cuypers, N.G. Deen, J.A.M. Kuipers: Flow regimes in a spout-fluid bed:
A combined experimental and simulation study. Chemical Engineering Science 60 (2005)
3425-3442
Simulation of the elastohydrodynamic contact with a piezo-viscous fluid
Thomas Leitz, K. Willner (Universität Erlangen-Nürnberg) Schedule

172 Section 7: Coupled problems
For the purpose of simulating the lubrication in bush bearings, the Reynolds equations, derived
from the Navier-Stokes equations, are widely accepted to be suitable. Since high pressures have
an impact both on the viscosity of the fluid as well as causing an elasic deformation of the
boundary surface, a piezo viscous model and an elasto-hydrodynamic model have been included
as an extension of the purely isoviscous model.
First a numerical solution based on the finite element method for the simple model consisting
of purely isoviscous flow bounded by rigid surfaces and being described by the 2D Reynolds equations
will be presented. A comparison of the numerical results to the analytical solution of the
Reynolds equations verifies the implementation. Secondly the coupling with two different models
for piezo viscosity, namely Barus and Roelands, has been investigated. Furthermore, to allow
elastic deformation of the surfaces, an elasto-hydrodynamic coupling based on a halfspace model
for the displacements has been included into the implementation. Combining the methods for
simulating piezo viscosity and elastic deformation, we expect to obtain more realistic simulations
of the lubrication in bush bearings.
Analysis and Modeling of the Hydro-Mechanics of Deformable Fractures
Carlo Vinci, Jörg Renner, Holger Steeb (Universität Bochum) Schedule
High pressure fluid injection into rock formations, e.g. hydraulic fracturing of reservoir rocks,
causes several coupled physical phenomena in the rock and in the fluid. In the present contribution,
we investigate and model the flow of a viscous fluid into a single deformable fracture and
the associated elastic deformation of the surrounding porous rock. In fact, fluid injection into a
fractured porous rock causes deformation, in particular dilatation, of existing fractures affecting
their hydraulic properties and generally leading to an increase of the effective permeability of the
rock. Otherwise, the elastic crack deformation influences the current pressure distribution in the
fracture, and, therefore, the diffusion process of the pore fluid in the joint. A deep and detailed
understanding of the coupling between fluid pressure diffusion and elastic deformation is needed
in order to model the infiltration process of a viscous fluid into a single fracture.
Despite the substantial number of previous modeling approaches, a clear insight into the numerical
solution procedure of high pressure fluid injection in a fracture has not been gained. Therefore, we
present numerical solution strategies to solve the system of a single joint in a porous rock matrix.
Due to the coupled nature of the problem, conceptually and technically different strategies have
be applied to model and solve the resulting hydro-mechanical system. We use different staggered
finite element-based solution schemes and compare them to a fully coupled one. The latter is
based on Biots quasi-static poroelastic equations. Rather than relying on a heuristic formulation
of the associated diffusion equation, we derive this from the conservation of mass avoiding any
of the frequently used approximations or simplifications. The physically-based model takes into
account the roles of non-linear diffusion of the fluid and elastic rock deformation during pumping
operations in boreholes.
We compare and critically discuss the results obtained with the two explored solution approaches.
This information provides an improved understanding of physical phenomena accompanying the
hydraulic part and the mechanical response and thus builds the basis for more complex multi-joint
hydraulic fracturing investigations on larger scale.
Numerical Simulation of organic binder decomposition and combined seepage- and
diffusive transport of the gaseous reaction products through a porous green body
during thermal debinding of ceramic parts.
I. Schmidt, H. Riedel (Fraunhofer Institut für Werkstoffmechanik, Freiburg), J. Svoboda (Czech
Academy of Sciences Brno) Schedule

Section 7: Coupled problems 173
In the powder technological production of ceramic parts, organic additives are admixed to the
ceramic powder so as to give the green part strength and/or facilitate the compaction. Before the
part is sintered to obtain its final strength and shape, these additives have to be removed from
the green body, e.g. by a thermal debinding process. During this process, the binder undergoes
thermal decomposition into gaseous reaction products which subsequently have to be transported
to the surface through the pore channels. Depending on the heating rate and the green bodys
permeability, a pressure develops inside the body, creating, in turn, stresses in the solid skeleton
which can cause damage. The paper presents a model which describes the chemical decomposition
of organic binders, the combined Maxwell-Stefan and Knudsen diffusion and the seepage
flow of multiple gaseous reaction products through a porous body and the implementation of the
model into a finite element framework. Special attention is paid to the correct formulation and
implementation of Robin-type boundary conditions for the multi-component diffusion problem.
Results are presented for a prototype problem, including the computation of the solid skeleton
stresses and a discussion of the relative importance of the different transport mechanisms.
Simulator Coupling for Predicting Nonlinear Rotor/Bearing Interactions
Daixing Lu, Martin Busch, Bernhard Schweizer (Universität Kassel) Schedule
Precisely calculating the dynamic oscillations of rotors supported in oil film bearings requires very
detailed and accurate bearing models. Performing dynamic simulations of rotors with hydrodynamic
bearings, usually models based on look-up tables are used, i.e. the nonlinear stiffness and
damping characteristic of the bearings is determined in a preprocessing step and incorporated
into the simulation model for the rotor by means of spline-approximation techniques [1]. Such an
approach is very time efficient, but suffers from a reduced physical accuracy. To improve the simulation,
the finite-element models for the bearings are directly coupled with the multibody model
for the rotor. Here, we discuss a weak coupling approach based on a semi-implicit integration
technique in combination with a master/slave simulator coupling strategy [2].
[1] B. Schweizer, Dynamics and Stability of Turbocharger Rotors, Archive of Applied Mechanics
80(9) (2010), 1017 – 1043.
[2] M. Busch, B. Schweizer, Coupled Simulation of Multibody and Finite Element Systems:
An Efficient and Robust Semi-Implicit Coupling Approach, Archive of Applied Mechanics
(2011), doi: 10.1007/s00419-011-0586-0.
S7.8: Miscellaneous Coupled Problems Thu, 16:00–18:00
Chair: Christian Linder S1|03–226
The Scattering map in two-linked rocking blocks
Albert Granados (Universität Stuttgart), John Hogan (University of Bristol), Tere Seara (Universitat
Politècnica de Catalunya) Schedule
The rocking block is not only a paradigm of a mechanical system with impacts, but also it is used
to model the behaviour of slender structures under an external forcing, such as water tanks or
nuclear fuel rods under earthquake excitation. In addition, the stacked coupling of such blocks
is also of interest for the modeling of structures in civil engineering or nano carbon tubes under
small vibrations.
In this work we consider a generalization of a simple model based on two rocking blocks linked
by a spring under a non-autonomous periodic forcing. Considering that the spring constant is

174 Section 7: Coupled problems
small, we treat the model as two impact oscillators under a general perturbation which includes
the forcing and the coupling. This leads to a 5-dimensional non-smooth system with two switching
manifolds.
We then focus on the configuration given by large amplitude oscillations for one block while the
other one oscillates with higher frequency and smaller amplitude. By means of the impact map
associated with the fast rocking block, we derive sufficient conditions for the existence of heteroclinic
connections and construct the so-called scattering map. The properties of this map allows us
to show that, under certain conditions, for any arbitrarily small amplitude of the periodic forcing,
energy is accumulated on the fast rocking block at every large oscillation of the slow motion rock.
Then, by properly concatenating such movements, it is possible to show that, for large time scales
and arbitrarily small amplitude of the forcing, arbitrarily high energy can be accumulated in the
system, hence leading to the instabilities as a consequence of the so-called Arnol’d diffusion.
Modeling and Simulation of Microwave Heating for Spalling of Radioactive Contaminated
Concrete
Andreas Melcher, Thorsten Kayser, Guido Link, John Jelonnek (KIT) Schedule
Microwave heating is becoming of growing importance in material sciences in the last ten years.
Due to the volumetric heating effect microwave heating offers an energy efficient way of processing
materials in several ways. The modeling and simulation of material processing with microwaves
with respect to the material structure is a challengeing task. In this talk we will analyze the
complexity of the problem, giving an appropriate modeling which result in a coupled, multiscale
problem in space and time consisting Maxwell equations, the heat equation and a description of
the electromagnetic material properties of the concerning materials. As example we discuss the
ablation of concrete with microwaves and give some experimental and simulation results
Quantifying diffusion for an ultrasonic wire bonding process by applying the theory
of material forces
Mohamad Sbeiti, Wolfgang H. Müller (TU Berlin), Martin Schneider-Ramelow (Fraunhofer Institut
für Zuverlässigkeit und Mikrointegration, Berlin), Ute Geißler (TU Berlin) Schedule
Ultrasonic wire bonding is a method applied in electronic packaging for interconnections between
two devices at ambient temperature. In this process, high frequency vibrations (f = 100 kHz)
combined with pressure are responsible for the deformation of a 25µm aluminum wire in vertical
direction and for the formation of an Au8Al3 intermetallic phase between the wire and the pad.
Due to the variety and complexity of the mechanisms occurring during the bonding process there
is an enormous demand to clarify some open issues for a thorough interpretation of the metallurgical
processes that take place at the interface of the bond and in the wire.
FE simulations of the temperature increase due to ultrasonic energy dissipation and plastic deformation
(Taylor-Quinney effect) during the bonding process show that it is too small in order to
explain the amount of intermetallic phase formed in terms of classical Fickian diffusion. Therefore
one of the open issues is to investigate the mechanical coupling on diffusion in terms of the strain
energy densities arising during the bonding process.
For clarification of this issue a thermo-mechanical FE model was first created to determine the
stress states and the strain energy densities around the interface. Then a post-processing tool
was written in C++ (based on an existing code developed by R. Müller and his group at the
University of Kaiserslautern) in order to calculate the thermo-mechanical driving force in terms
of the local jump of the Eshelby tensor across the interface.
Within the framework of material forces the local jump of the Eshelby tensor can be compared
with the thickness of the formed intermetallic phase for various bonding parameters. This will

Section 7: Coupled problems 175
allow us to predict an effective diffusion constant which takes temperature and mechanical driving
forces into account. After this relation has been established a subsequent objective of our
investigations is to optimize the growth of the Au8Al3 intermetallic phase in terms of bonding
parameters.
Electronic Structure Calculations with Finite Elements
Volker Schauer, Christian Linder (Universität Stuttgart) Schedule
The physical properties of materials, as for example electric and thermal conductivity, magnetism,
formation of microstructures as well as the mechanical response upon external excitations, are
finally determined by the electronic structure of the material. The quantum mechanical description
of electronic structure represents a coupled many body problem, consisting of the positively
charged atomic cores and the negatively charged, fermionic electrons. By the Hohenberg-Kohn
theorem a method was established to calculate the electron density of the ground state of an
atomic system as the minimum of a density functional [1]. The variation of the functional leads to
the Kohn-Sham equations, which represent a nonlinear eigenvalue problem. The originally coupled
problem has therefore been transformed into a nonlinear but single particle problem with
an effective potential that accounts for the Coulomb interactions between the particles as well as
for quantum mechanical effects [2]. The Kohn-Sham equations can be solved iteratively with the
so-called self consistent field algorithm. We implement a real space formulation for the calculation
of the electronic structure in the context of density functional theory. In a first step a finite element
based solution algorithm for the Kohn-Sham equations is developed, based upon which the
electron density can be obtained in a non periodic setting [3]. We will present the basic elements
of our implementation together with some typical examples for the electronic structure.
[1] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas, Phys. Rev. B 136 (1964), 864-871.
[2] R.M. Martin, Electronic Structure, Cambridge University Press (2004).
[3] P. Suryanarayana, V. Gavini, T. Blesgen, K. Bhattacharya, M. Ortiz, Non-periodic finiteelement
formulation of KohnSham density functional theory, Journal of the Mechanics and
Physics of Solids 58 (2010), 256-280.
Modifications of hypergraphs of subsystems of mechatronic system as an effect of
their analysis by means of different methods
Andrzej Buchacz (Silesian University of Technology) Schedule
Purpose of this paper is analysis of vibrating beams as subsystems of transverse vibraing mechatronic
system by the exact and approximate methods and creating the hypergraphs of the beams
in case of presented methods of analysis. Approach was to nominate the relevance or irrelevance
between the characteristics obtained by considered methods - especially concerning the relevance
of the natural frequencies-poles of characteristics of simply beam. The main subject of the research
are the continuous beams as the subsystems of continous-discrete vibrating mechatoronic
system. Findings this approach is fact, that approximate solutions fulfill conditions for vibrating
beams and can be introduction to synthesis of these systems modeled by hypergraphs of different
category. Practical implication of this study is the main point is the introduction to synthesis
of considered mechatronic system. Originality of this approach relies on application approximate
method of analysis of beams and modeling the ones by modifications hypergraphs.

176 Section 8: Multiscales and homogenization
Section 8: Multiscales and homogenization
Organizers: Andreas Menzel (TU Dortmund), Sergiy Nesenenko (TU Darmstadt)
S8.1: Multiscale analysis of laminated composites Tue, 13:30–15:30
Chair: Andres Menzel, Sergiy Nesenenko S1|01–A01
Non-laminate Microstructures in Monoclinic-I Martensite
Anja Schlömerkemper (Universität Würzburg), Isaac Chenchiah (University of Bristol) Schedule
The most common shape memory alloys are monoclinic-I martensite. We study their zero energy
states and have two surprising results:
First, there is a five-dimensional continuum in which the energy minimising microstructures
are T3s, i.e. infinite-rank laminates. To our knowledge, this is the first real material in which T3s
occur. We discuss some of the consequences of this discovery.
Second, there are in fact two types of monoclinic-I martensite, which differ by their convexpolytope
structure but not by their symmetry properties. It happens that all known materials
belong to one of the two types. We explore whether materials belonging to the other type would
have superior properties since they have different zero-energy states.
Our analysis uses algebraic methods, in particular the theory of convex polytopes.
An orientation-distribution-based multi-scale approach for modeling of flow-induced
anisotropy of polar ice for the EDML deep-drilling site, Antarctica
Swantje Bargmann (TU Dortmund), Hakime Seddik, Ralf Greve (Hokkaido University) Schedule
In this contribution we model the anisotropic flow in polar ice in order to gain a better understanding
for the underlying microstructure and its influence on the deformation process. In
particular, a continuum mechanical, anisotropic flow model, which is based on an anisotropic flow
enhancement factor, the so-called CAFFE model, is applied. The polycrystalline ice is regarded
as a mixture whose grains are characterized by their orientation.
The approach is based on two distinct scales: the underlying microstructure influences the
macroscopic material behavior and is taken into account phenomenologically. To achieve this
the orientation mass density is introduced as a so called mesoscopic field. The classical flow law
of Glen is extended by a scalar enhancement factor. Moreover, four different effects (local rigid
body rotation, grain rotation, rotation recrystallization, grain boundary migration) influencing
the evolution of the grain orientations are taken into account. A finite volume method is chosen
for the discretization procedure. Numerical results simulating the ice flow in the EPICA ice core
EDML, Antarctica, are presented.
[1] S. Bargmann, H. Seddik, R. Greve. Computational modeling of flow-induced anisotropy of
polar ice for the EDML deep-drilling site, Antarctica: the effect of rotation recrystallization
and grain boundary migration. International Journal for Numerical and Analytical Methods
in Geomechanics 2011, accepted for publication, DOI: 10.1002/nag.1034
[2] R. Greve,H. Blatter. (2009). Dynamics of Ice Sheets and Glaciers. Springer, Berlin, Germany
[3] L. Placidi, R. Greve, H. Seddik, S.H. Faria. A continuum-mechanical, anisotropic flow model
for polar ice, based on an anisotropic flow enhancement factor. Continuum Mechanics and
Thermodynamics 2009; doi: 10.1007/s00161-009-0126-0
[4] H. Seddik, R. Greve, L. Placidi, I. Hamann, O. Gagliardini. Application of a continuummechanical
model for the flow of anisotropic polar ice to the EDML core, Antarctica. Journal

Section 8: Multiscales and homogenization 177
of Glaciology 2008, 45(187):631-642.
The evolution of the crystallographic texture in terms of harmonic tensors
Jan Kalisch, Albrecht Bertram (Universität Magdeburg) Schedule
The crystallographic texture of polycrystals determines the anisotropy of both their elastic and
plastic behaviour. The texture is described by the orientation distribution function (ODF) giving
the volume fraction of single crystals with similar lattice orientation [1,2,3,4].
The Fourier expansion of the ODF on the space of orientations provides an infinite list of harmonic
tensors, called texture coefficients [1,2]. Alternatively, we can use the maximum entropy
approximation [5] to obtain the pseudo ODF [2]. It involves a finite list of harmonic tensors, called
pseudo texture coefficients.
Either set of tensors can be used as set of internal variables to account for the influence of the
crystallographic texture in macro-scale models of polycrystals.
Focusing on the crystallographic texture, we consider a single crystal model for which the internal
state is determined completely by the orientation. The homogenisation of the flow potential has
been discussed in [3,6].
In polycrystals consisting of such single crystals and homogeneous processes (Taylor or Sachs
model), the texture evolution follows an infinite system of linear ODEs for the texture coefficients
or a finite system of quasilinear ODEs for the pseudo texture coefficients, respectively. We discuss
aspects of both systems and provide numerical solutions for simple examples.
[1] J. Kalisch, A. Bertram, On the Evolution of the Crystallographic Texture of Cubic Polycrystals
in Coaxial Processes, Int. J. Mater. Form. 3 Suppl. 1 (2010), 57 – 60.
[2] T. Böhlke, Texture Simulation based on Tensorial Fourier Coefficients, Comp. Struct., 84
(2006), 1086 – 1094.
[3] T. Böhlke, The Voigt bound of the stress potential of isotropic viscoplastic FCC polycrystals,
Arch. Mech. 56 (2004), 425 – 445.
[4] B.L. Adams, J.P. Boehler, M. Guidi, E.T. Onat, Group theory and representation of microstructure
and mechanical behavior of polycrystals, J. Mech. Phys. Solids 40 (1992), 723
– 737.
[5] E. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106 (1957), 620 – 630.
[6] R. Tsotsova, T. Böhlke, Representation of effective flow potentials for polycrystals based on
texture data, I. J. Mat. Forming 2 Suppl. 1 (2009), 451 – 454.
A Texture-Based Two-Scale Finite Element Simulation of a Multi-Step Can Forming
Process
V. Glavas, T. Böhlke (KIT), D. Daniel (Constellium), C. Leppin (Suisse Technology Partners
AG) Schedule
Aluminum sheets used for beverage cans show a significant anisotropic plastic material behavior
in sheet metal forming operations. In a deep drawing process of cups this anisotropy leads to a
non-uniform height, i.e., an earing profile. The prediction of this earing profiles is important for
the optimization of the forming process. In most cases the earing behavior cannot be predicted

178 Section 8: Multiscales and homogenization
precisely based on phenomenological material models. In the presented work a micromechanical,
texture-based model is used to simulate the first two steps (cupping and redrawing) of a can
forming process. The predictions of the earing profile after each step are compared to experimental
data.
The mechanical modeling is done with a large strain elastic visco-plastic crystal plasticity
material model with a Norton type flow rule for each crystal. The response of the polycrystal is
approximated by a Taylor type homogenization scheme. The simulations are carried out in the
framework of the finite element method. The shape of the earing profile from the finite element
simulation is compared to experimental profiles.
[1] T. Böhlke, G. Risy, A. Bertram, Finite element simulation of metal forming operations with
texture based material models. Modelling and Simulation in Material Science and Engineering
(2006) 365–387.
[2] K. Jöchen, T. Böhlke, Preprocessing of Texture Data for an Efficient Use in Homogenization
Schemes. Proc. 10th Int. Conf. Techn. Plast. ICTP (2011) 848–853.
[3] G. I. Taylor, Plastic strain in metals. Journal of the Institute of Metals 62 (1938) 307–322.
Construction of Statistically Similar RVEs for 3D Microstructures
Lisa Scheunemann, Daniel Balzani, Dominik Brands, Jörg Schröder (Universität Duisburg-Essen)
Schedule
The microstructure of advanced high-strength steels influences significantly the overall material
properties and should thus be incorporated in numerical calculations. For this purpose, the
FE 2 method, also known as direct micro-macro transition, is a suitable numerical tool, see e. g.
[1], [2]. In this context, the definition of a representative volume element (RVE), which is characterized
by a significantly reduced complexity compared with the real microstructure, reduces time
and memory costs. Therefore, we propose the construction of statistically similar RVEs (SSRVEs)
which still represent the mechanical response of the material accurately, cf. [3]. The construction
method is based on the minimization of a least-square functional considering the differences of
suitable statistical measures characterizing the inclusion morphology of a given real microstructure
and of the SSRVE. In 2D the construction of SSRVEs turned out to be successfull in a series
of numerical examples, cf. [3], [4].
The focus of this talk is on the construction of three-dimensional SSRVEs based on the inclusion
phase fraction, the spectral density and the lineal-path function. SSRVEs are constructed for a
real microstructure of a DP-steel from 3D measurement obtained by 3D Electron Backscatter
Diffraction (EBSD) combined with a Focused Ion Beam (FIB). To demonstrate the performance
of the proposed method we discuss several numerical examples.
[1] C. Miehe, J. Schröder, J. Schotte: Computer Methods in Applied Mechanics and Engineering,
171:387–418, 1999.
[2] J. Schröder: Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart, Habilitation
thesis, 2000.
[3] J. Schröder, D. Balzani and D. Brands: Archive of Applied Mechanics, 81:975-997, 2011.
[4] D. Balzani, D. Brands, J. Schröder, C. Carstensen: Technische Mechanik, 30/4:297-315, 2010.

Section 8: Multiscales and homogenization 179
[5] R. N. Singh, N. Zaafarani, D. Raabe, F. Roters and S. Zaefferer: Acta Materialia, 54:1863-
1876, 2006.
S8.2: Discrete-to-continuum and homogenization methods Tue, 16:00–18:00
Chair: Jörg Hohe, Bernhard Eidel S1|01–A01
Numerical quadrature for coarse-grained molecular statics
Bernhard Eidel (Universität Duisburg-Essen) Schedule
Recent research in atomistic-to-continuum coupling methods and in particular in the Quasicontinuum
(QC) method has shown a strong interest in numerical quadrature because it largely
determines the methods accuracy and efficiency. Mathematical analyses of new quadrature rules
often restrict to (i) the 1D case of atomic chain models, to (ii) simple pair potentials and to (iii)
additional ad-hoc assumptions and simple applications. These simplifications (i)-(iii) make the
problem tractable by analytical means or alleviate numerical analysis. Doing this, mathematics
has brought new insights into atomistic-based finite element methods. However, it is not clear,
how the quadrature rules shall be reformulated without these strongly simplifying assumptions.
The main aim of the present contribution is the numerical analysis of different quadrature rules
within the QC method in a more realistic physical setting, namely (i) in 3D, (ii) using EAMpotentials
and (iii) analyzing paradigmatic multiscale settings of nano- and micromechnics. In
particular, we compare the method proposed by Gunzburger & Zhang (SIAM Multiscale Model.
Simul., 8:571–590, 2010) with the cluster-based summation rule as proposed by Knap & Ortiz
(J. Mech. Phys. Solids 49:1899–1923, 2001). The different quadrature schemes are assessed and
compared in representative numerical examples.
Partial Damping for Weak Coupling between MD and FE models
Wenzhe Shan, Udo Nackenhorst (Universität Hannover) Schedule
The weak coupling method enables us to decompose the solution into a high-frequency part and
low-frequency part. The low-frequency part can be approximated by the FE shape functions while
the high-frequency part, without extra treatment, will be reflected back into the MD domain. By
frequency analysis, we found the weak coupling method, despite its complexity, does not offer
smoother transition for mechanical motions between the FE and MD domains, in comparison
the more straightforward bridging domain method. However, the motion decomposition from the
weak coupling method provides us convenient way to handle the transmissible and untransmissible
motions separately. And due to the orthogonality of such decomposition, the influences of the
manipulation applied to one part are minimized to the other.
When dynamic problems are of interest, the high-frequency waves reflected from the coupling
boundary will pollute the solution in the MD domain quickly and render the results from the
multiscale model meaningless. In this contribution, we show that by applying artificial damping
only to the high-frequency part of the displacement field in the coupling domain in the weak
coupling method can significantly reduce the reflections in the MD domain while not affecting the
low-frequency part that can be transmitted into the FE domain. The frequency analysis shows
the errors in the magnitudes and phases of wave components are orders of magnitudes smaller
than that in the bridging domain model or undamped weak coupling model.
Simulation of texture evolution during rolling by using a homogenization method of
Hashin-Shtrikman type
Katja Jöchen, Thomas Böhlke (KIT) Schedule

180 Section 8: Multiscales and homogenization
In this contribution, the development of rolling textures in metals is investigated by using a
homogenization method that is based on a homogeneous comparison material [4]. Assuming piecewise
constant stress polarizations in the polycrystalline aggregate and restricting to ellipsoidal
two-point statistics, a localization rule for the strain field is derived. Varying the stiffness of
the comparison medium, the proposed scheme inherently includes a smooth transition between
Taylor- and Sachs-type textures, the latter are obtained using infinitely stiff and infinitely compliant
comparison materials. As an example, the texture evolution during rolling of an aluminum
sheet is simulated with initial orientation data taken from [1]. It is shown that the application of
different comparison materials in the homogenization scheme leads to the development of different
main texture characteristics [3]. Especially the initially dominant cube component shows a strong
dependence on the choice of the comparison material.
To speed up the simulations using experimental texture information of the polycrystalline material,
the data is representatively reduced by using a partitioning technique of the orientation
space [2] before entering the homogenization framework.
[1] L. Delannay, S. R. Kalidindi, and P. Van Houtte, 2002, Quantitative prediction of textures
in aluminium cold rolled to moderate strains, Mat. Sci. Eng. A, 336, 233 - 244
[2] K. Jöchen, and T. Böhlke, 2011, Preprocessing of texture data for an efficient use in homogenization
schemes, ICTP2011 Proceedings, 848-853
[3] K. Jöchen, and T. Böhlke, 2011/12, Prediction of texture evolution in rolled sheet metals by
using homogenization schemes, submitted to Key Engineering Materials, 6 p.
[4] P. Ponte Castañeda, and P. Suquet, 1998, Nonlinear Composites Adv. Appl.Mech. 34, 171-302
Local probabilistic homogenization schemes for assessment of material uncertainties
in solid foams
Jörg Hohe, Carla Beckmann (Fraunhofer-Institut für Werkstoffmechanik) Schedule
Solid foams gain increasing importance as lightweight construction materials e.g. as core materials
in sandwich construction. Their main advantage is their low specific weight due to their high void
volume fraction and the resulting advantageous stiffness-to-weight ratio. On the other hand, solid
foams have the disadvantage of a random, disordered microstructure causing a distinct scatter in
their effective stiffness and strength.
The present study is concerned with a local probabilistic homogenization scheme far a stochastic
analysis of the effective stiffness and strength of solid foams. For this purpose, a standard
homogenization procedure is adopted, defining the effective stresses and strains as their volume
averages with respect to a mesoscopic volume element. In contrast to the homogenization of
regular microstructured media or randomly microheterogeneous media with small characteristic
internal length scales, especially metallic foams may feature a microstructure with internal lengths
(e.g. cell sizes) which are not much smaller than the smallest characteristic length of the macroscopic
structure, e.g. a sandwich core thickness. Hence, a rigorously deterministic homogenization
is not feasible and a stochastic approach is required.
For this purpose, a large-scale, statistically representative volume element is considered. The
volume element features a disordered microstructure defined in terms of a set of random variables.
The computational foam model is generated randomly using a Voronoï process in Laguerre
geometry. In contrast to previous approaches, the homogenization is performed locally, using the

Section 8: Multiscales and homogenization 181
individual cells of the large-scale volume element as small-scale testing volume elements. Alternatively,
a moving-window approach is employed. The testing volume elements themselves are
non-representative, however, the entire set of testing volume elements has to be sufficiently large
in order to be representative. Determining the effective stiffness and strength for the individual
testing volume elements provides the mean values and the corresponding probability distributions
for the effective material properties. Furthermore, the spatial correlation of the effective properties
and its decay can be analyzed.
As a result, the stochastic information for a probabilistic structural analysis of foam structures
on the macroscopic level is obtained, where the material properties are defined in terms of random
fields.
Short-fiber reinforced thermoplastics – A geometrically non-linear two-scale approach
V. Müller, B. Brylka, T. Böhlke (KIT) Schedule
Short-fiber-reinforced composites are increasingly used not only because of their advantageous
ratio of stiffness to weight in comparison to pure thermoplastics but also in consequence of the
possibility of low-cost manufacturing. Usually composites of this kind are manufactured in injection
or compression molding processes. Therefore, short fiber reinforced polymers show heterogeneities
on different length scales concerning micro-structural properties like fiber orientation
distributions [1].
Micromechanical models offer the opportunity of a mechanism-based modeling. In contrary
to FE 2 schemes the application of mean field approaches at the integration point level of the
finite elements represents a compromise between computational effort and accuracy [2]. Mean
field approaches can predict phase averages of mechanical fields as well as stress and strain
heterogeneities in the phases based on a simplified description of microstructure [3].
In the presentation short-fiber reinforced thermoplastics with spatially varying orientation
distributions of fibers are considered. The micromechanically based model is developed in a geometrically
nonlinear setting. To demonstrate the effect of the microstructure on the macroscopic
material behavior a model problem is generated with specially heterogeneous orientation distributions
of fibers. This data is used within finite element simulations of shell type structural
elements.
[1] M. Laspalas, C. Crespo, M.A. Jimènez, B. García, J.L. Pelegay Application of micromechanical
models for elasticity and failure to short fibre reinforced composites. Numerical
implementation and experimental validation, Computers and Structures, 2008, 86, 977–987
[2] V. Kouznetsova, W. A. Brekelmans, F.P.T. Baaijens An approach to micro-macro modeling
of heterogeneous materials, Computational Mechanics, 2001, 27, 37–48
[3] Charles L. Tucker III, Liang Erwin Stiffness predictions for unidirectional short-fiber composites:
Review and evaluation, Composites Science and Technology, 1999, 59, 655–671
Discrete model of a non-symmetric elasticity theory
Maksym Berezhnyi (TU Darmstadt) Schedule
We consider a discrete network of a large number of pin-type homogeneous rods oriented along
a given vector and connected by elastic springs at each point. The asymptotic behavior of small
oscillations of the discrete system is studied in the case where the distances between the nearest
rods tend to zero. For generic non-periodic arrays of rods, we deduce equations describing the
homogenized model of the system. It is shown that the homogenized equations correspond to

182 Section 8: Multiscales and homogenization
a non-standard dynamics of an elastic medium. Namely, the homogenized stress tensor in the
medium depends linearly not only on the strain tensor but also on the rotation tensor:
σ[u] = A D e[u] + A R ω[u], (1)
where the fourth-rank tensors A D and A R can be considered as the deformative and rotational
parts of the elasticity tensor respectively. Moreover, those parts don’t possess the symmetry properties
postulating in classical continuum mechanics.
S8.3: Generalised continua Tue, 16:00–18:00
Chair: Sergiy Nesenenko, Evgen Khruslov S1|01–A04
On oscillation of elastic medium with small cavities filled by viscous incompressible
liquid
Evgen Khruslov (Verkin Institute for Low Temperature Physics, Kharkiv) Schedule
We consider equations describing non-stationary oscillations of elastic medium with small cavities
filled by viscous incompressible liquid. The asymptotic behaviour of the solution for the Cauchy
problem for these equations is studied when the diameters of the cavities tend to zero and their
density increases. We obtain the homogenized equation describing the first term of the asymptotics.
Further, we study the long time behaviour of the solution for the homogenized equation. We
prove that the solution decays exponentially.
Parameteridentification in Discrete Element Methods via Comparison with Cosserat
Theory
Nicola Wessels, Klaus Hackl (Universität Bochum) Schedule
One of the main challenges using the Discrete Element Method is that there is no direct compliance
to the well known continuum parameters such as elastic moduli. In this presentation we
show how homogenization procedures using representative volume elements composed of discrete
particles lead to Cosserat continua.
Simulating a shear test with discrete elements it becomes obvious, that the evolving microstructure
is mainly composed of contact chains that form triangles and quadrilaterals. For these contact
chains we set up contact energies in normal and shear directions and combine those to derive the
effective energy of the material. By comparison of this energy to a Cosserat energy we can derive
formulas for the Lamé and Cosserat parameters. They are now only dependent on the interaction
energies and radii of the particles.
To show the validity of our assumptions and derivations we present some discrete element simulations
of shear tests.
Complete asymptotic decomposition in the problem of elestic frameworks deformation
A.G. Kolpakov (Siberian State University of Telecommunications and Informatics, Novosibirsk),
S.I. Rakin (Siberian Transport University, Novosibirsk) Schedule
Frameworks, considered as three dimensional elastic structure, consists of thin beams and joints,
which assemble the beams in a unity. Thus, analysis of frameworks consists in both analysis of
beams and analysis of joints. The classical structural engineering approach does not ffeelßpecific
properties of a joint: geometry, material characteristics, etc. We demonstrate that asymptotic analysis
based approach allows integrated analysis of framework structure and joints. We demonstrate
that the problem allows complete asymptotic decomposition: solution to the original problem can
be separated into solution of a problem about deformation of a system of one dimensional beams

Section 8: Multiscales and homogenization 183
and solution of the elasticity theory problems separately for any joint.
We start our consideration with the case of two joined beams with one joint. The left beam
places between x1 = −1 and x1 = 0, the right beam places between x1 = 0 and x1 = 1, the joint
places around the origin of the coordinate system x = 0. We assume that the diameters of beams
and dimensions of the joint in all directions are proportional to a small parameter ε.
We use the method of local perturbation [1] and find solution in the form
u ε (x) = εw1(x1)e1 + w2(x1)e2 − w ′ 2(x1)x2e1 + (1)
+w3(x1)e3 − w ′ 3(x1)x2e1 + (x2e3 − x3e2)Θ(x1) + εv(x/ε)
The leading six terms in the right-hand side of (1) correspond to structural mechanics hypothesis.
The novelty is the last term in the right-hand side of (1). It is introduced to account the perturbation
of solution associated with the joint. We assume that the function v(y) is perturbed near
x = 0.
The representation (1) is similar to the solution representation on the homogenization theory.
The difference is that the perturbation v(y) is periodic in the homogenization theory, but v(y) is
perturbed near x = 0 in our consideration. It leads to the significant differences in the final results.
In particular, the joint is ignored in the limit problem. But local stress-strain state essentially
depends on the specific properties (both geometrical and material) of the joint.
We expand our method to beams with many joints and joint assembling several beams.
The research was supported through Marie Curie actions FP7: project PIIF2-GA-2008-219690.
[1] Gaudiello A., Kolpakov A.G.: Influence of nondegenerated joint on the global and local
behaviour of joined rods. Int. J. Engng Sci. 2011, 49, 295-309.
Periodic elliptic operators with preassigned spectral gaps
Andrii Khrabustovskyi (B. Verkin Institute for Low Temperature Physics, Kharkiv) Schedule
We deal with differential operators in R n (n ≥ 2) of the form
A = − 1
b(x)
n�
k,l=1
∂
∂xk
�
a kl (x) ∂
where akl(x), b(x) are measurable functions satisfying the conditions
a kl (x) = a lk (x), ∀ξ ∈ R n , |ξ| = 1 : 0 < a − ≤ a kl (x)ξkξl ≤ a + < ∞
0 < b − ≤ b(x) ≤ b + < ∞
∂xl
∀i ∈ Z n , ∀x ∈ R n : a kl (x + i) = a kl (x), b(x + i) = b(x)
It is known (E. Green (1997), A. Figotin and P. Kuchment (1997), R. Hempel and K. Lienau
(2000), L. Friedlander (2002), O. Post (2003), V. Zhikov (2005)) that for an arbitrary m ∈ N one
can construct an operator of the form (1) with at least m gaps in its spectrum.
Our goal is to solve the following inverse problem: for an arbitrary set of m pairwise disjoint
finite intervals on the positive semi-axis to construct an operator of the form (1) with (at least)
m gaps that are close (in some sense) to these preassigned intervals.
The precise statement of this problem and its solution are presented in [1], where the functions
a kl (x) and b(x) are chosen in the form
a kl (x) = g kl (x) � det G(x), b(x) = � det G(x)
�
(1)

184 Section 8: Multiscales and homogenization
Here G(x) = {gkl(x)} n
k,l=1 is some positively defined symmetric matrix, gkl (x) are the components
of G −1 . Hence the operator A is the Laplace-Beltrami operator on the manifold M = R n equipped
with the metrics G.
We also discuss another method of constructing the appropriate functions a kl (x) and b(x)
which has no geometrical interpretation.
The ideas and methods are based on the previous results of the author related to homogenization
theory for PDE’s.
[1] A. Khrabustovskyi, Periodic Riemannian manifold with preassigned gaps in spectrum of
Laplace-Beltrami operator, J. Differ. Equ. 252 (2012), 2339 – 2369.
Numerical assessment of disorder effects in metal foam core sandwich beams based
on a local homogenization procedure
Carla Beckmann, Jörg Hohe (Fraunhofer-Institut für Werkstoffmechanik) Schedule
Solid foams are interesting materials for the core of sandwich constructions because of their
low specific weight. However, the random microstructure is disadvantageous because disorder
effects are the cause of spreading in the material behaviour of the whole device. To predict the
uncertainties in the structural response of materials with random microstructure the numerical
assessment gains more and more in importance because it is cost-efficient in contrast to extensive
experimental analyses.
In the present study, a numerical analysis of disorder effects in foam core sandwich beams is
performed in order to assess the scatter due to the disordered foam microstructure. To determine
the macroscopic effective material properties, a repeated numerical generation and analysis of
representative volume elements for the microstructure of the material is applied. Computational
models for the foam microstructure are generated randomly using a Voronoï tessellation in
Laguerre geometry. Using a large-scale volume element, a local homogenization procedure based
on a moving window technique is applied which yields a sufficient large quantity of data in order
to determine probability distributions and the spreading as well as the spatial correlation
and the correlation between different material properties. In consideration of these statistical values,
random fields are generated which make it possible not only to compute the mean effective
properties in a numerical efficient way but also to determine the corresponding scatter. This is
especially important in the assessment of the material strength because the local extreme values
are responsible for the material failure.
In order to illustrate the essential difference between computations where on the one hand the
microstructure is replaced by a homogenous substitute medium and on the other hand by random
fields, both methods are applied to a single edge clamped metal foam core sandwich beam which
is loaded by a force at the free end.
S8.4: Time-dependent and thermo-mechanical processes Wed, 13:30–15:30
Chair: Daniel Juhre, Sandra Klinge S1|01–A01
Viscoelastic effects and shrinkage as the accompanying phenomena of the curing of
polymers. Single- and multiscale effects
Sandra Klinge, Alexander Bartels, Klaus Hackl (Universität Bochum), Paul Steinmann (Universität
Erlangen-Nürnberg) Schedule
The presentation deals with the modeling of two phenomena that are characteristic for the curing
of polymers, namely the increasing viscosity and the volume decrease known as autogeneous

Section 8: Multiscales and homogenization 185
shrinkage. Both of these processes are caused by the cross-linking of polymer chains during polymerization.
In order to model the viscoelastic effects the free energy consisting of an equilibrium
and a non-equilibrium part is proposed. The former is related to the elastic processes and depends
on total deformations. The latter is caused by the viscoelastic effects and depends only on the elastic
part of deformations. It is assumed that the material parameters in the non-equilibrium part
are constant while the evolution of the elastic deformations is controlled through the evolution of
the inelastic deformations and the inelastic material parameters. Different from the viscous process,
the modeling of shrinkage effects does not require a new assumption for the free energy but a
split of the total deformation gradient into a shrinkage and a mechanical part. The model suitable
for simulating both of the mentioned phenomena is implemented in the single- and multiscale FE
program. In the numerical examples, the focus is placed on the investigation of a combination of
a curing polymer with a standard elastic material of a high stiffness. This combination is used to
represent the reinforced polymers, a group of nowadays widely applied materials.
The maximal advance path constraint for the homogenization of materials with random
network microstructures
Mykola Tkachuk, Christian Linder (Universität Stuttgart) Schedule
Many materials such as elastomers, biopolymer gels, soft fibrous materials and open-cell foams
possess a characteristic microstructure which is a random spatial network of long strands. Those
undergo essentially non-affine microscopic deformation that consists in reorientation and axial
stretch [1] when the macrodeformation is applied. A newly proposed statistical treatment based
on the formalism of network paths allows to determine the non-affine deformation of the network
and yields the homogenized elastic response of the material.
Network paths with the maximal advance in a certain direction, called maximal advance paths,
are used to formulate the constraints relating the macroscopic strain to the microscopic stretch
of one-dimensional strands. These paths are defined in the initial undeformed configuration of
the network where all the strands have unit stretch and are oriented equally in all directions.
The end-to-end vector of a path made by a large selection of strands from this assembly becomes
a macroscopic object and deforms correspondingly. On the other hand, this deformed path is
composed of the deformed strands and is defined by the average of the microstretch vectors over
the path. The given macroscopic extension of such paths restricts the variation of the stretch in
the network.
The equilibrium state of the network at the given macroscopic strain should be characterized by
the minimum of the free energy. This principle leads to a formulation of a constraint minimization
problem from which the stretch distribution is derived. The homogenized response of the material
is then computed by the averaging over the relaxed network. In the developed model the choice of
the free energy as a function of the microstretch distribution plays a crucial role. In particular, it
should enforce the existence and uniqueness to the constrained minimization problem. Different
generic energy terms are considered with respect to the fulfillment of this requirement. Furthermore
the stability properties of the homogenized material with respect to the choice of network
energy complement these studies. Finally, the numerical implementation of the developed model
is proposed. This is based on the approximation of the variable microstretch on the microsphere
of space orientations as in [2].
[1] P. D. Wu, E. van der Giessen, On improved network models for rubber elasticity and their
applications to orientation hardening in glassy polymers, Journal of the Mechanics and
Physics of Solids, 41 (1993), 427-456.
[2] C. Miehe, S. Göktepe, F. Lulei, A micro-macro approach to rubber-like materials – Part I: the

186 Section 8: Multiscales and homogenization
non-affine micro-sphere model of rubber elasticity, Journal of the Mechanics and Physics of
Solids, 52 (2004), 2617–2660.
Plane stress finite element analysis of filler reinforced polymers
Deepanshu Sodhani, Stefanie Reese (RWTH Aachen) Schedule
The characteristics of elastomers such as force-deformation behaviour, strength, fatigue and wear
resistance, can be tailored by embedding it with filler particles. The influence of the fillers on the
characteristic material behaviour significantly depends on the size and geometric form of the filler
aggregates, which vary under mechanical loading.
The polymer bulk can be divided into polymer matrix and primary aggregate. A new finite
element-based simulation method proposed by Böl and Reese [1] has been used to represent the
polymer matrix, which is characterized by chain like macro molecules linked together at certain
points to form an irregular network.
One of the classical reinforcing fillers are carbon blacks, which are produced in a variety
of classes and types, depending on the required performance of the final product. In general,
they consist of randomly ramified compositions of filler particles that are bonded together by
strong sinter bridges. These compositions are referred to as primary aggregate. In this work, we
investigate the polymer matrix being reinforced with primary aggregate.
Suitable number of triangular elements are assembled to create a mesh unit referred to as
filler element for each filler particle. Degrees of freedom of internal nodes in each filler element
are eliminated using static condensation. The sinter bridges are modelled by adding another layer
of elements around the filler element. Primary aggregate is now modelled using an assembly of
filler elements. This is now coupled with the polymer matrix to generate a finite element model
of filler reinforced polymers.
The proposed method provides the possibility to observe and understand how changes in size
and geometry of filler particles (at microscopic level) affect the macroscopic behaviour of the filler
reinforced polymers.
[1] M. Böl and S. Reese, 2006, Finite element modelling of rubber like polymers based on chain
statistics. International Journal of Solid and Structures 43, 2–26
Keywords: filler element, primary aggregate, polymer matrix, sinter bridge
Finite element simulation of the deformation behaviour of cellular rubber components
Rathan Raghunath, Daniel Juhre (Deutsches Institut für Kautschuktechnologie) Schedule
Cellular rubber is a heterogeneous material consisting of a filled elastomer matrix with embedded
pores. It is characterized by a high compressibility with good resilience. Due to these properties
cellular rubber is distinguished for a variety of sealing products. In practice cellular rubber gaskets
are exposed to high mechanical loadings in which they have to combine a soft closing behaviour
and a sufficent reset for a guaranteed sealing. By varying the rubber mixture and the specific
volume fraction of the pores, the behaviour of the cellular rubber can be adapted to its field of
application. To optimize this process a comprehensive characterization of the material concerning
its mechanical properties is inevitable. However, in contrast to conventional materials, there are
no suitable techniques for the material characterization of heterogeneous cellular rubber. Even
both, the experimental testing as well as the finite element simulation of the material behaviour is
not possible in the usual way. Indicative of this is that until today no reliable models for cellular
rubber material are avaible in commercial FE programs. In this work a material model to describe

Section 8: Multiscales and homogenization 187
the mechanical behaviour of cellular rubber is proposed. This model is intende to represent the
highly complex material behaviour of cellular rubber under varying loading conditions. The model
combines the material characteristics of the solid rubber with the explicit definition of the volume
fraction of the embedded pores which facilitates the identification of the material parameter.
Additionaly, it allows the distinct adjustment of the pore distribution within the gasket geometry
which is induced by the production process and can be measured by micro-CT analyses.
Microscopical investigation of wave propagation phenomena in residual saturated
porous media
Patrick Kurzeja, Holger Steeb (Universität Bochum), Marcel Frehner (ETH Zürich), Stefan
Schmalholz (University of Lausanne) Schedule
Wave propagation through partially saturated porous media can be of great interest, e. g. with
respect to groundwater remediation and ganglia mobilization. Typical systems contain a solid
skeleton and two non-miscible fluids, of which one is distributed discontinuously due to its low
saturation. Therefore, a model of such a system requires to allow for two continuous phases (solid,
non-wetting fluid) as well as for the fragmented wetting fluid. Models for continuous phases are
well-established for two and three phases, e. g. [2]. The challenge is now to include the discontinuous
fluid in a macroscopic description.
First, we discuss wetting fluid patches and their dynamic behaviour on the microscale, i. e. 10 −5
- 10 −3 m. The focus concentrates on the eigenfrequency and damping of their oscillations, which
is influenced by the geometry, viscosity and surface tension. The weak formulation of this physical
problem is solved and discussed against the background of other numerical and analytical
solutions.
These microscopic patches will be included in the macroscopic model as distinct damped oscillators
after [1]. The homogenization between both scales conserves information about the microscopic
density, eigenfrequency and damping to account for the discontinuity via probability density
functions.
The final model delivers insight into the behavior of propagating waves on the macroscale, influenced
by different properties of the microscopic fluid clusters. Furthermore, the dispersion
relations allow a comparison with continuous models and characteristic values, which might be
helpful for experimental studies.
[1] H. Steeb, M. Frehner and S.M. Schmalholz, Waves in residual-saturated porous media, in:
G.A. Maugin and A.V. Metrikine, eds., Mechanics of generalized continua: One hundred
years after the Cosserats, Springer, New York, USA, pp. 179-187, 2010.
[2] H. Steeb, P. Kurzeja, M. Frehner and S.M. Schmalholz, Phase velocity dispersion and attenuation
of seismic waves due to trapped fluids in residual-saturated porous media. submitted
to: Vadose Zone Journal, 2011.
A two scale model for coated hybrid forming tools under thermo-mechanical loading
K.-H. Sauerland, R. Mahnken (Universität Paderborn) Schedule
Hybrid forming processes with simultaneous mechanical and thermal loading conditions show a
high potential for mass production of functionally graded structures and components [1]. In these
processes the workpiece is loaded once with large deformations, high thermal gradients and phase
transformations while the forming tool is loaded cyclically with small deformations and high
thermal gradients. For protection of the forming tool from the high temperatures of the hybrid

188 Section 8: Multiscales and homogenization
forming process in the process under consideration coated forming tools are applied, which should
increase the tool lifetime.
This work presents the finite element simulation of a coated hybrid forming tool subjected
to thermo-mechanical loading conditions. The coating system consists of different coating layers
which are considered on a meso level with particular constitutive equations and particular material
parameters. On a macro level the complete coating system is discretized within one finite element
over the thickness. For scale transitions between macro and meso level the Taylor assumption is
applied for strains and temperatures and volume averaging procedures are applied for stresses
and heat fluxes.
[1] K. Steinhoff, H. J. Maier, D. Biermann, Functionally Graded Materials in Industrial Mass
Production, Wissenschaftliche Scripten (2009).
S8.5: Computational homogenization methods Wed, 16:00–18:00
Chair: Holm Altenbach, Rainer Glüge S1|01–A01
Multi-material simulation utilizing the Finite Cell Method
Meysam Joulaian, Alexander Düster (TU Hamburg-Harburg) Schedule
The finite element method (FEM) is a powerful and robust mathematical approach to deal with
a wide variety of applications in engineering and science. Yet, fulfilling many prerequisites of this
method, such as generating an appropriate mesh, in the case of complex geometries is computationally
expensive. In addition, modeling problems with discontinuous or singular solutions is
always a challenging task. Therefore, considerable effort has been devoted to circumvent these
difficulties in an elegant way. Recently, new categories of this method, such as element free methods,
partition of unity (PUM) based methods and the finite cell method (FCM), have been
proposed to maintain the accuracy and increase the versatility of the FEM. The FCM is a new
method, which uses the p-version FEM on Cartesian grids composed of rectangular cells that not
necessarily coincide with the boundaries of the geometry. This method has an inherent capacity
to easily handle linear and nonlinear problems with complicated geometries in 2D and 3D [1, 2].
Furthermore, thanks to the use of high order shape functions in this method, a high rate of convergence
is achievable. This method has successfully been applied in simulating various problems
such as biomechanical applications, homogenization and topology optimization.
Despite the accuracy and simplicity of the FCM, there is still an open area of research for
modeling multi-material interfaces using this method. Considering heterogeneous problems including
different materials, the solution features weak discontinuities introduced at the material
interfaces which need to be resolved in order to obtain reliable results. For the purpose of our
discussion, we thoroughly address this problem in the original version of the FCM and investigate
possible remedies that fit effectively into the FCM framework. Different approaches including
domain decomposition methods, the hp-d method, local enrichment, as well as their combinations
are considered. The advantages and disadvantages of each method are investigated and an
appropriate solution is suggested. Finally, some numerical examples are presented to investigate
performance of the method.
Keywords
Finite cell method, discontinuity, local enrichment, hp-d method
[1] J. Parvizian, A. Düster, and E. Rank. Finite cell method – h- and p-extension for embedded
domain problems in solid mechanics.Computational Mechanics 41 (2007), 121–133.

Section 8: Multiscales and homogenization 189
[2] A. Düster, J. Parvizian, Z. Yang, and E. Rank. The finite cell method for three-dimensional
problems of solid mechanics.Computer Methods in Applied Mechanics and Engineering 197
(2008) 3768–3782.
Computational homogenization of materials with small deformation to determine
configurational forces
Md Khalaquzzaman, Ralf Müller (TU Kaiserslautern), Bai-Xiang Xu (TU Darmstadt) Schedule
Computational homogenization has become increasingly important in determining the macroscopic
material response of inhomogeneous materials, e.g. piezoelectric materials. In this work,
two-scale classical (first-order) homogenization of materials for mechanical response using a FE 2 -
approach is discussed. The literature shows that the strain tensor is often used for small deformation
problem to determine the boundary conditions for the boundary value problem on the
micro level. Use of this boundary condition gives consistent homogenized mechanical quantities,
e.g. stress tensor as well as elasticity tensor, but it does not produce consistent results for configurational
forces. Here, it is shown that the use of the displacement gradient for the determination
of the boundary conditions of the micro problem is the appropriate one to determine homogenized
configurational forces. The homogenized coefficients of the elastic tensor for small strain
are explicitly formulated. Different representative volume elements (RVEs) are used to capture
the inhomogeneities of the microstructure of the material. Based on the multiscale model and
the homogenized configurational force, the mode-I crack problem of a microstructured material
is simulated. The effect of the different microstructures on configurational forces at the crack tip
is investigated.
Comparison of different boundary conditions on spheric and cubic RVE
Rainer Glüge, Martin Weber, Albrecht Bertram (Universität Magdeburg) Schedule
The representative volume element (RVE) technique is routinely used to compute the macroscale
material properties of a micro-structured material. In this talk, the influence of the shape of
the RVE on the quality of the results is investigated. Specifically, the performance of cubic and
spherical RVEs is compared. Spherical RVEs have a better surface to volume ratio, allowing for
a minimization of the influence of the choosen boundary conditions. Also, unlike a cubic RVE,
no anisotropy is induced into a spherical RVE. The two latter issues are quantified, using an
elasto-plastic matrix-inclusion material.
Computational Homogenization for Linear and Nonlinear Heat Conduction in Concrete
Tao Wu (Universität Hannover), İlker Temizer (Bilkent University), Peter Wriggers (Universität
Hannover) Schedule
Concrete is an extremely complex heterogeneous material with a random microstructure at different
length scales. It is critical to investigate heat conduction at different scales of concrete in
engineering applications, such as fire resistance, deterioration due to high temperature exposure
and so on. In this contribution, a three-scale framework of computational thermal homogenization
for linear and nonlinear cases are carried out. First of all, the homogenization process is implemented
at the microscale, and then the resulting effective quantity could be directly applied to
thermal homogenization at the mesoscale, which specifically yields the multiscale framework of
thermal analysis in concrete.
At the microscale of cement paste, computational thermal homogenizaiton with statistical tests
are implemented in the mesh from 3D micro CT-scans with a resolution of 1 µm. The principle

190 Section 8: Multiscales and homogenization
of partitioning is used to prove numerical results with different types of boundary conditions. On
the other hand, aggregates with a random distribution embedded in a homogenized cement paste
matrix is used for the mesoscale thermal homogenization. Each step simulation is strictly verified
through available experimental data. Finally, nonlinear effects arising from various physical
mechanisms such as pore radiation, dehydration, microcracking etc, will be considered within a
thermodynamically consistent homogenization framework.
Thermodynamically Consistent Thermo-Mechanical Micro-Macro-Structural FE 2
Scheme for Thermo-Elasto-J2-Plastic Solids Exhibiting Solid-State Phase Transformations
- Application to Ti6Al4V
Benjamin Regener, Christian Krempaszky, Ewald Werner (TU München), Martin Stockinger
(BOHLER Forging, Kapfenberg, Austria) Schedule
Titanium alloys generally and the alloy Ti6Al4V in particular possess an exceptionally high
strength to density ratio with superior durability at elevated temperatures. This predestines
Ti6Al4V for applications in highly stressed jet engine rotating components such as fans, blades
and disks within the low- and high-pressure compressor units of jet engines. These components
typically originate from complex production routes involving multi-stage thermomechanical processing.
Thus the macrosopic material performance is governed by the morphology, constitutive
behaviour and deformation history of the microstructural constituents.
To gain a physically based understanding of the evolution of microscale heterogeneities and residual
stresses in aircraft components, a fully coupled thermomechanical multi-lengthscale finite
element based model is introduced. Each integration point of the macro-scale model is coupled
with a periodic microfield model providing temperature and displacement degrees of freedom on
both lengthscales. Processing conditions are applied to the macroscale model representing the
investigated component, whereas the attached microscale models provide the constitutive behaviour
and display the microstructure evolution.
The microstructure evolution of Ti6Al4V during thermomechanical processing is modelled morphologically
by a differential Johnson-Mehl tessellation for the primary and secondary α-phase.
The nucleation sites and times result from two heterogeneous Poisson point processes with
temperature-dependent intensity. The microstructure evolution is tracked individually for each
micro-constituent in an integral sense by means of the Minkowski functionals estimated at high
accuracy using a spatial lattice.
In order to maintain a fair ratio of computational costs to benefits, a thorough investigation of the
micromodels with respect to numerical convergence and representativity is carried out. Furthermore,
different meshing techniques and their influence on homogenised and local field quantities
is quantified.
Inelastic analysis of polycrystals based on Voronoi tessellation
Oleksandr Prygorniev, Konstantin Naumenko, Holm Altenbach (Universität Magdeburg) Schedule
In this work algorithms are presented to generate finite element polycrystal models based on
Voronoi tessellation. They include a polycrystal unit cell, a uni-axial specimen and a circumferentially
notched specimen. The behavior of a grain is governed by the anisotropic elasticity with
the cubic symmetry. For the inelastic strain rate tensor the anisotropic power law type function of
the stress tensor is utilized. Benchmark problems are proposed to verify the developed numerical
techniques including the quality of the mesh and accuracy of the implicit time step procedure.

Section 8: Multiscales and homogenization 191
S8.6: Dislocation dynamics and polycrystals Thu, 13:30–15:30
Chair: Malek Homayonifar, Thomas Hochrainer S1|01–A01
Higher order alignment tensors in continuum dislocation dynamics
Thomas Hochrainer (Universität Bremen), Michael Zaiser (University of Edinburgh), Stefan
Sandfeld (KIT) Schedule
Crystal plasticity is mainly mediated by the motion of line like crystal defects called dislocations.
Continuum descriptions of dislocations reentered the focus of continuum mechanics after
the partly known and partly newly discovered size-effects in crystal plasticity became relevant in
micro- and nanotechnology. Because the dislocation density tensor is given by a suitable curl of
the plastic distortion tensor, its consideration in constitutive equations renders resulting theories
size-dependent. That the dislocation density tensor can be obtained via a curl operation may
have obstructed its nature as a statistical object which may be obtained from averaging actual
dislocation configurations. In the current talk we derive the scalar total dislocation density and
the dislocation density tensor from statistical averages and clarify theirs nature as the first two
terms in a tensor expansion of dislocation density distributions. Theses tensors are known as
alignment tensors in the theory of liquid crystals. From a higher dimensional dislocation density
theory [1] we derive a hierarchy of evolution equations for the dislocation density tensors of all
orders which are coupled to the evolution equations for a similar tensor expansion of the dislocation
curvature. Assumptions for terminating the tensor expansions at low order are discussed
and their implications are illustrated at numerical examples.
[1] T. Hochrainer, M. Zaiser, P. Gumbsch, A three-dimensional continuum theory of dislocation
systems: kinematics and mean-field formulation, Philos. Mag. 87, 8–9 (2007), 1261 – 1282.
Data-driven estimation of atomistic support for continuum stress using the Gaussian
mixture model
Sean J. Moran (University of Edinburgh), Manfred H. Ulz (TU Graz) Schedule
Recent developments in multiscale modelling include the treatment of atomistic scale interactions
via molecular dynamics simulations. While existing methods in solid state physics and continuum
mechanics model their fields very successfully albeit independently of each other, bridging those
fields would lead to a fruitful synergy in material science and is therefore an area that is currently
of significant interest. The notion of stress being an inherent continuum concept at macroscale has
been a matter of discussion at microscale. The atomistic stress measure at a given spatial point
contains a space averaging volume over nearby atoms to provide an averaged macroscopic stress
measure. The atoms in this averaging volume are clearly correlated. Consequently the stress and
position data of the atoms should implicitly contain this correlation information as well as the
characteristic length of the space averaging volume. Previous work on atomistic stress measures
introduce the characteristic length as an a priori given parameter and is therefore by no means
directly determined from the physical problem at hand. In this contribution we motivate the
Gaussian mixture model as a means to estimate the correlation between atoms in our lattice and
therefore to derive the characteristic length of the space averaging volume in an entirely data
driven manner. We fit a Gaussian mixture model to our data that captures the distribution of
subpopulations of atoms within the lattice. We learn the maximum likelihood model parameters
using the Expectation Maximization (EM) algorithm. Rather than selecting the number of subpopulations
a priori, we learn the optimal subpopulation configuration directly from the data
by searching through the model space for the model which best describes our dataset. To form

192 Section 8: Multiscales and homogenization
a parsimonious representation of the dataset we regularise our model search using the Bayesian
Information Criterion (BIC) which maintains an optimal balance between too few and too many
subpopulations of atoms through the penalization of overly complex (more parameters) models.
The characteristic length is calculated directly from the subpopulations of atoms discovered by
the Gaussian mixture model by averaging over the maximum extent of each subpopulation. Furthermore
we demonstrate how our model is able to leverage the correlation of atoms in the lattice
to calculate the value of unknown stress values at given macroscopic continuum positions. Thorough
evaluation is conducted on a numerical example of an edge dislocation in a single crystal.
We show that our model is able to derive estimates of the atomistic support that are within close
agreement to the corresponding analytical solution.
Towards a general multiscale framework based on Ritzs approximation: Application
to atomistic and continuum models
Malek Homayonifar (TU Dortmund), Jörn Mosler (TU Dortmund, Helmholtz-Zentrum Geesthacht)
Schedule
Material modeling using multiscale methods is in great demand because they allow achievement of
a higher physical resolution compared to classical continuum models by incorporating the effects
of the underling micromechanical processes into the analysis of the macroscopic response. The core
ingredients of these methods are the scale bridging schemes which can be realized by the relevant
physical assumptions. For instance, a more frequently applied approach for atomistic-continuum
multiscale simulations is the Cauchy-Born rule and the principle of energy equivalence. In the
present contribution, a similar approach is proposed, however, with a more relaxed kinematic
constraint and an emphasized numerical efficiency. Within the advocated model, the kinematics
of the smaller scale is coupled to that of the larger scale in standard manner, i.e. by volume
averaging. Moreover, the principle of energy equivalence is approximated by Ritzs method. Accordingly,
the set of the larger scales material parameters is chosen which fits the average energy
of the lower scale best. The applicability and the efficiency of the resulting homogenization approach
are demonstrated by selected numerical examples ranging from the atomistic scale to the
macroscopic scale.
Invariance of Parrinello-Rahman molecular dynamics and its relation to continuum
mechanics
Manfred H. Ulz (TU Graz) Schedule
Parrinello-Rahman molecular dynamics [1] has proved to be a reliable technique for the investigation
of phase transitions in solids. This type of molecular dynamics may lead to a proper
description of the atomistic scale in multi-scale analysis of engineering problems. However, the
employed Lagrangian in [1] is proposed without a derivation and lacks invariance under modular
transformations.
A reinterpretation of the Lagrangian in [1] in terms of continuum mechanics can be found in
[2]. The new formulation is derived in a consistent physical manner and only quantities native
to continuum mechanics are incorporated into this Lagrangian. However, numerical examples
demonstrating the performance of the proposed model are not provided in [2].
Based on this recent continuum-related derivation, the invariance of the new Lagrangian under
modular transformations is investigated. The implication that the obtained dynamics is invariant
to the chosen unit cell agrees with results in solid state physics and is a mandatory requirement
for the suitability of multi-scale analysis. We conduct a numerical simulation of a phase transition
in nickel which scrutinises the validity of the Lagrangian in [2] and its invariance under modular
transformations.

Section 8: Multiscales and homogenization 193
[1] M. Parrinello, A. Rahman, Polymorphic transitions in single crystals: A new molecular dynamics
method, J. Appl. Phys. 52 (1981), 7182–7190.
[2] P. Podio-Guidugli, On (Andersen-)Parrinello-Rahman molecular dynamics, the related metadynamics,
and the use of the Cauchy-Born rule, J. Elasticity 100 (2010), 145–153.
S8.7: Damage processes and contact problems Thu, 13:30–15:30
Chair: Julia Orlik, Dorothee Knees S1|01–A02
Derivation of an effective damage evolution model using two-scale convergence techniques
Hauke Hanke, Dr. Dorothee Knees (WIAS Berlin) Schedule
This lecture is addressed to the question of deriving an effective damage evolution model by investigating
the limit process of damage models with a “simple” micro-structure.
Thereto, microscopic damage models are introduced, where there are only two phases of material
- damaged and undamaged. This microscopic structure is non-periodic and a regularization for
piecewise constant functions correlated to this microstructure is introduced. Then, classical twoscale
convergence techniques are used to identify an effective damage model, wherein the damage
is described by a damage variable z : [0, T ] × Ω → [0, 1] reflecting the micro-structure induced
by the micro-models. Here, z(t, x) = 1 means that no damage occurs in point x at the time t
and z(t, x) = 0 means the material cannot take any more damage but is still allowed to perform
elastic deformations (i.e. no complete damage).
This approach suggests in which way phenomenological damage models could depend on the damage
variable. Furthermore, anisotropy is allowed in the microscopic damage models, which leads
to an anisotropic limit damage model.
A toy model for dynamic debonding
Giuliano Lazzaroni (Universität Würzburg), Renaud Bargellini (EDF RD, Laboratoire de Mécanique
des Structures Industrielles Durables), Pierre-Emmanuel Dumouchel (Peugeot-Citroen
Automobile), Jean-Jacques Marigo (École Polytechnique) Schedule
We study the dynamic debonding of a one-dimensional inextensible film, subject to a monotonic
loading and under the hypothesis that the toughness of the glue can take only two values. We
first consider the case of a single defect of small length in the glue where the toughness is lower
than in the remaining part. The dynamic solution is obtained in a closed form and we prove
that it does not converge to the expected quasi-static one when the loading speed tends to zero.
The gap is due to a kinetic energy which appears when the debonding propagates across the
defect at a velocity which is of the same order as the sound velocity. The kinetic energy becomes
negligible again only when the debonding has reached a critical distance beyond the defect. The
case of many defects is then considered and solved using an exact numerical solution of the wave
equation and the Griffith law of propagation. The numerical results highlight the effects of the
time evolution of the kinetic energy which induce alternate phases of rapid and slow debonding,
these oscillations depending essentially on the volume fraction of the highest toughness.
Multiscale modelling for the simulation of damage processes at refractory materials
under thermal shock
Dimitri Henneberg, Andreas Ricoeur (Universität Kassel) Schedule

194 Section 8: Multiscales and homogenization
Refractory materials, for example ceramic materials, initially contain a multitude of defects such
as voids, microcracks, grain boundaries etc. Particularly for refractory ceramics being exposed
to high temperatures above 1200 C and loaded by thermal shocks, the macroscopic properties
such as effective compliance, strength and lifetime are essentially determined by these microscopic
features of the material. The deformation process and failure mechanisms are going along with
the creation of new microdefects as well as the growth and coalescence of cracks. A brittle damage
model based on multiscale considerations and homogenisation procedures is presented. Cell
models are developed as representative volume elements (RVE) including different microstructural
features. The material laws themselves are formulated on the continuum level. Local failure
occurs if the damage variable reaches a critical value. In order to properly model the thermomechanical
coupling, the temperature-dependence of material constants is taken into account.
Moreover, fracture and damage mechanical approaches are combined using different techniques.
Thus, interactions of macroscopic crack tips and microstructural features can be taken into account.
Crack face contact within a 3d XFEM multiscale framework
D.S. Mueller-Hoeppe, P. Wriggers, S. Loehnert (Universität Hannover) Schedule
Many materials, like e.g. ceramics, exhibit micro cracking in the vicinity of a macro crack front.
These micro cracks have a significant influence on the macro crack propagation behavior.
As the micro cracks are in general arbitrarily arranged, crack closure occurs in many cases. The
eXtended Finite Element Method (XFEM), which is a popular method for numerical fracture mechanics,
does not prevent unphysical crack face penetration. As a remedy, [1] develop a contact
formulation which accounts for crack closure in hexahedral XFEM elements. Due to a projection
of the contact contribution on the hexahedral element nodes, the introduction of additional degrees
of freeedom is avoided.
This contact formulation is applied to the XFEM multiscale projection method introduced by [2]
and extended to the three-dimensional case by [3] in order to account for micro crack closure.
[1] D.S. Mueller-Hoeppe, P. Wriggers and S. Loehnert. Crack face contact for a hexahedral-based
XFEM formulation. Submitted to Comput. Mech.
[2] S. Loehnert and T. Belytschko. A multiscale projection method for macro/microcrack simulations.
Int. J. Numer. Meth. Eng., Vol. 71, 1466 -1482, 2007
[3] S. Loehnert and D.S. Mueller-Hoeppe. Multiscale methods for fracturing solids. IUTAM
Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media, 79–
87, 2008
Homogenization via unfolding in periodic elasticity with contact on oscillating interface
J. Orlik (Fraunhofer ITWM) Schedule
In this paper, we consider the elasticity problem in a heterogeneous domain with ε−periodic
micro-structure, ε

Section 8: Multiscales and homogenization 195
interface, implying their two-scale convergence. Furthermore, this implies the weak convergence
of the nonlinear continuous convex functions applied to these interface jumps.
The limiting problem describes elasto-plasticity, where the micro-sliding on the oscillating
interface reasons plastic deformations, determined by solving a local contact elasticity problems on
the standard periodicity cell. The multiscale algorithm provides an effort for numerical solution of
periodic multiphase problems containing multiple contact in their microstructure. It is illustrated
by simulation of the effective properties of two fabric materials.
[1] D. Cioranescu, A. Damlamian and G. Griso: Periodic unfolding and homogenization, C. R.
Acad. Sci. Paris, Ser. I, 335 (2002), 99-104.
[2] Damlamian, A.: An elementary introduction to periodic unfolding, Multi Scale Problems and
Asymptotic Analysis 24 (2005), 119-136.
Asymptotics for thin elastic fibers in contact
Zoufine Bare, Julia Orlik (Fraunhofer-ITWM) Schedule
In this work a 3-D uni-lateral contact elasticity problem for a thin fiber with a rigid foundation
is studied. We approximate the contact condition by a linear Robin-boundary-condition (by
meaning of the penalized and linearized non-penetration and friction conditions, [1]). The Robin
parameters are scaled differently in the longitudinal and cross-sectional directions. The dimension
of the problem is reduced by a standard ([2], [3]) formal asymptotic approach with an additional
expansion suggested to fulfill the contact conditions. The 3-D contact conditions result into
1-D Robin-boundary-conditions for corresponding 1-D PDEs. The Robin-coefficients of the 1-D
problem depend on the ones from the 3-D statement, on the cross-section of the fiber and on the
solution of auxiliary problems in the boundary layer. The error is estimated and the theoretical
results are illustrated by a numerical comparison of the solutions to the contact problems for 3-D
and 1-D beams for validation.
[1] Kikuchi, N and Oden, J.T.:Contact problems in elasticity: A study of variational inequalities
and finite elements methods, SIAM, USA, 1988.
[2] Panasenko, G.: Multi-scale modelling for structures and composites, Springer, 2005.
[3] Trabucho, L. and Viano, J.M.: Mathematical modelling of rods, Handbook of Numerical
Analysis, Vol. IV, 1996.
S8.8: Composites and fiber-reinforced structures Thu, 16:00–18:00
Chair: Udo Nackenhorst, Robert Fleischhauer S1|01–A01
FE 2 Modelling of laminated plates
Cécile Helfen, Stefan Diebels (Universität des Saarlandes) Schedule
Laminated plates are nowadays widely used, especially in transport and automobile industry.
However, their mechanical behaviour is complex and a multi-scale consideration proved to be
useful. In the scope of this work, the modelling of the mechanical behaviour of a hybrid sandwich
laminate under bending is made with a numerical homogenisation.
The principle of a numerical homogenisation (or so-called FE 2 ) for plates is based on the
separation of the investigated problem into different scales. Whereas the macroscale is defined

196 Section 8: Multiscales and homogenization
as a plate, the mesoscale is computed as a three dimensional problem discretizing the different
layers stacking order. A first Finite Element computation is made on the macroscale, which
is following the plate kinematics and resolving the balance equation of the plate. From each
integration point, the deformations are projected to the mesoscale, where an other Finite Element
computation is made. On this level, a Representative Volume Element (RVE) is defined, resolving
the different layers of the laminate and a local boundary value problem is solved. Then, the
macroscopic forces, moments and hyperstresses are computed as stress resultants and higherorder
stress resultants from the mesoscopic stresses and transferred back in the macroscale. At
this stage, the macroscale is following a plate theory with thickness change enabling better results
as the classical theories of Reissner-Mindlin or Love-Kirchhoff, especially towards the shear forces.
Concerning the mesoscale, it resolves a three dimensional boundary value problem incorporating
non-linear material behaviour.
Further improvements has to be made concerning the contact interface between the different
layers.
Numerical aspects on computational homogenization of epoxy/glass composites
Robert Fleischhauer, Hüsnü Dal, Michael Kaliske (TU Dresden) Schedule
Numerical aspects of two-scale modeling of epoxy/glass composites are presented. Special focus
is given to the use of a computational homogenization scheme and the micromechanical modeling
of interphases and interfaces. The homogenization process is carried out under consideration of
periodic boundary constraints of the representative volume element (RVE) due to the periodic
structure of glassfiber reinforced epoxy systems. Generally, the homogenization process employed
is based on an internal variable formulation for the constitutive model of inelastic materials.
An objective energy storage function is needed to derive micro-stresses and micro-moduli. The
numerical treatment of the micro-scale requires the incremental stress potential function, that is
the result of the solution of the minimization problem of the constitutive response of standard
dissipative materials. Therein, the stored and dissipated energy is minimized within a finite increment
of time, with respect to the internal state of the material. It provides the potential for the
micro-stresses at the end of the current time step. The deformation of the microstructure is assumed
to be driven by a prescribed macro-deformation and a superimposed micro-scale fluctuation
field. The fluctuation field has to vanish in an averaged sense over the surface of the RVE. This
constraint is fulfilled demanding e.g. periodic deformations on the boundary of the microstructure.
Therewith, it is possible to achieve the linking of the periodicity constraint to the energy
minimization problem by using a Lagrange multiplier method. Numerical aspects of solving this
minimization problem are presented. Due to protective coating of fibers and chemical reactions
during the manufacturing process, interphases between bulk- and fiber material build up. In order
to simulate the overall macroscopic mechanical response of an epoxy/glass composite, we present
a constitutive model to couple the newly developed mechanical material model for epoxy with the
hyperelastic Neo-Hookean glass fiber material under consideration of the designated failure layer.
Two-scale simulations are carried out for RVEs with and without interface/interphase interaction
and the comparison of the results will be presented.
A stochastic procedure for the homogenization of damaging composites
André Hürkamp, Udo Nackenhorst (Universität Hannover) Schedule
The mechanical properties of materials are mainly influenced by the microstructure. In particular,
the global phenomena like fatigue and fracture start at the microscale. Randomly distributed
initial microcracks or other defects are the source of fatigue. Regarding composite materials also
the combination of different materials obeys uncertainties. The arrangement of all of these inho-

Section 8: Multiscales and homogenization 197
mogeneities is a random process. In order to give precise information about the global mechanical
properties, a possible degradation or the risk of failure, the microstructure has to be described
with the aid of related statistical methods.
Exemplarily, investigations on short fibre reinforced concrete are made. Its microstructure can be
described by a matrix material of concrete which includes randomly distributed microcracks and
short fibres of steel. Additionally, the material parameters itself are assumed to be random, so that
a multidimensional stochastic problem is obtained. Classical analytical homogenization schemes
like the Mori-Tanaka-Method or the self-consistent scheme are extended with statistical methods.
In that way, we are able to compute effective material properties with respect to their statistics.
The statistics for the homogenization are captured by advanced Monte-Carlo simulations using a
Latin Hypercube sampling.
For the further processing of the homogenized material model a spatial random field is generated
using the Karhunen-Loève expansion.
Tolerance modeling of heat conduction in bidirectional gradedthin walled cellular
structures.
Eugeniusz Baron, Sylwia Czarnecka (Silesian University of Technology) Schedule
The aim of this contribution is to formulate a certain new mathematical model for the analysis of
heat conduction In functionally graded plane lattice composite structure. The composite consists
of two isotropic components, with very different thermo mechanical properties, constituting a thin
walled skeleton and a matrix. The structure is homogeneous in direction normal to its mid-plane.
The proposed model describes the behavior of the composite on the macroscopic level i.e.
by means of partial differential equation with smooth coefficients. The model of equation has
a simple analytical form obtained under certain simplified heuristic assumptions. Obviously, for
the composite under consideration there are partial differential equations with highly oscillating
functional coefficients.
The modeling method is based on the tolerance averaging procedure. This procedure was
investigated and discussed in a series of papers and summarized in [1]. This contribution introduces
a certain revisited tolerance averaging technique foundation of which will be exposed of the
83 GAMM conference in a separate presentation [2]. The modeling procedure applied in this
contribution also takes into account the new concept of a virtual cell and a local shape functions.
They are concepts which make it possible to describe functionally graded (non periodic) structure
of the skeleton lattice.
The proposed tolerance modeling procedure is based on new heuristic assumption. It states
that heat flux along every family of parallel lattice walls can be treated as independent of the
thickness of these walls. This is a good approximation, provided that the walls are sufficiently
thin.
In the contribution there are obtained two model equations for the averaged temperature field
and that is called the fluctuation amplitude of temperature field. These equations have smooth
functional coefficients and stand for the basis of analysis for specific engineering problems.
[1] Woźniak Cz., [ed.], 2008, Termomechanics of Micro heterogeneous Solids and Structures,
Łódź, Wydawnictwo Politechniki Łódzkiej.
[2] Nagórko W., Woźniak Cz., 2012, On a certain model of heat conduction in laminated media
with interlaminar defects, 83 GAMM Conference.

198 Section 8: Multiscales and homogenization
A model of the heat conduction in functionally graded laminates with interlaminar
defects
Czesław Woźniak (Technical University of Lodz), Monika Wągrowska (Warsaw University of Life
Sciences) Schedule
Modelling and analysis of laminates with non ideal contact between adjacent laminae are not
new problems in thermomechanics. So far, one can mention here a list of contributions by A.
Kaczyński, S.J. Matysiak, V.J. Pauk, [1] and many others in which a single interlaminar defect
as well as systems of these effects were discussed. Term defect stands here for a crack and/or a
thin inclusion. Alternative modelling approaches, which also take into account the delamination
problem, were proposed by Z. Naniewicz, Cz. Woźniak, [2]. At the same time the unilateral contact
between adjacent laminae was studied by M. Woźniak, [3].
In this contribution the object of analysis will be restricted to the heat conduction in two
component functionally graded laminates. The non ideal contact between adjacent laminas is
modelled by sufficiently thin interlaminar inclusion. Term sufficiently thin suggests the applicability
of a specific tolerance asymptotic modelling. This approach was recently investigated by Cz.
Woźniak and M. Wągrowska, [4].
The aim of this presentation is to propose a certain refined version of a tolerance asymptotic
modelling procedure.
[1] Kaczyński A., Matysiak S. J., Pauk V. J., 1995: Stress intensity factors for an interface
penny-shope crack in laminated elastic layer, J. Theor. Appl. Mech., 33, 361-373.
[2] Naniewicz Z., Woźniak Cz., 1988: On the quasi-stationary models of debonding processes in
layered composites, Ing. Arch., 58, 403-412.
[3] Woźniak M., 1995: On the dynamic behaviour of micro- demaged stratified media, Int. J.
Fract., 73, 223-232.
[4] Cz. Woźniak, M.Wągrowska, Asymptotic modelling of some functionally graded materials,
PAMM Proc. Appl. Math. Mech., 10, 349-350, 2010.
Multiscale failure modeling of composites using generalized finite element method
Mahendra Kumar Pal, Amirtham Rajagopal (Indian Institute of Technology Hyderabad) Schedule
In this work multiscale Generalized Finite Element Method (GFEM) is used for failure modeling
of laminated composites. The GFEM [1] is used to construct higher order function spaces for the
solution of partial differential equations. The enrichment functions for the GFEM approximation
are computed using a Proper Orthogonal Decomposition (POD) technique [2]. Higher accuracy is
achieved through addition of enrichment functions to the classical finite element basis functions.
The approximation is then used in a Galerkin scheme for multiscale failure analysis of composites.
Numerical examples are presented to demonstrate the multiscale failure modeling of composites.
[1] J. M. Melnek, I. Babuska, The partition of unity finite element method, Computer Methods
in Applied Mechanics and Engineering, 139, pp. 289-314, 1996.
[2] W. Aquino, J. B. Brigham, C. J. Earls, N. Sukumar, Generalized finite element method
using proper orthogonal decomposition, International Journal for Numerical Methods in
Engineering, 79(7), pp. 887-906, 2008.

Section 9: Laminar flows and transition 199
Section 9: Laminar flows and transition
Organizers: Suad Jakirlic (TU Darmstadt), Ulrich Rist (Universität Stuttgart)
S9.1: Laminar flows and transition I Tue, 13:30–15:30
Chair: Suad Jakirlic, Ulrich Rist S1|01–A2
Transition Prediction and Modeling in External Flows Using RANS-based CFD Codes
Andreas Krumbein, Normann Krimmelbein, Cornelia Seyfert (DLR Göttingen) Schedule
Besides wind tunnel testing and flight tests, CFD simulation based on RANS solvers has become
a standard design approach in industry for the design of aircraft. For the design point of aircraft
a positive assessment of the numerical results was achieved for many validation and application
tests and the prediction capabilities of the software tools could be positively evaluated. As
a consequence, high confidence in numerical simulations could be achieved in industry and will
eventually allow more simulation and less physical testing. However, and despite of the progress
that has been made in the development and application of RANS-based CFD codes, there is still
the need for improvement, for example, with regard to the capability of a proper capturing of all
relevant physical phenomena. This can only be achieved if capable and accurate physical models
are available in the codes. On the one hand, the combined use of turbulence and transition models
is indispensable for flows exhibiting separation, because otherwise the close interaction between
the laminar-turbulent transition and its impact on flow separation is not reproduced. On the other
hand, it is not possible to fully exploit the high potential of todays advanced turbulence models
if transition is not taken into account. Thus, in modern high-fidelity CFD codes a robust transition
prediction and modeling must be established together with reliable and effective turbulence
models.
At DLR, the RANS codes for external flows, [1]-[2], have been provided with transition prediction
and modeling functionalities which can be applied to three-dimensional aircraft configurations.
Two different basic approaches are currently at hand: the streamline based and the transport
equation approach.
The streamline based approach uses information from the current flow solution along defined
integration paths in order to compute the laminar boundary layers, either using a laminar
boundary-layer method or by direct extraction from the RANS solution. A fully automated, local
linear stability code analyses the laminar boundary layers and detects transition due to Tollmien-
Schlichting or cross flow instabilities. The stability code, which applies the e N -method, [3]-[4], and
the two N factor approach, [5], for the determination of the transition points, uses a frequency estimator
for the detection of the relevant regions of amplified disturbances for Tollmien-Schlichting
instabilities and a wave length estimator for cross flow instabilities. Also separation induced transition
is covered. Alternatively, different empirical transition criteria for streamwise and crossflow
transition are available and, in addition, criteria for attachment-line and by-pass transition. Using
this approach transition is predicted either along spanwise line-in-flight cuts through a wing or
along the boundary-layer edge streamline. The latter is the only possible way in the case of fully
three-dimensional flow about fuselages or nacelles. The streamline approach has been validated
by numerous test cases and is the standard transition prediction approach currently used in production
simulation. Here, it is usually applied in parallel mode on large compute cluster systems,
[6].
The transport equation approach, [7], is relatively new and based exclusively on local variables
so that it is inherently parallelizable and, thus, very well suited for unstructured CFD codes and

200 Section 9: Laminar flows and transition
large applications which can only be tackled by massively parallel computations. The boundarylayer
quantities are resolved by the RANS computational grid and approximated by the modeling
approach reflected by two transport equations. The prediction of the locations of transition onset
is based on empirical criteria which can and must be evaluated locally. While the original model
formulation was restricted to the prediction of streamwise transition mechanisms the model is
currently extended in order to predict crossflow transition, [8].
The two different approaches and methods will be presented and explained, their applicability
ranges are discussed and numerical results are compared to a number of validation test cases demonstrating
the prediction accuracy of the different methods. The results from the application of
the methods to large and partially very complex, industrial configurations are presented and discussed.
Eventually, an outlook is given to the challenges placed by complex aircraft configurations
and to the way forward to tackle the still open issues.
[1] Krumbein, A., Automatic Transition Prediction and Application to Three-Dimensional Wing
Configurations, Journal of Aircraft, Vol. 44, No. 1, 2007, pp. 119-133; also: AIAA Paper
2006-914, January 2006.
[2] Krimmelbein, N., Radespiel, R., Transition prediction for three-dimensional flows using parallel
computation, Computers Fluids, No. 38, Elsevier, 2009, pp. 121-136, doi:10.1016/j.compfluid.2008.
01.004.
[3] Smith, A.M.O., Gamberoni, N., Transition, Pressure Gradient and Stability Theory, Douglas
Aircraft Company, Long Beach, Calif. Rep. ES 26388, 1956.
[4] van Ingen, J.L., A suggested Semi-Empirical Method for the Calculation of the Boundary
Layer Transition Region, University of Delft, Dept. of Aerospace Engineering, Delft, The
Netherlands, Rep. VTH-74, 1956.
[5] Rozendaal, R. A., Natural Laminar Flow Flight Experiments on a Swept Wing Business
Jet-Boundary-Layer Stability Analysis, NASA CP 3975, March 1986.
[6] Krimmelbein, N., Krumbein, A., Automatic Transition Prediction for Three-Dimensional
Configurations with Focus on Industrial Application, AIAA-2010-4292, 40th AIAA Fluid
Dynamics Conference and Exhibit, June 28 July 1, 2010, Chicago, Illinois, USA.
[7] Langtry, R.B., Menter, F.R., Correlation-Based Transition Modeling for Unstructured Parallelized
Computational Fluid Dynamics Codes, AIAA Journal, Vol. 47, No.12, 2009, pp.
2894-2906, DOI: 10.2514/1.42362.
[8] Seyfert, C., Krumbein, A., Correlation-Based Transition Transport Modeling for Three-
Dimensional Aerodynamic Configurations, to be presented as AIAA paper at the 50th
Aerospace Sciences Meeting, 9-12 January 2012, Nashville, Tennessee, USA.
Preliminary results of the conditional analysis of wall friction during laminarturbulent
transition of a rough wall boundary layer
Pavel Jonás, Ondřej Hladík, Oton Mazur, Václav Uruba (Czech Academy of Sciences Praha)
Schedule
The transitional intermittency is investigated in the zero pressure gradient boundary layer developing
on the surface covered with sand paper (grits 60). The free stream mean velocity is 5 m/s

Section 9: Laminar flows and transition 201
and the turbulence level is either 0.3 percent or risen by means of the square mesh plane grid to
3 percent and the dissipation length parameter 3.8 mm.
Records (25 kHz, 750000 samples, 16 bit) of the instantaneous wall friction in various locations
are evaluated from the records of the single wall wire CTA output signal. The procedure of the
constant temperature anemometer signal transformation to the wall friction has been developed
formerly and presented in [1, 2]. The adjustment of this procedure to rough surface conditions
is based on the mean wall friction distribution which has been determined in advance. This
procedure is described in the paper.
Then the transitional intermittency factor distribution is derived by means of the TERA
method [3]. Next the conditional analysis of the wall friction records is done which sorts the wall
friction records in passages with the non-turbulent structure (intermittency factor g = 0) and
those with the full turbulent structure (g = 1).
Evaluated are the probability density function and the conditioned probability density functions
of the wall friction, relevant moments and the mean residence time of the wall friction in
laminar and turbulent state. Results are compared with analogous characteristics received during
investigations of smooth wall boundary layers.
[1] Jonás, P. - Mazur, O. - Uruba, V. (1999) Statistical characteristics of the wall friction in a
flat plate boundary layer through by-pass transition. ZAMM 79, S3, S691-S692.
[2] Jonás, P. - Mazur, O. - Uruba, V. (2002) Problem of the intermittency distributions in
transitional boundary layers under flows with various scales of turbulence. PAMM, Proc.
Appl. Math. Mech. 1, Section 10.5, 298-299.
[3] Zhang, D.H. - Chew, Y.T. - Winoto, S.H.: (1996) Investigation of intermittency measurement
methods for transitional boundary, Exp. Thermal and Fluid Sci. 12, 433-443.
Velocity and shear stress distributions in laminar-turbulent transition of unsteady
boundary layer on aerofoil in high accelerating and decelerating fluid flow
Decan J. Ivanovic, Vladan M. Ivanović (University of Montenegro, Podgorica) Schedule
The corresponding equations of unsteady boundary layer, by introducing the appropriate variable
transformations, momentum and energy equations and similarity parameters set, being transformed
into generalized form. These parameters are expressing the influence of the outer flow velocity
and the flow history in boundary layer, on the boundary layer characteristics. Since the generalized
equation contain summ of terms equal to the number of parameters, it is necessary to limit
the number of parameters for numerical integration. The numerical integration of the generalized
equation with boundary conditions has been performed by means of the difference schemes and
by using Tridiagonal Algorithm Method with iterations in the two once localized approximation,
where the first unsteady and dynamic parameter will remaine, while all others will be let to be
equal to zero, and where the derivatives with respect to the first unsteady parameter will be
considered equal to zero. So obtained generalized solutions are used to calculate the distributions
of velocity and shear stress in laminar-turbulent transition of unsteady incompressible boundary
layer on aerofoil, whose center velocity changes in time as a degree function. It’s found that for
both in confuser and in diffuser aerofoil regions the decelerating flow reduces the shear stress and
favours the separation of flow, which occurring for lower contour values. The accelerating fluid
flow postpones the boundary layer separation, i.e. laminar-turbulent transition, and vice versa

202 Section 9: Laminar flows and transition
the separation is occurring for greater contour values of aerofoil. Boundary layer characteristics
are found directly, no further numerical integration of momentum equation.
Unsteady convective diffusion of a solute in a Hagen-Poiseuille flow through a tube
with permeable wall
Alexandru Dumitrache, Florin Frunzulica (POLITEHNICA University of Bucharest and Institute
of Mathematical Statistics and Applied Mathematics) Schedule
Effects of Interphase Mass Transfer (IMT) on the unsteady convective diffusion in a fluid flow
through a tube surrounded by a porous medium is examined against the background of no IMT.
The three coefficients namely exchange coefficient, convection coefficient, and dispersion coefficient
are evaluated asymptotically at large-time using Gill Sankarasubramanian model [1]. The
exchange coefficient exists due to IMT.
The convective diffusion equation and the corresponding initial and boundary conditions are
used for the beginning
∂C
∂t
+ u(r)∂C
∂x
� 2 ∂ C 1
= D +
∂x2 r
�
∂
r
∂r
∂C
��
∂r
(1)
C(0, x, r) = F (x, r) (2)
C(t, ∞, r) = 0 = ∂C
(t, ∞, r) (3)
∂r
−D ∂C
∂r (t, x, r) = KsC at r = ±R. (4)
where D is the molecular diffusivity and Ks is the rate of mass transfer of solute at the walls of
the cylinder. The condition (3) means that solute does not reach distances far down stream. The
condition (4) implies that the flux of concentration at the walls is due to a first order chemical
reaction.
Then the dimesionless parameters will be used to transform equation.
The convection and dispersion coefficient of solute are studied as a function of slip parameter,
IMT parameter and porous parameter. All-time analysis is made analytically when there is no
IMT. The mean concentration distribution is measured at a point inside and outside the slug.
The peak of mean concentration is higher than that of pure convection and it is further enhanced
with increase of porous parameter (or decrease of particle size).
The results have applications in heat exchangers, petroleum and chemical engineering problems,
chromatography and biomechanical problems.
[1] R. Sankarasubramanian and W. N. Gill, Unsteady convective diffusion with interphase
mass transfer, Proc. Roy. Soc. London A, 333 pp. 115–132, 1973.
On the Optimum Efficiency of a Flapping Foil And Its Application to Valveless Pumps
Markus Müllner (TU Wien) Schedule
Several different working principles exist to drive a valveless pump. An efficient pump may be
constructed by placing a flapping foil into a channel. For the case of inviscid flow, the pressure

Section 9: Laminar flows and transition 203
difference along the channel is equivalent to the thrust force acting on the propulsor. The effect
of the channel walls on the forces is briefly discussed. The focus in this talk is on the determination
of movements of highest propulsive efficiency for a given thrust. In order to treat the
optimization problem analytically, the case of a slender foil placed in a free stream, flapping in
time-harmonic motion with small deflections, is investigated. Novel results for the heaving- and
pitching amplitude and for the pivot point of the pitching motion are presented as a function
of the reduced frequency σ. A surprising outcome is that for a certain range of the thrust force,
the reduced frequency needs to be infinitely large to obtain maximum efficiency. Unfortunately,
the optimum movements are accompanied by some drawbacks. An important issue is to reduce
the lateral forces acting on the structure. Therefore, foil movements with zero lateral force are
investigated and the deficit in efficiency is compared to the optimum foil motion. Furthermore,
instead of the foil, an undulating wave motion is considered. The analytic result for different wave
numbers k is presented and the efficiency is compared to the optimum solution of the foil.
S9.2: Laminar flows and transition II Tue, 16:00–18:00
Chair: Ulrich Rist, Suad Jakirlic S1|01–A2
Global flow instabilities in plane sudden expansions
Hendrik Christoph Kuhlmann , Daniel Lanzerstorfer (TU Wien) Schedule
The three-dimensional linear stability of the two-dimensional, incompressible flow in a plane symmetric
sudden expansion is considered. The geometry is varied systematically, covering expansion
ratios (steps to outlet height) from 0.25 to 0.95. The stability analysis reveals that the primary
symmetry-breaking bifurcation is two-dimensional. The asymmetric flow solution, however, becomes
unstable to different secondary three-dimensional instabilities. The critical modes depend on
the expansion ratio. An energy-transfer analysis is used to understand the nature of the instabilities.
In the limit of vanishing step height, the critical mode is stationary and the amplification
process is caused by a shear instability. For high expansion ratios, the basic jet-like flow and
becomes unstable due to centrifugal forces leading to an oscillatory mode. For intermediate expansion
ratios, an elliptic instability mechanism is identified and the instability characteristics
change continuously with the expansion ratio. For an asymmetric geometry the disconnected
primary solution branches are readily shifted to very high Reynolds numbers. The connected twodimensional
solution branch is found to be very similar to the asymmetric flow of the symmetric
channel thus showing the same type of secondary instability.
Connecting the dots: Symmetry Analysis in Linear Stability Theory of a Linear Shear
Flow
Andreas Nold, Martin Oberlack (TU Darmstadt) Schedule
A novel self-similar base solution for linear stability analysis of an unbounded linear shear flow
employing symmetry methods is presented. Symmetry analysis is used to derive a full classification
of symmetries of the linearized Navier-Stokes-Equations for two-dimensional perturbations
of a linear shear flow. It is shown that the normal mode approach leading to the Orr-Sommerfeld
equation and the Kelvin mode approach are both special classes of self-similar ansatz functions
systematically derived in the framework of symmetry analysis. A third novel class of ansatz
functions is presented. In the viscous case, known solutions of the initial value problem can be
recovered by superposition of the novel self-similar modes. In the inviscid case, a new closed-form
solution of traveling, energy-conserving modes localized in spanwise direction is presented.

204 Section 9: Laminar flows and transition
An Exact Navier-Stokes Solution for Three-Dimensional, Spanwise-Homogeneous
Boundary Layers
M. O. John, D. Obrist, L. Kleiser (ETH Zürich) Schedule
In some boundary layer flows the incompressible Navier-Stokes equations are amenable to exact
similarity solutions. Two such cases are the plane stagnation flow onto a wall (Hiemenz boundary
layer, HBL) and the asymptotic suction boundary layer flow (ASBL) over a flat wall. The Hiemenz
solution has been extended to the swept Hiemenz configuration by superposition of a third,
spanwise-homogeneous sweep velocity. This solution, however, becomes singular as the chordwise,
tangential base flow component vanishes. Similarly, the ASBL does not contain any chordwise
velocity.
This work presents a generalized three-dimensional similarity solution, using a novel similarity
coordinate. The HBL and ASBL are shown to be two limits of this solution which describes threedimensional
spanwise-homogeneous impinging boundary layers at arbitrary wall-normal suction
velocities.
Further extensions may consist of oblique impingement, or different boundary suction directions,
such as slip walls or stretching walls.
Near critical laminar flow past an expansion ramp
A. Kluwick, S. Braun, R. Szeywerth (TU Wien) Schedule
Steady two-dimensional laminar flows past an expansion ramp are known to exist up to a critical
ramp angle αc in the limit as the Reynolds number tends to infinity. The theory of viscousinviscid
interaction combined with a local bifurcation analysis is used to study the evolution of
three-dimensional unsteady perturbations if |α − αc| ≪ 1 for both sub- and supercritical conditions.
Special emphasis is placed on the effects of controlling devices and the phenomenon of
bubble bursting.
Asymptotic description of incipient separation bubble bursting
Stefan Braun, Stefan Scheichl, Alfred Kluwick (TU Wien) Schedule
The appearance of short laminar separation bubbles in high Reynolds number wall bounded flows
due to appropriate adverse pressure gradient conditions is usually associated with minor effects on
global flow properties (e.g. lift force). However, localized reverse flow regions are known to react
very sensitively to perturbations and in further consequence may trigger the laminar-turbulent
transition process or even cause global separation. The present investigation of marginally separated
boundary layer flows is based on a high Reynolds number asymptotic approach. Special
emphasis is placed on solutions of the corresponding model equations which blow up within finite
time indicating the ejection of a vortical structure and the emergence of shorter spatio-temporal
scales reminiscent of the early transition scenario (‘bubble bursting’). Among others, an adjoint
operator method is used to formulate the consequential evolution equations of the viscous-inviscid
interaction process beyond blow up. Recent analytical and numerical findings regarding this new
stage will be presented.
Cauchy Problems and Breakdown in the Theory of Marginally Separated Flows
Mario Aigner, Stefan Braun (TU Wien) Schedule
Flow separation can be viewed as one of the trigger events of laminar-turbulent boundary layer
transition. Thus, intensive investigations have been carried out as to when and how laminar boundary
layers break down. In the special case of marginal separation, i.e. the formation of short
laminar separation bubbles, high Reynolds number asymptotic theory yields integro-differential
equations governing the essential flow behavior. Since transition, which can be associated with

Section 9: Laminar flows and transition 205
”bubble bursting”, is an inherent time dependent phenomenon, initial value problems (IVPs) were
formulated, using appropriate time scales within the according asymptotic setting. We will present
further considerations of these problems in planar and three-dimensional flow cases regarding
the general ill-posedness, using analytical and numerical techniques to depict the spatio-temporal
manifestation of short-scale instabilities. To regularize such disturbances, higher order asymptotic
terms comprising the streamline curvature in the boundary layer region are taken into account.
Evidence for well-posedness of this modified problem will be given in terms of a dispersion relation
and numerical solutions of the full problem, especially by performing backward in time
calculations. Even though the regularized IVPs admit limiting steady states in their time evolution,
the phenomenon of finite time blow-up, which can be interpreted as ”bubble bursting”, is
still present. As a consequence, the inevitable breakdown of the according flow description leads
to the emergence of a new asymptotic structure of shorter spatio-temporal scales (yielding a so
called nonlinear triple deck stage). Deeper insight into this next stage of the bursting process is
still to be gained and we will conclude by presenting some first attempts in solving this problem.
S9.3: Laminar flows and transition III Wed, 13:30–15:30
Chair: Andreas Krumbein, Suad Jakirlic S1|01–A2
Transition Modelling for Aerodynamic Flow Simulations with a Near-Wall Reynolds-
Stress Model
Axel Probst (DLR Göttingen), Ulrich Rist (Universität Stuttgart), René-Daniel Cécora, Rolf Radespiel
(TU Braunschweig) Schedule
Transition from laminar to turbulent flow plays a significant role in modern aircraft designs. Numerical
simulations of flows around flying aircrafts still mostly rely on RANS (Reynolds-averaged
Navier-Stokes) approaches which use semi-empirical closures to model turbulent flow. The most
general level of RANS closures is achieved by modelling the six individual transport equations
of the Reynolds-stress tensor (Reynolds-stress model, RSM). To account for near-wall turbulence
effects additional low-Reynolds number damping functions can be applied which locally alter the
model calibration.
Our present approach uses the ε h -based near-wall RSM [1] in an extended formulation which
is combined with an e N -transition-prediction method within the finite-volume flow solver DLR-
TAU. Due to its DNS-based calibration the model is able to accurately predict the anisotropic
Reynolds-stress and dissipation-rate profiles down to the wall. However, the damping terms were
found to delay or even suppress transition in the low-disturbance environments of flying aircrafts.
The simulation method is therefore extended by a novel approach to incorporate the usually neglected
Reynolds-stress contributions by the unstable transitional modes into the RANS solution
[2]. To derive realistic input quantities at turbulence onset a linear-stability eigenfunction analysis
of the incoming laminar boundary layer is performed. It provides the wall-normal shapes of the
transitional Reynolds stresses which are derived from the amplitudes and phase shifts of the most
amplified Tollmien-Schlichting or crossflow wave at the end of linear amplification. Closure of
the yet missing magnitudes is obtained by an additional calibration based on DNS results of an
adverse-pressure-gradient flow.
The talk provides a detailed overview on both the near-wall Reynolds-stress closure and the
linear-stability-based transition model. To demonstrate the validity of the approach, computations
of different 2D and 3D flow cases are presented, such as generic boundary layers, airfoil
flows and a flow-through nacelle near stall. Moreover, a recent extension for combined Tollmien-
Schlichting/crossflow transition scenarios is addressed.

206 Section 9: Laminar flows and transition
[1] Jakirlić, S., Hanjalić, K., A new approach to modelling near-wall turbulence energy and stress
dissipation, J. Fluid Mechanics, 459 (2002), 139 – 166.
[2] Probst, A., Radespiel, R., Rist, U., Linear-Stability-Based Transition Modeling for Aerodynamic
Flow Simulations with a Near-Wall Reynolds-Stress Model, to appear in: AIAA Journal
(2012).
An investigation of the separate flow and stall delay for horizontal-axis wind tubine
Florin Frunzulica (POLITEHNICA University of Bucharest), Razvan Mahu (TENSOR SRL,
Bucharest), Horia Dumitrescu (Institute of Mathematical Statistics and Applied Mathematics
Bucharest) Schedule
The flow characteristics and stall delay phenomenon of a stall regulated wind turbine rotor due to
blade rotation in steady state non-yawed conditions are investigated. An incompressible Reynoldsaveraged
Navier-Stokes solver is applied to carry out the separate flow cases at high wind speeds
from 11 m/s to 25 m/s with an interval of 2 m/s. The objective of the present research effort is
to validate a first-principles based approach for modeling horizontal-axis wind turbines (HAWT)
under stalled flow conditions using NREL/ Phase VI rotor data. The computational results are
compared with the predicted values derived by a new stall-delay model and blade element momentum
(BEM) method.
An insight into the rotational stall delay
Horia Dumitrescu, Vladimir Cardos (Institute of Statistical Mathematics and Applied Mathematics
Bucharest) Schedule
Blade element and momentum methods (BEM) are the traditional design approach to calculate
drag and lift forces of wind turbine rotor blades. The major disadvantage of these theories is
that the airflow is reduced to axial and circumferential flow components. Disregarding radial flow
components leads to underestimation of lift and thrus. Therefore, correction models for rotational
effects are often used in the case of the stall controlled rotors at a constant rotation speed. At
inboard locations, there is a strong interaction between the fast rotating flow of wake and the 3-D
boundary layer close to the blade surface rotating with an angular velocity smaller than that of
the fluid. This behaviour is visible from the streamlines over the blade surface during operation in
deep stall. The knowledge extracted from the physical mechanism of 3-D rotational effects can be
then used to develop an improved BEM model for the design of stall control-wind turbine rotor
blades. In this study the pressure fields generated by the wake and blade are superimposed and
the main contributions for the rise of the three-dimensional and rotational effects are described.
Analytical and Numerical Modelling of the Safe Turn Manoeuvres of Agricultural
Aircraft
Bosko Rasuo (University of Belgrade) Schedule
In this paper, a theoretical study of the turn manoeuvre of an agricultural aircraft is presented.
The manoeuvre with changeable altitude is analyzed, together with the, effect of the load factors
on the turn manoeuvre characteristics during the field-treating flights. The mathematical model
used describes the procedure for the correct climb and descent turn manoeuvre. For a typical
agricultural aircraft, the numerical results and limitations of the climb, horizontal and descending
turn manoeuvre are given. The problem of turning flight with changeable altitude is described
by the system of differential equations which describe the influence of the normal and tangential
load factors on velocity, the path angle in the vertical plane and the rate of turn, as a function of
the bank angle during turning flight. The system of differential equations of motion was solved

Section 9: Laminar flows and transition 207
on a personal computer with the Runge-Kutta-Merson numerical method. Some analytical and
numerical results of this calculation are presented in this paper.
Ariel treating has become an integral part of modern agriculture. However, agricultural flying
has been plagued by a great number of accidents. The manoeuvres of an agricultural aircraft
are divided into those carried out while entering or leaving the spraying line. Despite low height
of the aeroplane while spraying, this part of the flight is considered to be the safest because
of an appreciable flight velocity. Upon completing a spraying run, the aircraft enters the turn
manoeuvre procedure.
The low altitude of the turn manoeuvre procedure and the vicinity of terrain are main causes
of numerous accidents. The pilots assert that the procedure is the most dangerous manoeuvre
and most of the accidents occur when these manoeuvres are performed, due to low altitude and
the possibility of stall during the manoeuvres. There are many secondary factors that influence
the safety of agricultural flying and some of them will be treated in this paper.
In this paper a criterion has been established for determining the margin of the speed over the
stalling speed (safety speed) after the agricultural aeroplane increases its height above the ground
by a given amount. The required altitude may be different for different types of aeroplanes and
will depend on their capability to perform rolling and turning manoeuvres. The minimum margin
of velocity allowed is determined from the requirements of the rolling manoeuvre.
A numerical study of vortex structures behind an harbor seal vibrissa
Daniel Matz, Albert Baars (Bionik Innovations Centrum) Schedule
Harbor seals (Phoca vitulina) use whiskers (vibrissa) to detect prey by their trailing wake. These
whiskers are not circular cylinders, but show wavy elliptical structures in spanwise direction.
This geometry is found to substantially reduce vortex shedding in the wake of the vibrissa in
comparison to circular cylinders and elliptical structures. In this work we want to contribute to
the question, to what extent wave length and amplitude of the shape are optimized for reduction
of self induced oscillations. Therefore, numerical flow simulations at Re = 230 are performed to
investigate the influence of amplitude and wavelength on vortex structures, drag and lift coefficient,
as well as the Strouhal number. The 3D calculations are carried out with a finite volume
code with discretization of second order in space and time. The block structured grids consists of
around 1 · 10 7 volumes. For the basic geometry the amplitude of the lift coefficient range lower by
a factor of 120 in comparison to a cylinder and a factor of 30 in comparison to an ellipse. This is in
accordance with literature. The separated shear layer in the wake of the vibrissa forms complex
3D flow pattern, which show a periodical structure in spanwise direction. For overflow length
greater than 800 this structure gets unstable and deforms in spanwise direction. This influences
the temporal progression of drag and lift coefficient.
S9.4: Laminar flows and transition IV Wed, 16:00–18:00
Chair: Martin Oberlack / Florian Kummer, Stefan Braun S1|01–A2
A discontinuous Galerkin solver for steady incompressible flows based on the SIM-
PLE algorithm
Benedikt Klein, Florian Kummer (TU Darmstadt) Schedule
For the numerical simulation of incompressible flows the finite volume method (FVM) and the
continuous finite element method (FEM) are widely used. Besides, a newer method, the discontinuous
Galerkin method (DGM), which has got favorable properties of both the FVM and the
FEM, is becoming more popular. The DGM provides a convergence order of O(∆x k+1 ), where k
is the order of the approximating polynomials.

208 Section 9: Laminar flows and transition
When simulating incompressible flows one has to deal with certain difficulties, like the nonlinearity
in the momentum equation, a strong coupling between velocity and pressure and the lack
of an explicit equation for the pressure. The well-known SIMPLE algorithm, which was originally
proposed by Patankar and Spalding [1], has shown to be very efficient in the context of the FVM
and the FEM [2]. For the SIMPLE algorithm, by introducing an iterative process the discrete
equations are linearized and decoupled. An equation for the pressure, more precisely speaking,
for the pressure correction is derived on the discrete level.
Using a discontinuous Galerkin discretization of the momentum and continuity equation [3],
we present how the SIMPLE algorithm can be adapted to the DGM. Various test cases are carried
out, which show the expected convergence rate of k + 1.
[1] S.V. Patankar and D.B Spalding, A calculation procedure for heat, mass and momentum
transfer in three-dimensional parabolic flows, Int. J. Heat Mass Transfer 15 (1972), 1787 –
1806.
[2] V. Haroutunian, M.S. Engelman and I. Hasbani, Segregated finite element algorithms for the
numerical solution of large-scale incompressible flow problems, Int. J. Numer. Meth. Fl. 17
(1993), 323 – 348.
[3] K. Shahbazi, P.F. Fischer and C.R. Ethier, A high-order discontinuous Galerkin method for
the unsteady incompressible Navier-Stokes equations, J. Comput. Phys. 222 (2007), 391 –
407.
Energy conserving incompressible flows on collocated and distorted grids
Julius Reiss (TU Berlin) Schedule
An energy preserving finite difference scheme for incompressible, constant density flows is presented.
It is based on the idea of the skew-symmetric formulation of the non–linear transport term
of the Navier–Stokes Equation
∂tuα + 1
2 (div (uuα) + u · grad (uα)) + (gradp)α = 0
div(u) = 0
with u = (u1, u2, u3), and α = 1, 2, 3. In contrast to established schemes collocated Euclidean grids
can be used while exactly preserving the energy and momentum conservation, yet avoiding the
odd–even decoupling of the Laplacian of the pressure Poisson equation. The essential idea is to use
different discretizations for the different derivatives in the above equations. High order derivatives
in space and time can be used. The generalization to transformed grids is discussed and full
conservation for arbitrary transformations in two dimensions and for restricted transformations
in three dimensions is found.
On a reduced mixed s-v least-squares finite element formulation for the incompressible
Navier-Stokes equations
Alexander Schwarz, Jörg Schröder (Universität Duisburg-Essen) Schedule
In the present work a mixed finite element based on a least-squares approach is proposed. Here,
we consider a formulation for Newtonian fluid flow, which is described by the incompressible
Navier-Stokes equations. First, a div-grad first-order system is derived resulting in a three-field
approach with stresses, velocities, and pressure as unknowns. Following the idea in [1], this threefield
formulation can be transformed into a reduced stress-velocity (s-v) two-field approach. The

Section 9: Laminar flows and transition 209
L2-norms of the residuals of the derived equations yield then the least-squares functional, which is
the basis for the associated minimization problem. Besides some numerical advantages, as e.g. an
inherent symmetric structure of the system of equations and an error estimator, it is known that
least-squares methods have also a drawback concerning accuracy, especially when lower-order
elements are used, see e.g. [2,3]. Therefore, the main focus of the presentation is on performance
and implementation aspects of triangular mixed finite elements with different interpolation order.
In order to approximate the stresses, shape functions related to the edges are chosen. These
vector-valued functions are used for the interpolation of the rows of the stress tensor and belong
to a Raviart-Thomas space, which guarantees a conforming discretization of the Sobolev space
H(div). Furthermore, standard polynomials associated to the vertices of the triangle are used for
the continuous approximation of the velocities. The talk closes with some numerical examples,
which focus on well-known benchmark problems for incompressible Newtonian fluid flow and
demonstrate the performance of the mixed finite element formulation.
[1] Z. Cai, B. Lee, P. Wang, Least-squares methods for incompressible Newtonian fluid flow:
linear stationary problems, SIAM J. Numer. Anal. 42 (2004), 843–859.
[2] O. Kayser-Herold, Least-squares methods for the solution of fluid-structure interaction problems,
PhD Thesis, Technische Universität Braunschweig (2006).
[3] A. Schwarz, J. Schröder, A mixed least-squares formulation of the Navier-Stokes equations
for incompressible Newtonian fluid flow, Proc. Appl. Math. Mech. 11 (2011), submitted.
Allocation of the particle concentration for the SPH-method depending on the gradients
of flow parameters
Anika Stein, Olaf Wünsch (Universität Kassel), Markus Rütten (DLR Göttingen), Jens Kuenemund,
Stefan Saalfeld (Universität Göttingen) Schedule
The Smoothed Particle Hydrodynamics method (SPH) is a Lagrangian, mesh free method to
discretize partial differential equations like the Navier-Stokes-Equation by interpolating flow properties
directly at a set of particles. It was first developed 1977 by [1] and [2] for astrophysical
Problems. Today it is applied more and more for mechanical problems. It is comfortable to use
for fluid and multiphase flow problems, large deformation problems and free surface flows because
it is possible to allocate different properties to each particle. Moreover the differential set of the
Momentum-Equation is particularly suitable for complex rheological problems like polymer melts,
[3]. All the information about the flow like velocity, temperature, viscosity and so on are recorded
at each particle for a optional number of departed time steps. It brings a lot of advantages as
described above, but another outcome of that are costs in memory and a rising need of calculation
power, the more particles are inside a domain. Taking in account that in some areas of a flow field
nearly nothing happens and in some areas the gradients of flow parameters are very high, it is
not the best choice to use the same particle concentration at those different regions. In this paper
a method is presented to optimise this number of particles according to the gradients of the flow
parameters. The functional principle of this operation is to generate particles at domains with
highly alternate flow properties and to turn them out where they are not needed. This algorithm
is able to generate more accurate solutions, which is shown by different examples like a leaked
tank or a breaking dam. Finally the influence of the procedure is discussed.
[1] R. A. Ginglod and J. J. Monaghan, Smoothed particle hydrodynamics theory and application
to non-spherical stars, Mon. Not. R. Astron. Soc. 181, 375 (1977)

210 Section 9: Laminar flows and transition
[2] L. B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 83, 1013
(1977)
[3] M. Ellero, Smoothed Particle Dynamics Methods for the Simulation of Viscoelastic Fluids,
Dissertation, Universität Berlin,(2004), urn:nbn:de:kobv:83-opus-7658
Internal flow analysis for slow moving small droplets in contact with rough surfaces
Raheel Rasool, Roger A. Sauer, Muhammad Osman (RWTH Aachen) Schedule
Motivated by the self-cleaning phenomena, internal fluid flow behavior for slow moving small
droplets in contact with rough surfaces is analyzed. The shape of the droplet is first computed
using the Young-Laplace equation. For this purpose a Finite Element (FE) model [1], in which
contact constraints are enforced through Penalty and Augmented Lagrange Multiplier methods,
is used. The flow field within the droplet is then analyzed through the Stokes flow model, constituting
a decoupled approach. Similar to the membrane deformation model, the formulation for
the flow analysis is also expressed in the framework of FE analysis. Both, stabilized (Pressure
Stabilizing/Petrov-Galerkin PSPG) and Galerkin FE formulations are considered. The motion
of the fluid inside the droplet is governed by the slip condition enforced on the membrane of
the droplet. Numerical examples for droplets rolling steadily on smooth and rough surfaces are
presented.
[1] M. Osman and R.A. Sauer, A two-dimensional computational droplet contact model, Proc.
Appl. Math. Mech., 11 (2011), 103-104.
Pattern formation and mixing in three-dimensional film flow
Thilo Pollak, Christian Heining, Nuri Aksel (Universität Bayreuth) Schedule
The effect of inertia on gravity-driven free surface flow over different three-dimensional periodic
corrugations is considered analytically, numerically and experimentally. In the case of high bottom
undulations the results predict complex free surface structures especially in cases where the
topography is not fully flooded by the liquid film. The investigation of the flow field shows a rich
variety of pattern formation phenomena depending on the interplay between the geometry of the
topography and the inertia of the film. Finally, we show how the complex topographical structure
enhances the laminar mixing within the film.
S9.5: Laminar flows and transition V Thu, 13:30–15:30
Chair: Ulrich Rist S1|01–A2
Modelling study of turbulent-to-laminar transitional features of a strongly heated
pipe flow
S. Jakirlic (TU Darmstadt), R. Jester-Zuerker (Voith Hydro Holding GmbH Co. KG-tts, Heidenheim)
Schedule
A flow in a circular pipe subjected to increasingly enhanced wall heating is computationally investigated
by means of a differential, near-wall second-moment closure model based on the solution
of transport equations for second moments of the fluctuating velocities and temperature, � u ′′
i u′′
j and
�u ′′
i
θ respectively. Both Reynolds stress model and heat flux model represent wall-topography free
formulations with quadratic pressure-strain term and pressure-temperature-gradient correlation.

Section 9: Laminar flows and transition 211
The transport equations for the turbulent stress tensor and the turbulent heat flux are solved in
conjunction with the equation governing a novel length-scale determining variable, the so-called
homogeneous dissipation rate, Jakirlic and Hanjalic (2002, J. Fluid Mech., 539:139-166). Such an
approach offers a number of important advantages: proper near-wall shape of the dissipation rate
profile was obtained without introducing any additional term and the correct asymptotic behaviour
of the stress dissipation components by approaching the solid wall is fulfilled automatically
without necessity for any wall geometry-related parameter. In order to account for the influence
of the temperature field and associated fluid property variation on the velocity field, the Favreaveraged
equations for mass, momentum and energy are solved. The temperature dependence on
viscosity and heat conductivity is defined via a power-law formulations, while Prandtl number
P r and specific heat at constant pressure Cp were kept constant. Density is evaluated from the
equation for ideal gas.
The flow configuration considered presently, representing a vertical circular tube with air flowing
in upward direction, was experimentally investigated by Shehata and McEligot (1998, Int. J.
Heat and Mass Transfer, 41:4297-4313) and by means of DNS by Satake et al. (2000, Int. J. Heat
and Fluid Flow, 21:526-534) and Bae et al. (2006, Physics of Fluids, 18(075102)). After a portion
of a fully-developed pipe flow (length = 4D, with D being the pipe diameter) with constant wall
temperature Θw the air enters a 30D-long pipe subjected to intensive heating (with negligible
buoyancy effects). The thermal boundary conditions correspond to a constant heat flux. Three
different heating rates were considered q +
i = 0.0018, 0.0035 and 0.0045. According to the reference
data originators, these values relate to the turbulent, sub-turbulent and laminarizing regimes. In
the latter case some laminarization phenomena have been observed. The influence of strong heating
of a gas flow (as, e.g., encountered in gas combustors and similar high-temperature reactors) is
primarily manifested through a severe variation of the fluid properties (density, viscosity) leading
consequently to important structural changes. The most important changes are concentrated in
the immediate wall vicinity. The strongest modification of flow structure, deviating substantially
from the equilibrium conditions, occurs in the inner part of the temperature layer. Accordingly,
the density decrease and viscosity increase led to the thermal boundary layer growth and
viscous sublayer thickening (relative to the boundary layer thickness reduction) causing the flow
acceleration, which, if sufficiently strong, can suppress turbulence resulting in flow laminarization.
The model results obtained follow closely the experimental and DNS findings manifested especially
through the laminar-like profiles of the velocity and temperature fields. The behaviour of
Reynolds stress components is in accordance with a severe suppression of the turbulence intensity
due to local acceleration caused by a strong viscosity increase.
Numerical and experimental investigations of thermal convection in an inclined narrow
gap
O. Sommer (TU Chemnitz), H. G. Heiland (SUVIS GmbH, Chemnitz), G. Wozniak (TU Chemnitz)
Schedule
The knowledge of the fluid behaviour in inclined cavities is of fundamental importance as far as
heat and mass transfer are concerned. The interest in this subject is particulary increasing due
to the rapid process in microtechnologies. We therefore studied the flow- and temperature field of
such flows numerically as well as experimentally using CFD and PIV/ T, respectively. We present
and discuss the numerical and experimental results of our investigations and explain the applied
techniques.
Gas exchange of almost leak-tight display cases
Johannes Strecha, Herbert Steinrück (TU Wien) Schedule

212 Section 9: Laminar flows and transition
A requirement for display cases for art objects is to be leak tight. However, due to design constraints
there a are tiny gaps resulting in a gas exchange between the interior of the show case and
its environment. Usually the leak-tightness is being quantified by the so-called air exchange rate,
the ratio of the gas volume exchanged between display-case and environment per unit time and
the volume of the display-case. Commonly the concentration of a tracer-gas in the display-case is
monitored to calculate the air exchange rate. For this purpose a certain tracer-gas exchange-law is
assumed, usually a linear exchange-law. We present experimental results that disqualify a linear
exchange law and find that it is a special case, not applicable in general.
We review the gas exchange mechanism through the gaps Taking hydro static pressure differences
due to temperature and concentration differences of the tracer gas and diffusion into
account a non linear exchange model is derived and validated experimentally.
We conclude that in general the tracer-gas concentration has a significant influence on the gas
exchange and therefore the assumption of a linear exchange-law is discouraged. Instead we suggest
the introduction of two parameters: one that characterizes the air-exchange in the diffusion-driven
limit and one that takes the influence of hydrostatic pressure into account. Strategies to identify
these parameters will be presented and demonstrated.
Non isothermal simulation of non-Newtonian flow in the shot sleeve of semi- solid
die casting processes
Roudouane Laouar, Olaf Wünsch (Universität Kassel) Schedule
This work deals with a numerical study of the flow of metal in the semi-solid state in the shot sleeve
of horizontal die casting machine during the injection process. With the discovery of shear thinning
and the thixotropic behavior of partially solidified alloys under vigorous agitation, a new era in
forming technology was started, namely semi-solid metal (SSM) processing. The new technology
promises several important advantages in comparison with the traditional die casting processes.
In the semi-solid state, metallic alloys consists of solid particles suspended in a liquid Newtonian
matrix and consequently modeling approaches known from classical suspension rheology can be
applied. In the equilibrium state, semi-solid alloys are shear-thinning and different descriptions in
form of material equation are used in literature. In the present work, the Herschel-Bulkley model,
which contains a yield stress and a shear-thinning viscosity, was used in order to demonstrate
the effect of the nonlinear viscosity to the flow pattern in the shot sleeve. The used numerical
model, which considers the problem as two-dimensional, is based on the conservation equations
of mass and momentum, and describes the free surface using the volume-of-fluid method. The
motion of plunger is simulated by using a layering dynamic mesh method. The numerical results
are obtained by using a CFD code that is based in the finite volume method. The influence of
different parameters as yield stress, the power law index and the temperature in the flow dynamics
is to be discussed. A comparison between a Herschel-Bulkley fluid and a shear-thinning fluid with
no yield stress limit is presented.
Simulating of a pressing process of a viscoelastic polymer melt
Ammar Al-Baldawi, Olaf Wünsch (Universität Kassel) Schedule
A well known and often used method to obtain anisotropic polymer films is the so-called pressing
process. Here, films are squeezed under high temperatures, pressure and deformation rates. To
simulate such a process, the polymeric matrix is treated as a non-Newtonian, viscoelastic melt.
Experimental investigations of it predict a shear thinning and elongational hardening/softening
behavior. The modeling of this behavior is done with a generalized Maxwell Model. Where the
generalization is obtained using a Phan-Thien and Tanner anisotropic molecule movement tensor
for high deformation rates [1,2].

Section 9: Laminar flows and transition 213
Simulating this process leads to a hyperbolic equation set of mass conservation, momentum
balance and material model. Therefore, the simulation needs to be stabilized; here the DEVSS
method is used. Furthermore, the ALE method is used to interpolate between the Euler and
Lagrange description method in connection with a cell-layering method to obtain big changes in
the calculation domain.
In this work we present some simulations to show the difference between the classical approaches
using a generalized Newtonian viscosity to model the polymeric matrix and the viscoelastic
model. Here, the major difference is shown to be the pressure field and its influence on the velocity
field and the extra stress tensor. For this end we use a flow type parameter to show the elongation
types in the regions and the differences [1].
[1] A. Al-Baldawi, O. Wünsch, Some new aspects of the invariants of the rate of deformation
tensor and their application on viscoelastic polymer melts, Accepted for publication in
Technische Mechanik (2011)
[2] O. Wünsch, Laminar Fluid Flow with Complex Material Behavior in Devices of Mechanical
Engineering, Int. Journal of Emerging Multidisciplinary Fluid Sciences, 1-4, 255-267 (2009)
S9.6: Laminar flows and transition VI Thu, 16:00–18:00
Chair: Suad Jakirlic S1|01–A2
Direct numerical simulation of MHD duct flow at high Reynolds number
Dmitry Krasnov (TU Ilmenau), Oleg Zikanov (University of Michigan), Thomas Boeck (TU Ilmenau)
Schedule
Evolution of turbulent flow of an incompressible, electrically conducting fluid is studied numerically
in a square duct subjected to a uniform magnetic field B. The magnetic field is applied in
the vertical (wall-normal) direction, the walls are perfectly insulating. The governing equations
are the Navier-Stokes system with the additional Lorentz force term j × B, where j is the electric
current. There are two governing parameters, the Reynolds number Re = UqL/ν and the Hartmann
number Ha = BL � σ/ρν, which characterizes the strength of the applied magnetic field B.
Here Uq are the mean flux velocity, L is the duct half-width and σ is the electrical conductivity.
The Joule dissipation selectively damps out fluctuations of velocity perpendicular to the magnetic
field that can result into anisotropy of turbulent eddies. For strong magnetic fields the
anisotropy can evolve into 2D structures stretched along the direction of the magnetic field. Two
major ingredients are necessary to achieve the 2D states: (i) the Reynolds number Re should
be large, that amounts to intensive turbulent fluctuations and (ii) the interaction parameter
N = Ha 2 /Re should exceed 1, which also means strong magnetic fields.
In our simulations Re = 100000 and Ha = 0 ... 400. For the present study a series of DNS was
performed at the grid resolution of 2048 × 769 × 769 points that amounts to more than 1 billion
points as a problem size. The numerical method is based on highly conservative finite-difference
discretization of the second order, the flow solver is hybrid-parallel (both MPI and Open MP
interfaces).
As Ha increases the flow transforms from nearly isotropic turbulence at Ha = 0 to a spatial
anisotropy at Ha > 200. At Ha = 300 the core flow becomes essentially laminar, the turbulence
remains small-scale near the side walls, but becomes large-scale, weak, and strongly anisotropic
towards the core flow. Finally, at Ha = 400 the fluctuations die out and the flow becomes laminar.
The quasi-2D structures have been identified in a clear-cut way by applying the so-called

214 Section 9: Laminar flows and transition
lambda-2 criterion. The results of the lambda-2 visualization at Ha = 300 and 350 show a region
with clearly expressed 2D structures stretched along the magnetic field. We have also found
transformation of the mean velocity similar to our previous study on channel flow under spanwise
magnetic field. This behavior is observed in the cross-section perpendicular to the magnetic field
for a range Ha ≈ 100 ... 200. During this transformation the classical log-layer almost disappears
and is replaced by a linear dependence.
Visualisation of the Ludford column
André Thess (TU Ilmenau), Oleg Andreev (Forschungszentrum Dresden-Rossendorf) Schedule
The formation of TTaylor columnsïn rotating flows is well known: When a liquid flows over a
truncated cylinder in a rotating systems, a stagnant region forms above the cylinder. It has been
known for quite some time that an analogous phenomenon, the LLudford columnëxists when a
liquid metal flows across a truncated cylinder under the influence of a magnetic field parallel
to the axis of the cylinder. Since liquid metals are opaque, it is impossible to visualise Ludford
columns. Using an electrolyte instead of a liquid metal and a high magnetic field created by
a superconducting magnet we visualise for the first time the Ludford column and discuss their
properties. We discuss further ways in which optical flow measurement can be applied to better
understand magnetohydrodynamic flows.
Separation of magnetic particles in channel flows by BEM
J. Ravnik, M. Hriberek (University of Maribor), F.Vogel, P. Steinmann (Universität Erlangen-
Nürnberg) Schedule
In-line separation of suspensions can become difficult in in case of particles with comparable values
of densities. For flows in micro devices in such cases gravitational settling is inefficient, and other
separation techniques must be applied. In case of magneto active particles, the action of Kelvin
magnetic force in a non-uniform magnetic field could be used in order to achieve a higher degree of
particles separation. The contribution therefoe deals with Euler-Lagrangian formulation of dilute
two-phase flows. The Boundary element based computational algorithm solves the incompressible
Navier-Stokes equations written in velocity-vorticity formulation. The nonuniform magnetic field
was defined analytically for the case of a set of long thin wires. The particle trajectories were
computed by applying the 4th order Runge-Kutta method. The computed test case consisted of
a narrow channel with laminar flow of suspension under Re=1-10. Particle trajectories under the
influence of a nonuniform magnetic field were computed for the case of magnetite and aluminium
particles suspended in water. The efficiency of separation on basis of particle trajectories for different
values of Re number and magnetic field strength was performed, clearly indicating superior
separation of magneto active particles.
Experimental investigation of the electrokinetic flow in microchannels with internal
electrodes
Carsten Gizewski, Peter Ehrhard (TU Dortmund) Schedule
In microfluidic devices, electrokinetic phenomena can be engaged to manipulate liquids, particles,
or cells. In general, electrokinetic phenomena are related to the existence of electrical double
layers (EDL), which are present e.g. where solid walls are in contact with electrolytes. Due to
surface charges of the solid, ions of opposite charge are attracted and lead to a thin electrically
non-neutral zone the EDL. The application of an electrical field, consequently, leads to forces
onto the fluid inside the EDL, capable of driving a flow within the microchannel. This particular
flow is termed electroosmotic. If further, the electrodes are placed inside the microchannel, due

Section 9: Laminar flows and transition 215
to small distances, strong inhomogeneous electrical fields can be induced, which in turn cause
complex flow fields. This is true despite low applied electrode potentials of a few Volts. Numerical
simulations of various authors have shown the potential for pumping and mixing of such complex
flows in microchannels with internal electrodes.
We focus on the electroosmotic flow within rectangular microchannels of 100 x 200 µm cross
section. In each microchannel eight pairs of electrodes are placed onto the top and bottom glass
covers, whereas the offset of the electrodes is chosen differently in each of the microchannels. Due
to the limited optical access through the glass covers, only the two velocity components which
are tangential to the glass cover are accessible by means of the micro-particle-image velocimetry
(µPIV). The expected electroosmotic flow, however, features vortices which cannot be recognized
within this velocity plane. Therefore, a number of two-dimensional, two-component velocity
fields are measured at different heights of the microchannel. From an integration of the continuity
equation, subsequently, the third velocity component, which is normal to the glass cover, can
be determined at reasonable accuracy. A further difficulty arises from the fact that the microparticles,
used for µPIV, are not electrically neutral. Hence, in addition to drag forces from the
electroosmotic flow, they experience electrophoretic forces. Hence, the particle movement appears
to be a superposition of electroosmotic and electrophoretic effects.
Flow characterization in a bioaffinity enrichment system for detection of relevant
microorganisms in food
A. Osorio Nesme, R. Benning, A. Delgado, (Universität Erlangen-Nürnberg) Schedule
In food industry the quality assurance and consumer protection represent essential requirements
for preserving high product ratings and competitiveness. Decreases in food quality or risks to
consumers health must be properly detected in time to avoid image damage to the companies
or risks from the product liability. In particular, the detection of microorganisms is of great
importance. In general, this can be carried out by the routine microbiological diagnostic, whose
negative results can be obtained only after 24 (Staphylococcus aureus) or 48 hours (Bacillus
cereus). Furthermore, the confirmation of positive samples can take up to 144 hours. From the
perspective of the current state of art, this analysis time could be for the microorganisms S.
aureus and B. cereus significantly reduced by means of the development and combination of new
analytical techniques. In the present study, a new system for direct detection of S. aureus and
B. cereus (spores) through bioaffinity enrichment is introduced by means of a fully automated
selective-microarray device (microporous columns) for milk and whey. The system consists of
a monolithic column with a microporous structure, in which biological receptors (monoclonal
antibodies or aptamers) are immobilized on the surface. These receptors have a specific interaction
with the microorganisms (bioaffinity). The matrix (milk) flows through the monolithic column,
allowing the microorganisms to come in contact with the receptors and get bound to the column
surface. It has been found that the amount of microorganisms captured during the process depends
not only on the binding kinetics but also on the flow characteristics. High flow rates signify
less residence time of the microorganism in the column and therefore less probability of getting
captured. The flow velocity and flow distribution along the column have a direct impact on the
binding process (microorganism enrichment). An important part of the present work consists of
the optimization of the column geometry by means of numerical simulations. The influence of the
inlet form of the monolithic column on both flow and pressure distribution is investigated.

216 Section 10: Turbulence and reactive flows
Section 10: Turbulence and reactive flows
Organizers: Stefan Braun (TU Wien), Reinhard Farwig (TU Darmstadt)
S10.1: Reactive flows and turbulent heat transfer Tue, 13:30–15:30
Chair: S. Braun, R. Farwig S1|01–A02
Free energy budgets in viscoelastic natural convection
Elisabetta De Angelis (University of Bologna) Schedule
It has been known for over fifty years that the introduction of a small amount of polymer additives
could significantly reduce friction drag in wall-bounded turbulent flows. However, in the last years
also the effect of polymers on turbulent thermal convection has drawn attention with controversial
results. In fact, a recent experiment has been conducted in an Rayleigh-Bénard convection cell
with and without polymers and a monotonic decrease of the Nusselt number (Nu, the ratio of
actual heat flux over that if there were only conduction) with increasing polymer concentration
was found. Whereas, a direct numerical simulation (DNS) study, where top and bottom walls
have been replaced by periodic boundary conditions, has shown an increase in Nu. Since it is not
easy to remove walls in the experiments, in order to assess the presumed role of the boundary
layers in the physics of the convection with polymers, new simulations are proposed. Namely, a
Direct Numerical Simulation of natural convection between parallel walls have been performed
at a modest but turbulent Rayleigh Number Ra, for varying polymers parameters. The present
results confirm an increase of the Nusselt number i.e. heat transfer for all the cases studied when
the polymer are highly stretched. Related to the enhancement of the heat transfer a deep modification
of the structure of the convection cells is observed. A detailed description of the polymer
free energy redistribution in such flows will be the subject of the present contribution.
Ahlers, G. and Nikolaenko, A., “Effect of a polymer additive on heat transport in turbulent
Rayleigh-Bénard convection,” Physical Review Letters, 104, 34503 (2010).
Benzi, R., Ching, E.S.C. and De Angelis, E., “Effect of Polymer Additives on Heat Transport in
Turbulent Thermal Convection,” Physical Review Letters, 104, 24502 (2010).
Numerical investigation of lean-premixed turbulent flame using combustion LES including
thickened flame model
A. Hosseinzadeh, A. Sadiki, J. Janicka (TU Darmstadt) Schedule
Lean premixed combustion is recently a theme of interest in gas turbines and other industrial
applications in an effort towards Nox emission reduction, which is a result of lower flame temperature
comparing to non-premixed flames. However, instabilities occurring in a combustion chamber
under lean premixed combustion, may lead to the operation efficiency and life cycle degradation.
Thus, LES as an adequate tool can be used to investigate the addressed unsteady phenomena.
In the present work a lean premixed turbulent Bunsen Type flame [1] is numerically investigated
using incompressible LES including the dynamic smagorinsky model for the flow filed, the eddy
diffusivity model for the scalar flux and thickened flame model coupled with tabulated chemistry
for the combustion [2]. The burner is equipped with a square matrix turbulence generator consisting
of 32 boreholes, which induce a turbulent intensity of Tu= 8% in the reaction zone.
The well known in house code FASTEST 3D, has been used for this investigation. The preliminary
results of flow characteristics, Temperature and combustion quantities of the investigated
configuration show a very good agreement to the experimental data.
[1] Zajadatz, M., Hettel, M., Leuckel, W. Burning velocity of high-turbulence natural gas flames

Section 10: Turbulence and reactive flows 217
for gas turbine application. In: International Gas Research conference. pp. 793-803.
[2] Künne, G. , Ketelheun, A. , Janicka, J. : LES modeling of premixed combustion using a
thickened flame approach coupled with FGM tabulated chemistry. In: Combustion and
Flame 158. pp. 1750-1767.
Large Eddy Simulation of Scalar Field in a High-Pressure Combustor fuelled with
Pre-Vaporized Kerosene
A.Hosseinzadeh, P. Pantangi, A. Sadiki, J.Janicka (TU Darmstadt) Schedule
Turbulent mixing is one of the important phenomena which govern the chemical reactions in both
chemical and combustion processes. In recent times the interest for developing comprehensive
numerical models, which are able to predict more precisely the mixing phenomenon of scalars in
complex systems, is increasing. In both cases of gaseous and liquid flows with chemical reactions,
scalar transport and mixing can be a rate determining step, so that there is a need of scalar flux
models that are accurate and efficient in both environments simultaneously.
In the present work the capability of an existing and a newly developed sub grid-scale (SGS)
model for the filtered scalar flux vector in the scalar transport equations of reactive scalars,
namely the dynamic eddy diffusivity model (EDM) and the dynamic anisotropic eddy diffusivity
model (AEDM), will be assessed for large eddy simulations (LES) of complex configurations. For
this purpose, the EKT high pressure kerosene combustion chamber operated with pre-vaporized
kerosene along swirled air as oxidant under non-premixed conditions is simulated using the in
house FASTEST-3D CFD code. The code includes additionally dynamic Smagorinsky SGS model
for the flow field and a flamelet generated manifold (FGM)-tabulated chemistry based approach
for the combustion.
Since comprehensive validation experimental data are available, the simulation results with
both SGS scalar flux models are compared with experimental data, respectively. Besides the model
sensitivity a grid sensitivity studies with coarse and fine meshes have been carried out to
highlight any parameter and grid dependency. The simulation in both grid levels showed that
the AEDM, that obviously involves more physical features, could provide better results than the
EDM. In particular, the investigations have proved that using advanced models for SGS scalar
uxes leads to a less mesh dependent simulation in complex configurations and to a reliable scalar
field prediction without additional computational costs.
A Tensorial Eddy Diffusivity based Subgrid Scale Model for Scalar Flux and its
Validation in Turbulent Reactive Flows
P. Pantangi (TU Darmstadt), H. Ying (Chinese Academy of Sciences Dalian), A. Sadiki (TU
Darmstadt) Schedule
In both diffusion and premixed combustion modes and in partially premixed combustion chemical
reactions that occur are promoted by mixing processes. While in a premixed flame, a thin reaction
layer propagates in the fuel/air mixture where the propagation speed is governed by chemical
reactions and diffusion of species between the reaction zone and the preheat zone, chemical reactions
in diffusion flames also occur in very thin layers where the combustion process is governed
by the diffusion of fuel and air to the reaction zones. In both cases turbulence length scales are
mainly larger than the thickness of reaction layers, so that one of the main effects of turbulence is
to wrinkle the reaction layers and to increase the surface area of the reaction layers and the fuel
conversion rate. Deeper understanding and reliable modelling of the turbulence/flame interaction
together with the mixing control are challenging for designers of spark-ignition engines (premixed

218 Section 10: Turbulence and reactive flows
flames), diesel engines (diffusion flames) and modern aircraft combustors (lean premixed flames or
partially premixed spray flames). To meet the need for a reliable predictive method, it is essential
that turbulent SGS models for scalar in CFD should be able to address accurately major mixing
transport effects at low computational cost.
This paper presents a newly developed Sub-Grid-Scale (SGS) scalar flux model and its validation
on diffusion and premixed configurations. The model that results from a general tensorial representation
theory is especially constrained by the second law of thermodynamic via the entropy
inequality to yield a practical model. This emerges in form of an explicit and algebraic expression
including a tensorial eddy diffusivity that is quadratic in terms of scalar gradients that can, in
turn, be linked to scalar dissipation rate. The model parameters are prescribed by the so-called
projection method allowing a dynamic evaluation.
The combustion LES tool includes additionally a dynamic Smagorinsky SGS model for the flow
field and a tabulated detailed chemistry based on a flamelet generated manifold (FGM) approach,
in which a variable local equivalence ratio due to a possible entrainment of the environment air
is included through a mixture fraction variable. A presumed pdf approach has been considered to
account for the turbulence-combustion interaction process. All these models are integrated into
the in house finite volume FASTEST3D code. To assess the prediction capability, LES results are
compared against experimental data and results achieved by using some existing SGS models. An
overall satisfactory agreement for the flow field quantities, species concentrations and SGS scalar
fluxes is accomplished with the new model.
Quasi-DNS of a Turbulent Premixed Flame treated as a Gasdynamic Discontinuity
S. Strein, C. Bruzzese, A. G. Class (KIT) Schedule
For a description of a premixed turbulent flame based on first principles, it is necessary to solve
a highly coupled system of equations including complex chemistry. The required spatial and temporal
resolution of a premixed turbulent flame leads to high computational costs. An attractive
approach reducing the effort is to describe a flame front as a gasdynamic discontinuity [1]. Governing
equations become the conservation equations for mass and momentum coupled to a level
set equation describing the kinematics of the flame front.
We present an implementation employing the level set approach using the open source C++
library OPENFOAM R○. A quasi-DNS (direct numerical simulation) of a turbulent premixed flame
in a two-dimensional box is realized to show the high efficiency of the method. Suitable deterministic
boundary conditions representing the unsteady nature of the turbulent flow field with a given
integral length scale are generated by a diffusion operator acting on a random field [2]. Statistic
values for the turbulent flame velocity are extracted and compared to previous investigations.
This work is supported by DFG grant SFB 606.
[1] A.G. Class, B.J. Matkowksy, A.Y. Klimenko, A Unified Model of Flames as Gasdynamic
Discontinuities, J. Fluid Mech 491 (2003), 11 – 49.
[2] A. Kempf, M. Klein, J. Janicka, Efficient Generation of Initial- and Inflow-Conditions for
Transient Turbulent Flows in Arbitrary Geometries, Flow, Turbulence and Combustions 74
(2005), 67 – 84.
Compressible Large-Eddy Simulation of Boundary-Layer Heat Transfer in a Turbulent
Convective Flow
Rodion Groll, Claudia Zimmermann, Hans J. Rath (Universität Bremen) Schedule

Section 10: Turbulence and reactive flows 219
Computing the heat transfer through the fluid between two heat controlled plates the compressible
fluid is accelerated by local density differences. Investigating the convective heat transfer of this
Rayleigh-Benard convection. The temperature distribution shows increasing temperature gradients
directly close to the wall. In the center region the heat transfer is defined by the convective
mass exchange.
The described convective mass transfer generates turbulent shear layers parallel to the gravity
direction. Because of the transient turbulence and the high local density gradients the simlation
works with a coupled model for the compressible Large-Eddy simulation.
The investigated Rayleigh numbers are in the region between 6 · 10 7 and 4 · 10 8 . Therefore
a direct correlation between Rayleigh number and Nusselt number is detected. Discussing the
results the asymmetric temperature profiles are explainable according to the density weighted
velocity profile. The simulation results are compared with experimental data [1] and analytical
model results [2].
[1] A. Ebert, C. Resagk, A. Thess, Experimental study of temperature distribution and local
heat flux for turbulent Rayleigh-Bénard convection of air in a long rectangular enclosure,
Int. J. of Heat and Mass Transfer, 51 (2008), 4238-4248.
[2] M. Hoelling, H. Herwig, Asymptotic analysis of heat transfer in turbulent Rayleigh-Benard
convection, Int. J. of Heat and Mass Transfer, 49 (2006), 1129-1136.
S10.2: Fundamental aspects of turbulent flows Tue, 16:00–18:00
Chair: R. Farwig, S. Braun S1|01–A02
Generating turbulent scaling laws from the multi-point equations using Lie theory
Andreas Rosteck, Martin Oberlack (TU Darmstadt) Schedule
The main aim is to give an analytic description of statistical turbulence behaviour and, in particular,
to determine turbulent scaling laws. The governing equations shall be analysed using the
Lie theory and the related Lie symmetries.
The starting point of the entire analysis is the infinite set of multi-point correlation (MPC)
equations, which are direct statistical consequences of the Navier-Stokes equations. In order to
gain differential equations for the multi-point correlations denoted by Ri {n+1} = Ri (0)i (1)...i (n) =
ui (0) (x(0)) · . . . · ui (n) (x(n)) , where the correlation of n + 1 turbulent velocity components is consi-
dered, the infinite set of correlation equations
Ti = {n+1} ∂Ri n�
�
∂
{n+1}
+ + Ri ∂t
{n+1}[i (l)↦→k (l)]
Ūi (x
(l) (l))
+ ∂xk (l)
∂Pi {n}
[l]
∂xi (l)
l=0
Ūk (l) (x(l)) ∂Ri {n+1}
∂xk (l)
−ν ∂2Ri ∂ui uk (x
{n+1}
(l) (l) (l))
−Ri ∂xk ∂xk {n}[i (l)↦→∅]
+ ∂xk (l) (l)
(l)
∂Ri {n+2}
[i
(n+1)
↦→k
(l) ][x (n+1)↦→x (l)]
∂xk (l)
�
=0 ,
for n = 1, 2, 3, . . . is introduced, which also has to be extended by additional continuity equations.
First we determine the Lie symmetries of the multi-point equations. It is clear that all Lie
symmetries of the Navier-Stokes equations can be transferred to the multi-point equations. However,
these are not the only symmetries holding for the MPC-equations. Additional symmetries,
which we call stastistical symmetries, can be found. At this point we have found an additional
scaling symmmetry and also translation symmetries of the MPC have been identified.
These new statistical groups have important consequences on our understanding of turbulent
scaling laws to be exemplarily revealed by two examples. Firstly, one of the key foundations of

220 Section 10: Turbulence and reactive flows
statistical turbulence theory is the universal law of the wall with its essential ingredient, the logarithmic
law. We demonstrate that the log-law fundamentally relies on one of the new translational
groups. Furthermore, we consider a rotating channel flow, whose scaling behaviour can only be
described using the new statistical symmetries. It can be seen that the direction of rotation axes
plays an important role, because different axes result in different scaling laws.
DNS of a Turbulent Poiseuille Flow with Uniform Wall Transpiration
V.S. Avsarkisov, M. Oberlack (TU Darmstadt), I. Vigdorovich (Institute of Mechanics, Moscow
State University), G. Khujadze (TU Darmstadt) Schedule
A fully developed, plane constant-mass-flux turbulent Poiseuille flow with wall transpiration
i.e. uniform blowing and suction on the walls is investigated by the direct numerical simulation
(DNS) of the three-dimensional, incompressible Navier-Stokes equations. The DNS is conducted
at Reτ = 250, 480 for different relative transpiration velocities by means of the numerical code
developed by School of Aeronautics, Technical University of Madrid [1]. Existance of the uniform
transpiration implies asymmetry of the mean velocity profile and the Reynolds shear stresses [2].
The flow on the blowing side is highly populated with small scale vortical structures, while on the
suction side vortical structures appear rarely and in larger scales. Thus, transverse velocity not
only redistributes, but also produces Reynolds stresses on the blowing side. As a result, viscous
sublayer becomes thiner on the blowing side and log-law region wider.
The DNS data are used to validate a new turbulent logarithmic scaling law derived from Lie
symmetry theory of the infinite dimensional multi-point correlation equation and is principally
different from the classical near-wall log-law [3,4]. It is shown that the DNS data agrees with the
new turbulent scaling law over practically the whole cross-section of the channel.
[1] S. Hoyas, J. Jiménez, Scaling of velocity fluctuations in turbulent channels up to Reτ = 2000,
Phys. of Fluids 18 (2006), 011702-1-3.
[2] Y. Sumitani, N. Kasagi, Direct numerical simulations of turbulent transport with uniform
wall injection and suction, AIAA Journal 33(7) (1995), 1220-1228.
[3] M. Oberlack, Symmetrie, Invarianz und Selbstähnlichkeit in der Turbulenz, Habilitation thesis
(2000), RTWH Aachen.
[4] M. Oberlack, A. Rosteck, New statistical symmetries of the multi-point equations and its
importance for turbulent scaling laws, Discrete Contin. Dyn. Syst., Ser. S 3 (2010), 451-
471.
Application of the extended group analysis to the functional formulation of the Burgers
equation
Wacławczyk Marta, Oberlack Martin (TU Darmstadt) Schedule
Description in terms of the characteristic functional is a one of the possible approaches to specify
statistical properties of random fields fluctuating in time or space. The functional calculus has
been introduced in the seminal work of E. Hopf [1] for the phenomenon of turbulence. In statistical
mechanics the system of N particles with positions x1, . . . , xN and velocities u1, . . . , uN can
be described by the probability density function P (x1, . . . , xN, v1, . . . , vN, t). We consider now
the continuum limit (e.g. hydrodynamics) where the number of particles go to infinity and the
elements of the phase space of velocity v1, . . . , vN become a continuous function v(x). In this case
the system is described by the probability density functional P ([v(x)], t). Its Fourier transform in

Section 10: Turbulence and reactive flows 221
the functional space is called the characteristic functional and will be denoted by Φ([y(x)], t). Multipoint
statistics of any order are computed by taking successive functional derivatives δ/δyα(x)
of Φ evaluated at y = 0
δk �
Φ([y(x)], t)
�
�
� = i
δyα(x1)δyβ(x2) . . . δyγ(xk) �
y=0
k uα(x1, t)uβ(x2, t) . . . uγ(xk, t) (1)
Hence, the characteristic functional fully characterises the random field. The time evolution of
Φ is described by a functional differential equation with functional derivatives. Such general
description is, however, hardly tractable due to missing analytical methods. We believe that the
Lie group analysis extended towards functional differential equations in Oberlack & Wacławczyk
[2] is a step towards development of such methods and may give a chance to treat such type of
functional equations. The analysis is applied to the functional formulation of the Burgers equation
which is often treated as a ”toy model” of the Navier-Stokes equations. We have shown that the
considered functional equation has an infinite set of symmetry transformations. After solving
a hyperbolic equation with the derived infinitesimals invariant solutions for the characteristic
functional of the Burgers equation equations are found. Next, by successive differentiation, cf.
Eq. (1) the multipoint statistics are derived and their physical meaning is discussed.
[1] E. Hopf, Statistical hydromechanics and functional calculus, J. Rational Mech. Anal. 1 (1952),
87 – 123.
[2] M. Oberlack, M. Wacławczyk, On the extension of Lie group analysis to functional differential
equations, Arch. Mech. 58 (2006), 597 – 618.
Length scale analysis in turbulent Poiseuille flow
Fettah Aldudak, Martin Oberlack (TU Darmstadt) Schedule
Geometrical structures in wall-bounded turbulent flow are investigated by means of dissipation
element (DE) and streamline segment (SLS) analysis. The scalar fields obtained by Direct Numerical
Simulations (DNS) for the turbulent channel flow are decomposed into numerous finite
size regions using the DE method proposed by [1]. Therefore, local pairs of minimal and maximal
points in the scalar field φ(x, y, z, t) are detected where ∇φ = 0. Gradient trajectories of finite
length starting from every point in the scalar field in the directions of ascending and descending
scalar gradients will reach a minimum and a maximum point with ∇φ = 0. All points belonging
to the same pair of extremal points defines a DE. Hence, the decomposition of the domain into
DEs follows from the structures of the flow itself and is completely space filling the turbulent
field.
The linear distance ℓD between the extremal points and the absolute value of the scalar
difference ∆φ at these two points mark the key parameters to parameterize the geometry and the
field variable structure of the DE. We find that the mean DE length is in the order of the Taylor
scale supporting the results in [1] for the case of homogeneous shear turbulence. In addition, DE
length scale reveals a clear dependency on wall-normal distance y.
Streamline segment analysis is another way to classify spatial structures in turbulent fields.
Here, extremal points of the velocity magnitude along streamlines are identified marking the
beginning and ending points of the respective segment. Dependent on the gradient of the velocity
magnitude, SLS are classified as positive or negative segments. We, again, investigate the length
ℓS of these structures in a turbulent channel flow as a function of distance from the wall y. In

222 Section 10: Turbulence and reactive flows
this context, a strong wall-normal dependency is found. Positive segments appear to be larger in
average.
Furthermore, we examine the probability density function (pdf ) P of both length scales in
different wall-normal regions. Large differences between the curves are observed. However, after
normalizing the pdf with the corresponding mean length, the curves coincide with each other
except for the near-wall layer. This behavior is a strong indication toward a Lie scaling group and
its corresponding similarity -revealing a self-similar behavior with respect to the wall distance.
[1] N. Peters, L. Wang, Dissipation element analysis of scalar fields in turbulence, C. R. Mech.
334 (2006), 433-506.
S10.3: Turbulent flows: measurements and simulations Wed, 13:30–15:30
Chair: R. Farwig, S. Braun S1|01–A02
Investigation of structure and non-gradient turbulent transfer in swirling flows
Ðorđe Čantrak (University of Belgrade), Martin Gabi (KIT), Novica Janković, Svetislav Čantrak
(University of Belgrade) Schedule
Non-gradient turbulent diffusion and non-local turbulent transfer are significant characteristics
of turbulent swirling flows. Turbulence structure is being investigated in this paper, on the basis
of experimental and theoretical numerical results. Investigation of the structure and mechanics
of turbulent transport processes is difficult because the turbulent swirling flows are threedimensional,
inhomogeneous and anisotropic flows with shear. Contemporary optical measuring
techniques laser Doppler anemometry (LDA) and stereo particle image velocimetry (PIV) are
applied. Analysis proves that the presence of swirl has, as a consequence, non-local turbulent
transfer, what should be modeled adequately. Experimentally determined distributions of correlation
and statistical moments of the second and higher order give closer insight into physics of
turbulence, which results in better modeling of very complex transport processes in turbulent
swirling flow in a pipe. Investigation of the structure and statistical properties in the vortex core
and shear layer in turbulent swirling flow is of special significance. This gives closer insight into
the physics of turbulent transfer processes in internal swirling flows.
Flow over back-facing step in a narrow channel
Václav Uruba, Ondřej Hladík, Pavel Joná (Czech Academy of Sciences) Schedule
Flow structure behind the back-facing step in a narrow channel will be studied in details. The
step height will be about 15 percent of the channel width. The contra-rotating secondary vortices
in corners of the input channel detach on the step edge and interact together forming impinging
structure on the channel floor behind the step. The vortices behavior will be observed using stereo
PIV technique. Time-mean 3D structures behind the step are to be evaluated and shown in the
paper.
Hot-wire measurement in turbulent flow behind a parallel-line heat source
Pavel Antos, Vaclav Uruba (Czech Academy of Sciences) Schedule
A paper describes used HWA method of measurement in non-isothermal flow. A dual hot-wire
probe was employed. Velocity and temperature calibration including static and dynamic part are
described were done. Procedure of evaluation observed quantities is described in detail. An interaction
of the free turbulent flow and the temperature field generated by parallel line heat sources
was investigated. The velocity and the temperature distributions behind the heat generator are

Section 10: Turbulence and reactive flows 223
presented in the paper.
Crude estimate of velocity distributions from Truckenbrodt’s energy and momentum
coefficients
Herbert Niessner (NiMa Baden-Rütihof/Switzerland) Schedule
One of the simplest models for the velocity distribution in a pipe cross-section dependent on two
parameters consists of two layers of different thickness and velocity. Unfortunately relative thickness
and velocity of the wall layer cannot be expressed analytically in terms of Truckenbrodt’s
energy and momentum coefficents. But relative thicknesses of a three layer model with wall and
intermediate layer having opposite core and zero velocity can be. Reasonable in case of strong
reverse wall flow only they allow a crude estimate of the parameters of the two layer model, which
may serve as initial values in computing them iteratively.
Coarse-Grid-CFD (CGCFD) using a Porous-Media formulation
A. G. Class, M. Viellieber (KIT) Schedule
Computational fluid dynamics (CFD) simulations for large complex geometries like the complete
reactor core of a nuclear power plant requires exceedingly huge computational resources. State
of the art computational power and CFD software is restricted to simulations of representative
sections of these geometries.
The conventional approach to simulate such complex geometries is 1D subchannel analysis
employing experimental correlations in the transport models. The development of the CGCFD
(1,2) provides an alternative method to the traditional 1D subchannel analysis and does not rely
on experimental data.
The CGCFD is based on strongly under-resolved CFD and inviscid Euler equations. Although
the use of the Euler equations and coarse grids does not capture the subgrid physics, i.e. viscous
dissipation or turbulence, the subgrid physical information is taken into account by volumetric
source terms derived from fully resolved representative CFD simulations. Non-resolved geometrical
information in the very coarse meshes is taken into account by appropriate volume and surface
porosities in the finite volume scheme. Such a porous media approach was originally used in the
COMMIX (3) code which was designed to compute complex flow applications in a time when
computational resources where limited.
The benefits and limitations of our technique are explored by simulating a section of a water
rod bundle containing a spacer. General recommendations for the proper application of our
technique are presented in this work.
[1] A. G. Class, M. O. Viellieber, A. Batta: Coarse-Grid-CFD for pressure loss evaluations in rod
bundles, International Congress of Advances in Nuclear Power Plants(ICAPP) 2011, Nizza
[2] S. R. Himmel: Modellierung des Strömungsverhaltens in einem HPLWR-Brennelement mit
Drahtwendelabstandshaltern, Dissertation Forschungszentrum Karlsruhe 2009
[3] T. H. Chien, H. M. Domanus, W. T. Sha: A Three-Dimensional Transient Multicomponent
Computer Program for Analyzing Performance of Power Plant Condensers Volume I: Equations
and Numerics, Argonne National Laboratory 1993
S10.4: Methodical aspects of turbulent flow computations Wed, 16:00–18:00
Chair: S. Braun, R. Farwig S1|01–A02

224 Section 10: Turbulence and reactive flows
Simulation of bubbly flow in a vertical turbulent channel
Claudio Santarelli, Jochen Fröhlich (TU Dresden) Schedule
Direct numerical simulations are performed to investigate the influence of bubble size and void
fraction on turbulent channel flow. An immersed boundary method is employed to simulate the
dispersed phase in an in-house finite-volume-based code, where each bubble is represented by Lagrangian
marker points on its surface connected to the Eulerian description of the fluid via suitable
interpolation algorithms and continuous direct forcing. The turbulent flow between two parallel
walls at distance H is directed upwards and three different bubble loadings have been simulated:
Sim.1: few small bubbles (Dp/H = 0.52, Np = 384, ɛ = 0.28%; being Dp the bubble diameter and
Np the number of bubbles); Sim.2: many small bubbles (Dp/H = 0.52, Np = 2880, ɛ = 2.2%);
Sim.3: many large bubbles (Dp/H = 0.75, Np = 913, ɛ = 2.2%). As expected, small bubbles are
more likely to be found near the wall and show almost no influence on the mean velocity of the
fluid. Large bubbles, with higher bubble Reynolds number, tend to accumulate in the center of the
channel, strongly modifying the mean velocity of the fluid, with the lateral migration of bubbles
apparently related to the bubble wake. Two-point correlations and flow visualizations show the
formation of flow structures and the influence of the bubbles on the generation of turbulence.
Statistical data for both, the liquid and the dispersed phase will be provided, including mean
velocity profiles, turbulent fluctuations and void fraction distributions.
Simulation of bed load transport in turbulent open channel flow
Bernhard Vowinckel, Jochen Fröhlich (TU Dresden) Schedule
In the present work direct numerical simulations of a particle laden open channel flow were carried
out to investigate the interaction between the dispersed and the continuous phase. The dispersed
phase is represented by an immersed boundary method. The particle-particle collisions are
accounted for by a physically based collision model that guarantees a fully resolved four-way
coupling of the flow [1]. Applying theses models, the fully turbulent open channel flow laden
with spherical particles over a rough bed is simulated choosing different particle densities. Two
cases, one with shear stress below the threshold of mobilization and the other with shear stress
above the threshold are compared (Dp/H = 1/10, Np = 2000, ɛ = 0.12, Dp being the particle
diameter, Np number of particles, H the depth of the fluid layer, and ɛ the volume fraction). The
different density ratios lead to different types of modification of the flow field by the formation of
density-specific patterns of the particle. Light particles do not come to resting positions saltating
evenly distributed in span-wise direction. Heavy particles tend to form stream-wise clusters of
inactive particles, that generate large scale flow structures. As a result different mechanisms of
transport occur. These mechanisms will be analyzed by means of particle statistics of both, rotation
and translation, that have not appeared in literature so far. Two-point correlations suggest
an alteration of the coherent structures.
[1] T. Kempe and J. Fröhlich. On Euler-Lagrange coupling and collision modelling for spherical
particles. ETMM8, p. 806-811, Marseille, France, 2010.
Numerical simulation separation in the hydrocyclones of nonspherical particles
Matvienko Oleg, Andropova Antonina (Tomsk State University of Architecture and Building)
Schedule
Hydrocyclones are used extensively for particle separation and classification in mineral, powderprocessing,
environmental and chemical engineering.
This paper presents the results of the mathematical modelling separation in the hydrocyclone
of the nonspherical particles. The turbulent Reynolds equations were used for description of the

Section 10: Turbulence and reactive flows 225
flow fields. The turbulence characteristics were calculated on the basis of two-equation k - ɛ model
with a Richardson number Ri correction to the dissipation equation. The parameters of the flow
depends on the solid concentration and the density and viscosity of the slurry. It is assumed that
concentrated suspension influence fluid velocities via density and viscosity. In order to account
the influence of particle concentration on the viscosity the Thomas expression was used. When
calculating trajectories of nonspherical particles, both translational and rotational motions should
be simultaneously considered, since these motions are coupled. The orientation distribution of
nonspherical particles in flows is an important factor affecting the cumulative transport properties
of the fluidparticle system. Spheroidal particles are chosen for the investigation of the effect of
nonsphericity on particle hydrodynamic interactions and trajectories, since the force and torque
acting on a stationary spheroid in creeping flows are well known for uniform flow, simple shear flow
and for an arbitrary oriented spheroid adjacent to a planar wall. A typical hydrocyclone consists
of a cylindrical section with a central tube connected to a conical section with a discharge tube.
An inlet tube is attached to the top section of the cylinder. The fluid being injected tangentially
into hydrocyclone causes swirling and thus generates centrifugal force within the device. This
centrifugal force field brings about a rapid classification of particulate material from the medium in
which it is suspended. Separation takes place in the radial direction, with coarse particles moving
towards the wall and fines towards the axis. Coarse particles leave through the underflow, and
fines through the overflow. The calculations of the cut size in several hydrocyclone geometries and
also particles trajectories are calculated for both inertial and inertialess particles, the orientation
of which is fixed or free. Lateral drift was found to occur for inertial particles with both fixed and
free orientations. The results demonstrate that separation characteristics of the hydrocyclone are
strongly depends on the flow shear rate, particle size, and particle shape. For a particle with a
fixed orientation the transverse motion also strongly depends on the particle orientation.
This research has been supported by the Alexander von Humboldt
Dynamic Mode Decomposition (DMD) for Swirling Jet Flows
Tobias Luginsland, Leonhard Kleiser (ETH Zürich) Schedule
Swirling jets undergoing vortex breakdown occur in many technical applications, e.g. vortex burners,
turbines and jet engines. At the stage of vortex breakdown the flow is dominated by a conical
shear layer and a large recirculation zone around the jet axis.
We performed Large-Eddy Simulations (LES) of compressible swirling jet flows at Re=5000,
Ma=0.6 in the moderate to high swirl number regime (S=0.5 and 1.0). A nozzle is included in
our computational setup to account for more realistic inflow conditions.
The obtained velocity fields are analyzed by means of temporal and spatial dynamic mode decomposition
(DMD) to get further insight into the characteristic structures dominating the flow.
We present eigenvalue spectra for the different cases and discuss the stability behaviour in time
and space. While the flows are temporarily stable, which is expected for quasi-steady flows after
transition, unstable structures are found in the spatial investigation. For both moderate and high
swirl numbers helical structures dominate the flow together with shear-layer instabilities.
Implementation of low-Reynolds turbulence models in boundary element fluid dynamics
algorithm
Janez Lupse, Leopold Skerget, Jure Ravnik (University of Maribor) Schedule
The article presents an implementation and testing of low-Reynolds RANS type turbulence models
in boundary element fluid dynamics code. The governing equations are cast in velocity-vorticity
form and are used to solve incompressible viscid fluid flow. In this form governing equations are
given for kinematic and kinetic aspect of flow instead of mass and momentum conservation equa-

226 Section 10: Turbulence and reactive flows
tions. Kinematics equations represent compatibility and restriction conditions between velocity
and vorticity field functions and local expansion fields while kinetics equations represent transport
of vorticity. For application of turbulence model, stress tensor has to be rewritten in such a way
that an appropriate form for application of boundary elements is obtained. For weighting functions
of governing equations integral representation Laplace and convective-diffusive fundamental
solutions were used.
Solution algorithm solves kinematics equation for unknown boundary vorticity values first,
using single domain boundary element numerical method. In all of the steps following sub-domain
technique is used to solve equations for unknown domain variables, e.g. velocity, vorticity, temperature...
Sub-domain technique in our case yields overdetermined system of equations which is
solved by LSQR type solver. When unknown boundary vorticity values are known calculation of
intermediate velocity field is possible. Next values of velocity field and boundary values of vorticity
are used to solve vorticity transport equation. For turbulent flows last step is calculation of
unknown turbulence variables from intermediate velocity and vorticity fields. Two representative
benchmark problems (channel flow and backward facing step) are used to assess the performance
of presented algorythm.

Section 11: Interfacial flows 227
Section 11: Interfacial flows
Organizers: Dieter Bothe (TU Darmstadt), Bernhard Weigand (Universität Stuttgart)
S11.1: Nucleation and Phase Transfer Tue, 13:30–15:30
Chair: Claus-Dieter Munz S1|03–123
Numerical Investigations on Nucleation Processes in Supercooled Droplets
K. Eisenschmidt (Universität Stuttgart), T. Němec (Czech Academy of Sciences Prague), P. Rauschenberger,
B. Weigand (Universität Stuttgart) Schedule
We intend to numerically investigate the behaviour of droplets in supercooled clouds regarding
freezing. These processes are of critical relevance for clouding.
The numerical code for the simulations is the in-house code Free Surface 3D (FS3D), which is a
solver for Direct Numerical Simulations (DNS) of incompressible multiphase flows. As a prerequisite
for the numerical investigations on freezing the treatment of three phases as ice, liquid water
and air has already been implemented.
In the present paper we focus on the simulation of nucleation and growth of the nuclei.
Nucleation in an undercooled droplet starts if water molecules form a cluster of critical size. The
nuclei that are formed in that way will grow and the whole droplet begins to freeze. The freezing
of the droplet is described on a macroscopic scale while the nucleation starts with few hundreds of
molecules and therefore takes place at a microscopic scale. The nucleation model that is currently
implemented in FS3D works as a subscale model and links the microscopic view to the macroscopic
description. The results will be shown in the presentation.
The nucleation model is based on the Classical Nucleation Theory (CNT) approach. It predicts
the ice nucleation rate J in supercooled water as a function of temperature. The nucleation rate
J can be evaluated in each cell of the computational domain that is placed inside the undercooled
droplet. From these nucleation rates J the number N of nuclei can be calculated as an integral
value from the whole volume of the droplet V
∆N
∆t =
�
JdV . (1)
The nuclei will grow and the macroscopic freezing starts. The microscopic growth is first calculated
from a subscale model by evaluating the energy equation in the ice and in the water. Once the
ice particle is large enough it could be tracked by the solver.
Parametrization of the homogeneous ice nucleation rate for the numerical simulation
of multiphase flow
Tomáš Němec (Czech Academy of Sciences Prague), Kathrin Eisenschmidt, Philipp Rauschenberger,
Bernhard Weigand (Universität Stuttgart) Schedule
The numerical modelling of the freezing process of supercooled water droplets in the atmosphere
requires a description of the nucleation of ice particles. The thermophysical property of interest
is the nucleation rate J [m −3 s −1 ] describing the number of newly formed particles in the system
per unit volume and unit time.
There are several parametrizations of the experimentally measured ice nucleation rates available
in the literature [1] for the temperatures 230 – 240 K relevant to homogeneous ice nucleation.
There is however an uncertainty of 2 K in the estimation of the temperature in these experiments
which is unsufficient for a precise simulation of atmospheric processes.

228 Section 11: Interfacial flows
In this work, we employed the Classical Nucleation Theory (CNT) approach [2] for the prediction
of the homogeneous ice nucleation rate. The evaluation of the CNT formulas requires
accurate thermophysical data of both supercooled water and ice, i.e. density, vapor-equilibrium
pressure, specific heat capacity, latent heat of melting, and the ice-water interfacial tension. As a
result, the CNT predicts the nucleation rate J, the initial (critical) size of the ice particle r ⋆ , and
the nucleation work W ⋆ needed to create the critical ice particle.
The predicted ice nucleation rates show a good agreement with the experimental data from
several authors. Some other experimental nucleation rates show a slight deviation from the CNT
which might hint that the nucleation process during the experiment was influenced by heterogeneities
or by surface effects. The temperature dependence of the theoretical homogeneous
nucleation rate was fitted to a simple formula applicable to numerical CFD calculations of the
freezing behavior of supercooled water droplets.
[1] B. J. Murray, S. L. Broadley, T. W. Wilson, S. J. Bull, R. H. Wills, H. K. Christenson, and
E. J. Murray. Kinetics of the homogeneous freezing of water. Physical Chemistry Chemical
Physics, 12 (35):10380–10387, 2010.
[2] Dimo Kashchiev. Nucleation - Basic Theory with Applications. Butterworth-Heinemann,
2000.
Volume of fluid based direct numerical simulation of ice growth
P. Rauschenberger, K. Eisenschmidt, B. Weigand (Universität Stuttgart) Schedule
In atmospheric clouds, water droplets may remain liquid down to a temperature of about −40 ◦ C.
When nucleation starts, the initial particle grows and starts to form dendrites when reaching
a certain critical radius. The freezing process of supercooled liquid water droplets in clouds is
of great interest for weather forecast and is still not well understood today. We intend to do
numerical investigations on this subject.
Our in-house code Free Surface 3D (FS3D) is applied for the Direct Numerical Simulation
(DNS) of incompressible multiphase flows and is based on the Volume of Fluid (VOF) method.
The Navier-Stokes equations are spatially discretized on a fixed Eulerian grid. One prerequisite
to perform the abovementioned simulations is the possibility to treat solid particles. This has
already been implemented and validated. The rigid particles are treated as Eulerian ones and
may move freely within the fluid phase. Furthermore, the code is currently extended to treat
more than two phases, since the two phases of water (ice and liquid) and the surrounding gas
phase appear simultaneously.
The energy equation is solved in temperature form. For the phase change problem, we use a
two-scalar representation of the temperature. This approach has already been applied for simulations
of droplet evaporation. Temperature advection and heat conduction are done separately for
the solid and the liquid temperature field (Ts and Tl), but they are coupled at the phase interface
by the energy jump condition
˙m ′′ ∆hs = λs∇T |s · nγ + λl∇T |l · nγ. (1)
This means that in interface cells, three temperatures are present: Ts, Tl and the interface temperature
Tγ, that can be determined with the Gibbs-Thomson relation.
The particle growth and temperature distribution will be validated against known solutions.
The growth of dendrites is subject for further research.

Section 11: Interfacial flows 229
Curvature Driven Liquid-Vapour Flow in Compressible Fluids
Christoph Zeiler (Universität Stuttgart) Schedule
We consider a mathematical model that describes the dynamics of compressible fluids which can
occur in a liquid and a vapour phase. Therein, the phase boundary is represented as a sharp,
shock-like interface. While for hydrodynamical shock waves it suffices to satisfy the homogeneous
Rankine-Hugoniot conditions and to control the sign of the entropy condition, more delicate conditions
characterise phase transitions: algebraic conditions to specify the correct amount of entropy
dissipations and differential conditions like the Young-Laplace law, which take into account curvature
effects. An essential numerical difficulty is the correct treatment of these conditions and
to overcome the difficulties posed by a mixed type model.
In our approach we separate the problem in two scales: with microscale models we treat the
fluid dynamics at phase boundaries and with macroscale models the behaviour in bulk phases.
Both scales are coupled with a ghost fluid approach.
We present a microscale solver based on a generalisation of the classical Riemann problem to
two-phase fluids. The phase transition is modelled as a discontinuous wave and effects of surface
tension are included via the curvature of the phase boundary.
The macroscale domain is divided in time dependent liquid and vapour domains and we use
standard fluid solvers for the single phase areas. More complicated is the correct treatment of the
interface. Detailed informations are present via the microscale solution and will applied here. In
particular we drive the interface with informations of the microscale solution.
Numerical solutions for multi-dimensional test settings display good accordance with the physical
behaviour of bubbles and droplets.
Bubble interaction during boiling process
E.O. Didinska (Oles Honchar Dnipropetrovsk National University) Schedule
Nevertheless a lot of new energetic technologies, boiling remain the most wide-spread and correspondingly
important process for transformation of thermal energy into electricity. Nevertheless
intensive investigation stimulated by importance of boiling study during enough long time, our
understanding of boiling process from the physical point of view and especially in mathematical
modeling is very far from satisfactory. The most complicated among variety of effects concerning
boiling process is, of course, bubble growth on a heater surface. There exist several physical and
correspondingly mathematical models of the last process; however neither boiling crises, nor separation
of bubble can be properly calculated in any model. We propose to develop a series of
extremely simplified mathematical models, every of which describes one separate specific feature
of boiling process. In particular, thermal interaction of bubbles growing on the heater surface is
main object of the present work. Mathematical model of slow phase transition and homothetic
growth are applied to the considered problems. Asymptotic model of slow phase transition gives
an opportunity to replace initial parabolic problem by series of elliptic boundary-value problems.
Consideration in the present work is restricted by zeroth and first approximations. BEM is used
for numerical calculation of temperature field on each time step. The proposed approach is illustrated
by several examples of numerical calculation.
Observation of mass transfer of selected organic substances in supercritical carbon
dioxide by means of shearing interferometer
Miao Hu, Rainer Benning, Özgür Ertunc, Antonio Delgado (Universität Erlangen-Nürnberg)
Schedule
The research interests lie in a deeper understanding of the mechanism of organic solutes diffusing
into the near- and supercritical state of a solvent, which counts as the most basic means of mass

230 Section 11: Interfacial flows
transfer in the process engineering industry, especially in extraction and particle handling processes.
Supercritical carbon dioxide, with a relatively low critical pressure and temperature, and
of being non-toxic is one of the most popular alternatives to the traditional organic solvents, as
well known in coffee and tea decaffeination, pharmaceutical separation, etc. With the increasing
awareness of environmental aspects, its promising potential is showing in more and more areas,
e.g. surface cleaning, etc. One reason for the limitations of commercial applications in industrial
scales is the disadvantage that the procedures in supercritical fluids related processes are basically
experience-based and fundamental knowledge of their thermodynamic behaviors are still to be
gained in order to achieve a better control of the process as well as to optimize the system [1].
Special attention was paid to the direct visualization of the diffusion process of oil droplets in
supercritical carbon dioxide as well as the quantitative analysis of the process by evaluating the
important parameter-diffusion coefficients, which were experimentally obtained with a shearing
interferometer. Considering the fact that diffusion is always accompanied by undesirable densitydriven
convection on earth, it is meaningful to carry out the experiments also under microgravity,
where the density variations causing the convection are largely reduced and a steady diffusion
process can be observed. Two parabolic flight campaigns were carried out to perform the experiments
under Microgravity (March 2010, 15th German Aerospace Agency (DLR) and May 2011,
54th European Space Agency (ESA)-parabolic flight campaign). The project was funded by DLR
under grant No. 50WM0840.
[1] Y. Arai, T. Sako, Y. Takabayashi, Supercritical Fluids, Molecular Interactions, Physical
Properties and New Applications (Eds.) Springer-Verlag, Berlin und Heidelberg (2002).
S11.2: Two-Phase Flow Numerics Tue, 16:00–18:00
Chair: Axel Voigt S1|03–123
Surface fluids - a finite element approach
Axel Voigt (TU Dresden) Schedule
A two-phase Newtonian surface fluid is modeled as a surface Cahn-Hilliard-Navier-Stokes equation
using a stream function formulation. This allows to circumvent the subleties in describing vectorial
second-order partial differential equations on curved surfaces and allows for an efficient numerical
treatment using parametric finite elements. The approach is validated for various test cases,
including a vortex-trapping surface demonstrating the strong interplay of the surface morphology
and the flow. Finally the approach is applied to a Rayleigh-Taylor instability and coarsening
scenarios on various surfaces.
Modeling the surface tension force using Discontinuous Galerkin FEM
N. Emamy, R. Mousavi, F. Kummer, M. Oberlack (TU Darmstadt) Schedule
In this study incompressible multiphase flow including the surface tension on the phase interface
is considered. Governing equations are the Navier-Stokes and continuity equations based on the
one-fluid approach. The interface is represented as the zero iso-value of the level set function φ.
To maintain the signed distance property of the level set function a re-initialization equation is
solved. The surface tension force is modeled using the continuum surface force (CSF) model [1]
in the form
�FS = σδ(φ)κ�n, (1)

Section 11: Interfacial flows 231
where σ is the fluid surface tension, δ dirac delta function, κ surface curvature and �n is normal
vector to the interface. The mentioned equations are solved using BoSSS [2] libraries, a general
framework for solving conservation laws with the discontinuous Galerkin Finite Element method
(DG-FEM). The surface tension term is calculated by using high degree polynomials for a precise
calculation of the normal vector and curvature. As a numerical test case a stationary droplet with
a surface tension induced inside to outside pressure difference is considered. Numerical results for
the normal vector and curvature are in good agreement with analytic values.
[1] J. U. Brackbill, D. B. Kothe, C. Zemach, A continuum method for modeling surface tension,
J. Comput. Phys., 100, 335–354, 1992.
[2] F. Kummer, The BoSSS Discontinuous Galerkin solver for incompressible fluid dynamics
and an extension to singular equations, 2011, PhD dissertation, Darmstadt University of
Technology.
Numerical integration and interface resolution for extended Discontinuous Galerkin
Methods
Björn Müller, Martin Oberlack (TU Darmstadt) Schedule
For the simulation of multi-phase flows consisting of compressible fluids separated by a sharp
interface, the classical Ghost Fluid Method [1] is widely-used. Even though it has originally been
described in the context of Finite Difference schemes, an extension to the Discontinuous Galerkin
Method (DGM) is straightforward [2]. This approach does not, however, exploit the full potential
offered by the DGM since the available sub-cell information in interface-cells is essentially lost.
We thus propose a new method for the treatment of the interface which is able to retain this
information.
Our method employs a high order DGM for the advection of the level set function Φ that
defines the interface I via the relation I = {�x ∈ Ω|Φ = 0}. This function can be used to enrich
the polynomial basis in all cells with points in I. By means of such an extended Discontinuous
Galerkin scheme, we gain an interface-conforming, piecewise polynomial representation of the
solution without the need for re-meshing.
Two main issues have to be resolved in order to make this approach practicable. First, we
need a fast and accurate method to integrate over the curved sub-volumes without knowing I
explicitly. We compared existing techniques based on the regularization of discontinuous/singular
integrands [3] to methods based on adaptive subdivisions of the cell. Second, the degrees of
freedom associated with the local enrichments have to be resolved. Here, we will discuss the
advantages and disadvantages of methods based on the direct enforcement of jump conditions,
cell splitting/merging [4] and the GFM [2].
[1] R. P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to
interfaces in multimaterial flows (the Ghost Fluid Method), J. Comput. Phys. 152 (1999)
[2] J. Qiu, T. Liu, B. C. Khoo, Simulations of compressible two-medium flow by Runge-Kutta
Discontinuous Galerkin Methods with the Ghost Fluid Method, Commun. Comput. Phys.
3 (2008)
[3] A.-K. Tornberg, Multi-dimensional quadrature of singular and discontinuous functions, BIT
42 (2002)

232 Section 11: Interfacial flows
[4] J. Qiu, T. Liu, B. C. Khoo, Runge-Kutta Discontinuous Galerkin Methods for compressible
two-medium flow simulations: One-dimensional case, J. Comput. Phys. 222 (2007)
A Navier-Stokes solver based on a discontinuous Galerkin FEM, coupled with a level
set interface tracker
R. Mousavi, N. Emamy, F. Kummer, M. Oberlack (TU Darmstadt) Schedule
A single fluid approach for modeling the multi-phase flows is followed by solving the multi-phase
form of the Navier-Stokes equation. The surface tension and gravity effects are not considered. A
velocity projection algorithm is applied to solve the the momentum equation accompanying the
continuity equation. A modal discontinuous Galerkin finite element method is used for the spatial
discretization. The density and viscosity distributions are obtained by tracking the interface as
the zero iso-value of a level set function. It is done by solving the level set advection equation.
As the interface is considered with a finite thickness requiring the signed distance property of the
level set function, the level set re-initialization equation is also solved in a pseudo time-stepping
sense. Considering the re-initialization equation as a Hamilton - Jacobi equation, the Hamiltonian
term is numerically approximated using a Godunov’s method. The in-house solver BoSSS is used
for all of the numerical calculations [1].
[1] F. Kummer, The BoSSS Discontinuous Galerkin solver for incompressible fluid dynamics
and an extension to singular equations, 2011, PhD dissertation, Darmstadt University of
Technology
A discontinuous Galerkin based multiscale method for compressible multiphase flow
F. Jaegle, M. Boger, S. Fechter, C.-D. Munz (Universität Stuttgart) Schedule
The numerical simulation of compressible multiphase flow introduces additional difficulties compared
to the incompressible treatment that is often found in two-phase numerical solvers today.
Two elements are crucial: A method that allows to define the geometry and the temporal evolution
of the interface between the two phases (level-set in this study) as well as a numerical strategy
to treat the discontinuous nature of the interface as well as the related physics such as impinging
waves, phase change or surface tension. We use a sharp interface multiscale approach, where the
numerical scheme only resolves the macroscopic scales of the flow and allows discontinuous states
at the interface position, where jump conditions have to be provided by an additional solver
for the micro-scale. Many micro-scale solvers are conceivable, in the present study, we rely on
Riemann-type solvers. The approach is suitable for general EOS.
The macro-scale solver for the bulk phases of the flow uses a discontinuous Galerkin spectral
element method, formulated for hexahedral elements. As no continuity constraint is enforced between
the elements, the flux function at cell boundaries is replaced by a numerical flux. In the bulk
phases, standard Riemann solvers are used. Near the phase interface, the jump in fluid quantities
is assumed to coincide with the nearest element boundary, where the Riemann solver is replaced
by the microscale solver. Instead of evaluating a single numerical flux, the microscale solver provides
discontinuous fluxes, which are applied on the liquid and gaseous side respectively.
The scheme allows high orders of accuracy with subcell resolution, which is particularly valuable
for the calculation of interface curvature that can be obtained from derivation of the ansatz polynomials
for the level-set variable. The model for surface tension is included in the microscale
solution and takes effect in the macroscale via the numerical fluxes, thereby eliminating the need

Section 11: Interfacial flows 233
for source terms to apply the surface force.
Test cases considered include steady and unsteady droplets and bubbles with surface tension and
phase change as well as shock droplet interaction without phase change.
On the coupling of compressible and incompressible flow regions
Markus Boger, Felix Jaegle (Universität Stuttgart), Rupert Klein (FU Berlin), Claus-Dieter Munz
(Universität Stuttgart) Schedule
In many cases, multiphase flows are simulated on the basis of the incompressible Navier-Stokes
equations. This assumption is valid as long as the density changes in the gas phase can be neglected.
Yet, for certain technical applications like fuel injection this is no longer the case and at
least the gaseous phase has to be treated as a compressible fluid.
In the present study, we present two different ways of coupling an incompressible flow region to
a compressible one. Therefore, the one-dimensional Euler equations are used for fully compressible
flows and in the case of their incompressible limit (vanishing Mach number limit). The first
approach is based on the coupling of the thermodynamic pressure in the zero Mach number limit
to the pressure of the compressible flow region. Hence, the primary variable for this iterative
procedure is the pressure. The second coupling procedure only takes into account the effects of
the hydrodynamic pressure. In this case, the iteration is performed with the velocity as primary
variable. In both cases, a half Riemann problem is solved at the interface. It consists of a shock
or expansion wave in the compressible region and a contact discontinuity that represents the
boundary between the compressible and the incompressible region.
The coupling schemes are implemented in a one-dimensional simulation framework using a
discontinuous Galerkin (DG) scheme with a sharp interface ghost-fluid type method for the coupling
at the material interface. While the compressible flow domain is discretized with the DG
scheme, the incompressible subdomain is solved analytically. As an alternative, the interaction
between a compressible and a weakly compressible region can also be analysed using the ghostfluid
approach of the simulation framework. In this case, both flow regions are described by the
compressible Euler equations and incompressibility is approached by increasing the speed of sound
in the weakly compressible region.
Two different test cases are presented to assess the coupling procedures. The first example
describes the pure compression of a liquid region. In the second case, the effects of hydrodynamics
are considered and the liquid region is accelerated due to a pressure gradient. The obtained
results are compared to simulations performed with the ghost fluid type scheme. We achieve a
good agreement between the iterative coupling procedures and the ghost fluid type scheme.
Linearly implicit time discretization for free surface problems
Stephan Weller, Eberhard Bänsch (Universität Erlangen-Nürnberg) Schedule
Time discretization for free surface problems is a widely neglected problem. Many existing approaches
use an explicit decoupling which is only conditionally stable. Only few unconditionally
stable methods are known, and known methods may suffer from too strong numerical dissipativity.
They are also usually of first order only [1]. We are therefore looking for unconditionally
stable, minimally dissipative methods of higher order.
Linearly implicit Runge-Kutta (LIRK) methods are a class of one-step methods that require
the solution of linear systems in each time step of a nonlinear system. They are well suited
for discretized PDEs, e.g. parabolic problems [2]. They have been used successfully to solve the
incompressible Navier-Stokes equations [3]. We suggest an adaption of these methods for free
surface problems and compare different approximations to the Jacobian matrix needed for such
methods.

234 Section 11: Interfacial flows
We compare the approach with existing fully implicit approaches, which require similar solution
techniques but are usually more expensive.
A numerical realization of the method using a moving mesh finite element discretization will
be presented. Extensions to more complex approaches (e.g. interface reconstruction methods like
levelset or volume of fluid) will be discussed.
[1] Bänsch, Eberhard (1998). „Numerical methods for the instationary Navier–Stokes equations
with a free capillary surface“. Habilitationsschrift. Universität Freiburg.
[2] Lubich, Ch. and A. Ostermann (1995). „Linearly implicit time discretization of nonlinear
parabolic equations“. In: IMA Journal Num. Anal. 15(4), pp. 555–583.
[3] Lang, Jens and I. Teleaga (2008). „Higher–order linearly implicit one–step methods for threedimensional
incompressible Navier–Stokes equations“. In: Studia Univ. „Babes–Bolyai“, Mathematica
LIII.1.
S11.3: Computational Fluid Dynamics Wed, 13:30–15:30
Chair: Bernhard Weigand S1|03–123
On Compressible Extension of VOF Method Using Low-Mach Assumptions for Capturing
Near Critical Behavior
Illya Shevchuk, Amsini Sadiki, Johannes Janicka (TU Darmstadt) Schedule
Due to continuous efficiency enhancement of technical combustion systems operating with liquid
fuels in carrier gas environment, such as combustion chambers of aircraft engines and diesel
engines, temperature, pressure or both these state quantities reach the vicinity of critical values
of used liquids or can even exceed them. Understanding and simulative reproduction of droplet
dynamics under these extreme conditions is essential for improvement of technical systems.
The characteristics of the liquid and gas behavior in the vicinity of the critical point have
strong dependence of their properties on temperature and pressure. Thus, assumptions of constant
density, viscosity, heat conductivity etc. typically made in multiphase simulations cannot be made
for these problems. The scope of the endeavor is to create a solver capable to capture major near
critical phenomena for investigation of single droplets and droplet groups.
In this contribution we present an approach to extend the existing incompressible solver from
the OpenFOAM R○ toolbox in order to treat compressible flows and variable material properties.
Focus is first put on low Mach number flows with constant mean pressure but steep temperature
gradients. For that purpose, the governing equations for mass, momentum and enthalpy in conservative
form are considered. Additionally a volume of fluid based method is used to capture the
position of the gas-liquid interface. Thereby severe assumptions are made to reduce the complexity,
e.g. heat production by viscous friction as well as heat transfer by radiation is neglected.
Further, the dependency of fluid properties on pressure is neglected while the dependency on
temperature is taken into account. The governing equations are discretized using finite volume
method on unstructured meshes and solved using segregated solution procedure.
To validate the modified solver, simulations of a natural convection driven single phase cavity
flow characterized by high Rayleigh numbers with perfect gas conditions were carried out and
compared to reference simulations found in literature [1]. Good agreement between the results
achieved and the reference calculations was established with a mean Nusselt number deviation
from the reference solution less than 3% (Nuref = 8.86 vs. Nusim = 8.61). A two-phase test

Section 11: Interfacial flows 235
case (droplet of acetone in nitrogen environment) is being investigated where the thermodynamic
droplet properties are described by Peng-Robinson equation of state. Preliminary results will be
included in the final version.
[1] P. Le Quéré et al., Modelling of natural convection flows with large temperature differences:
a benchmark problem for low Mach number solvers. Part 1. Reference Solutions, ESAIM:
M2AN 39 (2005), 609 – 616.
The Extended Discontinuous Galerkin discretization of singular equations.
Florian Kummer (TU Darmstadt) Schedule
In multiphase flow problems, the solutions for velocity and pressure usually contain jumps
and kinks. Indeed, for material interfaces, the introduction of surface tension models will induce a
jump in the pressure field, while the velocity field will contain a kink. Solutions for non-material
interfaces contain jumps in velocity and pressure field, even without any surface tension models.
Since the derivatives of these – discontinuous – solutions are singular, i.e. Delta - distributions,
we call the partial differential equations “singular”.
For the computational domain Ω ⊂ R D the disjoint decomposition Ω = A ∪ I ∪ B is given,
where I is an (D − 1) - dimensional interface that separates the phases A and B. On I, for
some property u that is discontinuous at the interface, one defines the jump operator [u] as the
difference between the value of u on B- and A - side. Given that, a discontinuous problem is e.g.
the Poisson equation ⎧ ⎨
⎩
div(ν∇u) = f in Ω \ I
[α1 u] = g1, [α2 ∇u · �n] = g2 on I
Dirichlet or Neumann b.c. on ∂Ω
Note that g1, g2, α1 and α2 are assumed to be non-constant and that especially [α1 ] �= 0 and also
[α2 ] �= 0.
The numerical treatment of discontinuities at the interface is considered to be challenging;
basically two options are available: either, the jumps and kinks are regularised (‘smeared out’) or
a special numerical discretisation which is capable of representing jumps and kinks is used. We
will present an Extended Discontinuous Galerkin (XDG) method that is able to represent jumps
mentioned above with sub-cell accuracy. In some “normal” computational cell, some field f(�x) is,
as usually in Discontinuous Galerkin (DG), approximated as a series fh(�x) = �N n=1 φn(�x) · ˜ fn,
where the polynomials φn are called the DG basis. In a “cut” cell K (i.e. I ∩ K �= ∅) these basis
polynomials are multiplied by the characteristic functions χA and χB yielding separate degreesof-freedom
for both phases, i.e.
fh(�x) =
N�
n=1
�
φn(�x) · χA · ˜ fA,n + φn(�x) · χB · ˜ �
fB,n . (2)
The work that is going to be presented will discuss the computation of the additional degrees-offreedom
in the XDG-Ansatz for linear boundary value problems like like the one given above.
Numerical study of a liquid/liquid slug flow in a rectangular microreactor
Ina Dittmar, Peter Ehrhard (TU Dortmund) Schedule
The great advantages of microreactors are associated with an extremely–high surface–to–volume
ratio. Hence, microreactors permit promising operating conditions, such as almost–perfect heat
(1)

236 Section 11: Interfacial flows
or mass transfer. The hydrodynamics of a liquid/liquid slug flow in a rectangular micro–channel
is characterized by a complex vortex structure in both the disperse and the continuous phase.
The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the
continuous phase persist between the disperse phase and the wall. Due to this phenomenon, a
relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding
of these complex phenomena allows for a control of the hydrodynamics, and thus,
to tailor the heat and mass transport in a desired manner. To study the physics of this complex
two–liquid system, a modified level–set method in conjunction with an immersed–boundary formulation
is engaged. Presently, the simulations are time-dependent and fully three-dimensional
in nature. The mesh resolution represents a challenge, as the spatial resolution has to resolve the
thin film between the disperse phase and the wall adequately. Different approaches to solve this
challenge are presented. All simulations are implemented within the software OpenFOAM.
A numerical investigation on the fluid flow at the interface of a porous and a free
flow domain
Timo Reisner, Holger Steeb, Joerg Renner (Universität Bochum) Schedule
Approaches in sediment transport modeling can be roughly subdivided into two categories: 1)
Models based on the theory of mixtures using a macroscopic, volumetrically-coupled two-phase
(fluid and sediment) continuum approach and 2) interface-coupled, i.e. staggered approaches assuming
a rigid boundary at the sediment bed, calculating the shear stresses at the bed surface, in
combination with an algebraic relation to calculate the sediment transport and in the last step,
the change in morphology.
Neither of these approaches takes into account the (Darcy / Brinkman) flow inside the sediment
bed and how the different physics of the flow patterns influence each other. Hence we have
developed a sediment transport model based on a three-phase mixture, which takes into account
the notion that the porous sediment bed and the mobilized particles (commonly termed bed load)
show distinctly different physical behaviours: The sediment bed can be described as a (more or
less) rigid porous medium, while the mobilized particles exhibit a fluid-like behaviour.
Here, we concentrate on a numerical investigation of the fluid flow at the interface between a
porous medium and a free flow domain using a range of different coupling mechanisms between
the equations governing the free (Navier-Stokes) and the porous medium (Brinkman) flows in
order to examine the interaction mechanisms between both domains. The goal of this study is
to answer the following questions: 1) How is the fluid flow in the porous domain influenced by
the flow in the free flow domain, and, conversely, what is the influence of the porous domain on
the free flow, and 2) Do these effects have a stabilizing or a destabilizing effect, i.e. are there
any forces induced by the interdependence of the flow patterns in the two different domains that
would lead to enhanced sediment erosion or deposition at the interface?
The current implementation is based on the FE-Code Comsol Multiphysics. For the Navier-
Stokes and Brinkman equations, common and widely-used stabilization schemes are applied for
numerical stability. To work out the interfacial effects, we numerically analyse three different geometries
each containing a free flow and a porous domain.
Numerical Study of the Primary Breakup of Plane Liquid Sheet with Co-flowing Air
Streams
K. Suresh Kumar, B. Peters (Universität Luxemburg) Schedule
The disintegration of a plane liquid sheet with co-flowing air streams is studied numerically using
the quasi-DNS/LES-Volume of Fluid (VOF) multiphase flow approach. The liquid-gas interface
is tracked using the interface compression scheme. A one equation eddy viscosity model has been

Section 11: Interfacial flows 237
used to resolve the sub-grid scale stresses, which solves a transport equation for sub-grid scale
kinetic energy. This numerical investigation is focused on demonstrating the capability of quasi-
DNS/LES-VOF approach to predict the highly complex primary breakup phenomena of liquid
sheet interacting with co-flowing air streams. As a first step the plane liquid sheet is modeled
using a two dimensional (2D) approximation. The effect of mesh refinement on the breakup length
and breakup characteristics is studied for the 2D case. Finally a three dimensional simulation of
the plane liquid sheet with co-flowing air streams is performed and results are compared with
published experimental results for breakup length.
Two-Phase Flow in Single-Screw Extruders
Martin Lübke, Olaf Wünsch (Universität Kassel) Schedule
In polymer processing industry extruders are used to perform functions such as melting, conveying
and devolatization. In the process of devolatization the detection of the free-surface is
important due to the fact that the degassing performance depends on the interfacial area. This
study concerns numerical simulation of free-surface flows of highly viscous liquids in single-screw
extruders. The numerical treatment of a partially filled extruder is a challenging task due to the
complex geometry and the large differences in density and viscosity between the two phases, e.g.
polymer melt and air. Furthermore, the rotation of the screw leads to a continuous renewing of
the free-surface. For this purpose an Euler-Euler two-fluid Volume of Fluid Method (VOF) within
the open source framework OpenFOAM is used. First, a simplified two-dimensional model of a
single-screw extruder consisting of a rotating cylindrical barrel and a fixed internal plate is considered.
Different flow phenomena, including the forming of an interface cusp, can be observed.
The resulting flow and the shape of the phase interface are compared against the experiments
by [1]. Good agreement is obtained between the numerical and experimental results. Finally, the
three dimensional flow in a partially filled single-screw extruder with dynamic mesh motion is
presented. In addition the power characteristics of a conveying screw element with varying degree
of filling is discussed.
[1] G. Böhme, G. Pokriefke, A. Müller, Viscous flow phenomena in a partially filled rotor-stator
system, Arch App Mech vol. 75 (2006), 619 – 634.
S11.4: Capillary Flows Wed, 16:00–18:00
Chair: Dieter Bothe S1|03–123
Temperature effects in thin droplets
K. Boettcher, P. Ehrhard (TU Dortmund) Schedule
In this presentation we present the spreading of a thin droplet on a plane solid, which may
be driven by gravity, centrifugal forces, and dynamic wetting. Viscous heating or an imposed
temperature of the solid lead to a inhomogeneous temperature field in the liquid. This may affect
several properties of a liquid, like free surface tension, viscosity or density.
It is well known, that temperature-dependent surface tension leads to Marangoni stresses
and convection cells in the liquid. The role of a temperature-dependent viscosity, though, has
neither been investigated experimentally nor theoretically. Because spreading flows are governed
by a Reynolds number Re ≪ 1, these flows are dominated by friction and the influence of a
temperature-dependent viscosity should be important.
Based on a lubrication approximation for droplets with a small contact angle, the conservation
laws may be transformed in one single evolution equation by using all boundary conditions at

238 Section 11: Interfacial flows
the interfaces. The influence of a temperature field on the velocity field and on the spreading rate
of a thin droplet is investigated. The spreading is modeled by the empiric law of Tanner, which
couples the speed of the contact line with a macroscopic contact angle, observable in experiments.
Direct numerical simulation of thermocapillary two-phase flows using the VOF method
and a 2-scalar approach for heat transfer
Chen Ma, Dieter Bothe (TU Darmstadt) Schedule
The thermal Marangoni effect can be used as an efficient way of enhancing heat and mass transfer
in two phase flows. Due to the complex interaction with different phenomena like instability
or film rupture, a direct numerical simulation of thermocapillary flows with a dynamically deformable
interface is often desired. This contribution presents a method for DNS of the above
mentioned thermocapillary flows. A continuum mechanical sharp interface model for incompressible
two-phase flow is employed containing the two-phase continuity, Navier-Stokes and energy
equations with suitably formulated jump conditions at the phase interface. For the numerical
solution with the finite volumes scheme a one-field formulation of the two-phase model is applied
based on spatial averaging of the equations. A rigorous separation of the different velocities due
to phase change is derived. The fluid interface is captured using an extended Volume of fluid
(VOF) method with additional piecewise linear interface reconstruction (PLIC). For a high accuracy
of the numerical computation of Marangoni forces, which is essential for the simulation
of thermocapillary flow, the modeling of interfacial heat transfer employs a two-scalar ghost-fluid
approach, where the temperatures of the two phases are represented by two sharp temperature
fields, i.e. without averaging. Validation on two-phase heat conduction shows very good results
compared to analytical solution. Two applications in 3D are studied using the 2-scalar approach:
the heat transfer enhencement in a liquid film on structured substrate due to Marangoni effect
as well as the thermocapillary flow in locally heated liquid films. The method shows potential in
simulating realistic thermocapillary flows with a dynamically deformable interface combined with
evaporation.
Integral analysis of the flow dynamics and mass transfer in a wavy liquid film on a
spinning disk
Doris Prieling, Helfried Steiner, Günter Brenn (TU Graz) Schedule
Wet chemical etching of silicon wafers is an important process in the semiconductor device fabrication.
The aqueous etchant is supplied through a vertical jet impinging onto the rotating
wafer. Driven by centrifugal forces, a thin liquid film is formed, which exhibits non-linear surface
waves. The etching process is mainly controlled by the convection dominated mass transfer of
the primary etchant component from the bulk liquid to the wafer surface. The combination of a
thin boundary layer with steep concentration gradients and the strong disparity between the two
governing length scales leads to excessively high computational costs of a fully resolved numerical
simulation of the flow, especially in the wavy region. The present work applies a thin film approximation
combined with the von Kármán-Pohlhausen method as a computationally efficient
alternative approach for the description of the flow. This integral method was successfully used
by Matar et al. [1] to analyze the gas absorption into a thin film flow on a spinning disk. The
purpose of the present work is to analyze in particular the effect of the surface waves on the mass
transfer characteristics from the liquid into the disk wall. The obtained results reproduce very
well the etching behavior observed in experiments reported by Staudegger et al. [2]. In the waveless,
radially inner region, the etching activity is determined by the growth of the concentration
boundary layer. Radially further downstream, irregular large amplitude waves accompanied by

Section 11: Interfacial flows 239
capillary ripples, distort the surface. In the troughs of the waves the etching rate is controlled by
the decrease of the film height and the abundance of etchant component in the bulk liquid. In the
regions around the wave crests the etching rate is controlled by the thickness of the concentration
boundary layer. The observed enhancement of the mass transfer in the wavy region can be mainly
attributed to the local thinning of the film. The analysis of the results makes it evident that the
integral method is capable to describe the mass transfer towards the wall realistically, also in a
film regime with a highly irregular surface.
[1] O. K. Matar, C. J. Lawrence, G. M. Sisoev, The flow of thin liquid films over spinning disks:
Hydrodynamics and mass transfer, Phys. Fluids 17 (2005), 052102
[2] F. Staudegger, M. W. Hofbaur, and H.-J. Kruwinus, Analyses and modeling of a wet-chemicaletch
process on rotating silicon wafers with an impinging etchant jet, J. Electrochem. Soc.
156 (2009), 340–345
Capillary transport between perforated plates under microgravity
Diana Gaulke, Michael E. Dreyer (Universität Bremen) Schedule
Propellant management devices are used to supply thrusters with gas free propellant. Therefore,
these devices have to be able to store a minimal amount of propellant during the ballistic phase.
This amount has to be sufficient for the chill down phase and the pre-acceleration for settling the
liquid in the tank. Normally, propellant acquisition takes place by means of capillary forces. This
includes modules for leading and holding the liquid.
In the thrusting phase these modules have a negative influence. They induce a higher pressure
loss in the propellant feeding system. Some parts are made out of perforated plates to reduce this
pressure loss. Such perforations influence the capillary transport and change the flow pattern.
In this talk, the application of perforated plates to propellant management devices is introduced.
An experimental study is presented to understand the influence of the perforations. Capillary
transport between parallel plates is analyzed and influence of certain macroscopic properties of
perforations is presented.
Stability limits of unsteady capillary channel flow: experiments on the International
Space Station (ISS)
P.M.Bronowicki, A.Grah, P.Canfield, M.Dreyer (Universität Bremen) Schedule
The main subjects of this work are numerical and experimental studies on capillary channel flow
in a compensated gravitational environment. Capillary forces are used in fluid management systems
to acquire the liquid and preserve a continuous, bubble- free path between two variable
points e.g., in surface tension tanks between fuel pool and outlet to the thruster.
The capillary channels considered in this work consist of glass plates with several geometric
configurations i.e., parallel plates, groove and wedge. For every configuration at least one channel
side remains open what results in a creation of the free surface between the liquid phase and the
ambient gas phase. The maximal flow rate is achieved when the pressure difference between the
liquid and gas phase is no longer balanced by the curvature of the free surface and the free surface
collapses. This leads to gas ingestion into the flow path, a phenomenon known as choking, which
may cause technical disadvantages. The critical flow rate depends on the channel geometry, the
liquid properties and the flow regime.
Prior to the experiments on the ISS, extensive research on capillary channel flows was performed.
One-dimensional and three-dimensional models were developed to study the unsteady
flow behavior. The one-dimensional model is based on the unsteady Bernoulli and the continuity

240 Section 11: Interfacial flows
equations. Critical steady flow rates were accurately predicted with one- and three-dimensional
computations. A theory for steady and transient surface stability was developed. A transient
stability constant, influenced by the system feedback effect, is observed and explained.
In 2011, series of experiments were performed on board of International Space Station to
study the capillary channel flows and verify the stability theory for steady and transient flows.
The experiment was controlled via telecommands from a Ground Station in Bremen (Germany).
Different geometric configurations and flow regimes were investigated. References: Grah et al.,
Phys. Fluids 22 (2010) Rosendahl et al., Phys. Fluids 22 (2010) Grah et al., J. Fluid Mech. 600,
271289 (2008) Rosendahl et al.,J. Fluid Mech. 518, 187214 (2004)
Stability limits of two-phase open capillary channel flow in a wedge
Peter Canfield, Michael Dreyer, Max Bronowicki (Universität Bremen) Schedule
Previous studies have shown that surface stability in steady open capillary channel flow is defined
by the flow rate, the physical properties of the liquid, and the geometrical properties of the
channel [1, 2]. Surface stability is a limiting factor in fluid management devices that use capillary
channels to position and transport liquid. Experiments have shown that once a critical flow
rate is reached the free surface of a capillary channel flow collapses and gas is ingested into
the channel. This phenomenon is called ‘choking’. In an operational scenario, inclusion of gas
bubbles in the liquid flow may be detrimental to the device that the liquid is being provided
to. A complete understanding of the underlying physics of this phenomenon will help improve
current mathematical models that are used to determine maximum flow rates for a given setup. In
turn, these models may be used to improve designs for fluid management devices that implement
capillary channel flow, e.g. propellant management devices that are used in space vehicles.
In 2011, experiments were conducted onboard the ISS in cooperation with Portland State
University and NASA to determine critical flow rates of single-phase and two-phase flow within
an open capillary channel with a triangular cross-section. The results of the experiments are
compared with the predictions that were determined numerically using a one-dimensional model
that incorporates the determining factors of the phenomenon or using a three-dimensional CFD
model based on VOF methods.
[1] U. Rosendahl, A. Ohlhoff, M. E. Dreyer, and H. J. Rath, Investigation of Forced Liquid Flows
in Open Capillary Channels Microgravity Sci. Technol. 13 (2002), 53 – 59
[2] Aleksander Grah, Dennis Haake, Uwe Rosendahl, Joerg Klatte, and Michael Dreyer Stability
limits of unsteady open capillary channel flow. J. Fluid Mech. 600 (2008), 271 – 289
S11.5: Complex Interfaces and Surface PDEs Thu, 13:30–15:30
Chair: Konrad Boettcher S1|03–123
Modeling the surface tension force using Discontinuous Galerkin FEM
N. Emamy, R. Mousavi, F. Kummer, M. Oberlack (TU Darmstadt) Schedule
In this study incompressible multiphase flow including the surface tension on the phase interface
is considered. Governing equations are the Navier-Stokes and continuity equations based on the
one-fluid approach. The interface is represented as the zero iso-value of the level set function φ.
To maintain the signed distance property of the level set function a re-initialization equation is
solved. The surface tension force is modeled using the continuum surface force (CSF) model [1]

Section 11: Interfacial flows 241
in the form
�FS = σδ(φ)κ�n, (1)
where σ is the fluid surface tension, δ dirac delta function, κ surface curvature and �n is normal
vector to the interface. The mentioned equations are solved using BoSSS [2] libraries, a general
framework for solving conservation laws with the discontinuous Galerkin Finite Element method
(DG-FEM). The surface tension term is calculated by using high degree polynomials for a precise
calculation of the normal vector and curvature. As a numerical test case a stationary droplet with
a surface tension induced inside to outside pressure difference is considered. Numerical results for
the normal vector and curvature are in good agreement with analytic values.
[1] J. U. Brackbill, D. B. Kothe, C. Zemach, A continuum method for modeling surface tension,
J. Comput. Phys., 100, 335–354, 1992.
[2] F. Kummer, The BoSSS Discontinuous Galerkin solver for incompressible fluid dynamics
and an extension to singular equations, 2011, PhD dissertation, Darmstadt University of
Technology.
Surface fluids - a finite element approach
Axel Voigt (TU Dresden) Schedule
A two-phase Newtonian surface fluid is modeled as a surface Cahn-Hilliard-Navier-Stokes equation
using a stream function formulation. This allows to circumvent the subleties in describing vectorial
second-order partial differential equations on curved surfaces and allows for an efficient numerical
treatment using parametric finite elements. The approach is validated for various test cases,
including a vortex-trapping surface demonstrating the strong interplay of the surface morphology
and the flow. Finally the approach is applied to a Rayleigh-Taylor instability and coarsening
scenarios on various surfaces.
Simulation of interfacial convection-diffusion equations by Discontinuous Galerkin
methods and a new conservative formulation
Christina Kallendorf (TU Darmstadt), Alexei F. Cheviakov (University of Saskatchewan), Martin
Oberlack, Yongqi Wang (TU Darmstadt) Schedule
We consider interfacial convection and convection-diffusion equations describing, for instance,
the transport of surfactants in an incompressible two-phase flow. In our setting, the interface
is presented implicitly by a level set formulation and all differential operators intrinsic to the
interface are defined in an extrinsic manner by projection of standard differential operators onto
their tangential components.
Using the direct construction method, infinite families of conservation laws that essentially
involve surfactant concentration are derived in both convection and convection-diffusion settings.
The conserved quantity is a combination of the surfactant concentration and some metric properties
of the local interface geometry. Hence, the system of governing equations, originally consisting
of the surfactant transport, level set and continuity equations, can be rewritten in a fully conserved,
i.e. divergence form. In consequence, the interfacial transport equation may be treated as a
conservation law by the Discontinuous Galerkin method, using a convenient embedding approach
based on the Eulerian grid defined in the three-dimensional domain.
ALE-FEM For Two-Phase Flows With Insoluble Surfactants
Andreas Hahn, Lutz Tobiska (Universität Magdeburg) Schedule

242 Section 11: Interfacial flows
We present a finite element method for the flow of two immiscible incompressible fluids in two
and three dimensions. Thereby the presence of surface active agents (surfactants) on the interface
is allowed, which alter the surface tension.
The model consists of the incompressible Navier-Stokes equations for velocity and pressure and
a convection-diffusion equation on the interface for the distribution of the surfactant. A moving
grid technique is applied to track the interface, on that account a Arbitrary-Lagrangian-Eulerian
(ALE) formulation of the Navier-Stokes equation is used. The surface tension force is incorporated
directly by making use of the Laplace-Beltrami operator technique. Furthermore, we use a finite
element method for the convection-diffusion equation on the moving hyper surface. In order to get
a high accurate method the interface, velocity and pressure are approximated by isoparametric
finite elements.
Iso-surface Computation in 3D using graph-theoretical Approach
Abdulaziz Ali, Dieter Bothe (TU Darmstadt) Schedule
Numerical computations of transport processes and adsorption of surfactants and their mixtures at
fluidic interfaces under dynamic conditions require a connected interface representation. Common
numerical approaches based on the Volume-of-Fluid (VOF) method do not provide connected
interfaces. Hence, we develop a new graph-theoretical method to compute a connected interface
(iso-surface) which can be applied for VOF-based numerical approaches in the context of twophase
and interfacial flow computations.
An iso-surface is a level set of a continuous function whose domain in 3d space is bounded.
Traditionally, the Marching Cubes method [1] is applied for the computation of iso-surfaces where
the domain is triangulated in cuboids. This method is not complete and hence surface connectedness
is not guaranteed, although a first step in this direction is given in [2]. Furthermore,
the usual combinatorical approaches lack information about surface neighbourships and surface
connectedness which are crucial for surface PDE computations.
We introduce a graph-theoretical method for the computation of iso-surface on which surface
PDE and surface integration can be carried on. Our aim is not only the computation of this
iso-surface but also the decomposition of the iso-surface into connected components. The application
of surface PDE and surface integration on each component is possible. The decomposed
components of the iso-surface are connected and oriented. The graph-theoretical method for the
computation of iso-surface enables us to find the complete iso-surface boundaries in each cuboid.
Using the boundary paths, we recover the underlying iso-surface. The appoach also includes a
discrete geometrical curvature computation.
[1] William E. Lorensen and Harvey E. Cline, Marching cubes: a high resolution 3d surface
construction algorithm, Proceedings of the 14th annual conference on Computer graphics
and interactive techniques (New York, NY, USA), SIGGRAPH ’87, ACM, 1987, pp. 163-169.
[2] Jacques-Olivier Lachaud, Topologically defined isosurfaces, IN PROC. 6TH DISCRETE
GEOMETRY FOR COMPUTER IMAGERY, Springer-Verlag, 1996, pp. 245-256.
Direct Numerical Simulation of Multicomponent Surfactant Transport on Fluidic
Interfaces
Kathrin Kissling, Holger Marschall, Dieter Bothe (TU Darmstadt) Schedule
In chemical industry dispersed fluid-fluid systems of immiscible phases are the basis for the synthesis
of various products. The systems are usually prepared by a mixing apparatus but the process

Section 11: Interfacial flows 243
can be substantially improved by adding surfactants, which will change the surface properties and
allow higher dispersion rates. The influence of the surfactants on the surface tension is usually
measured by drop methods, e.g., pendant or sessile drop methods. The present study focusses
on the numerical simulation of these processes and especially on the surfactant transport on the
fluidic interface based on the computational fluid dynamics library OpenFOAM [2] [6].
Crucial features of such simulations are: a sharp interface representation, the capability of
topological changes of the interface and the physically correct solution of the surfactant transport
equations along the interface. To model the area-based surfactant transport on the fluid interface,
the finite-area method of Tukovic and Jasak [5] is applied. The interface is represented by a two
dimensional polygonal computational grid, which deforms according to the surrounding fluid flow.
Large deformations and topological changes are achieved by applying the swapping-edge library
of Menon [4].
The surfactant is present both in the bulk phases and on the fluidic interface. While the surfactants
can be treated as dilute in the bulk, we find high concentrations on the interface.Therefore,
the transport of the surfactants on the fluidic interface is described by coupled species transport
equations and multicomponent diffusion is modeled applying the Maxwell-Stefan equations,
which need to be inverted in order to compute the diffusion fluxes. An iterative inversion method
according to Giovangigli [1] is adapted and implemented in the OpenFOAM library, to lower
the computational effort for systems with multiple surfactants. The resulting diffusive fluxes are
inserted into the species transport equations and the model is completed by the total mass balance
and the momentum equation. Since the transport processes of the surfactants are strongly
coupled, a segregated solution procedure does not lead to physically correct results. Hence, the
equation system is solved applying a block-coupled linear solver, which we adapted to fit the
finite-area method [3]. Since the surface tension is strongly dependent on the concentration of
surfactants, it cannot be treated constant on the interface. Therefore we model the local variation
of the surface tension. Sorption processes are modeled using a multi-region coupling algorithm,
in which different sorption isotherms can be adopted.
We show the application of the developed solver on pending drops and the influence of the
surfactant on the surface tension.
[1] V. Giovangigli, Convergent iterative methods for multicomponent diffusion. IMPACT Comput.
Sci. Eng. 3(2), (1991) 244–276.
[2] H. Jasak, A. Jemcov and Z. Tukovich: A C++ library for complex physics simulations.
In: International Workshop on Coupled Methods in Numerical Dynamics IUC, Dubrovnik,
Croatia, September, (2007) 19-21.
[3] K. Kissling, H. Marschall, D. Bothe: Direct numerical solution of multicomponent surfactant
transport on fluid interfaces. 6th International Berlin Workshop on Transport Phenomena
with Moving Boundaries 24th-25th November 2011, Berlin, Germany (2011).
[4] S. Menon, A Numerical Study of Droplet Formation and Behaviour Using Interface Tracking
Methods. PhD Thesis University of Massachusetts (2011).
[5] Z. Tukovic and H. Jasak, Simulation of Free-Rising Bubble with Soluble Surfactant using
Moving Mesh Finite Volume/Area Method. 6th International Conference on CFD in Oil &
Gas, Metallurgical and Process Industries (2008).
[6] H. G. Weller, G. Tabor, H. Jasak, and C. Fureby. A tensorial approach to computational
continuum mechanics using object orientated techniques. Comput. Phys., 12(6) (1998),
620-631.

244 Section 11: Interfacial flows
Molecular dynamics simulation of lubricated contact between textured surfaces
Oleg Khromov, Wenzhe Shan, Udo Nackenhorst (Universität Hannover) Schedule
The influence of surface texture on the evolution of lubricated contact is quite important. Careful
manufacturing of the contacting surface can lead to its drag reduction with further achievement of
superhydrophobic state. Besides, it changes the macroscopic boundary condition to allow nonzero
slip velocity.
In this contribution a sophisticated 3D molecular dynamic simulation approach is presented
and results for the lubricated contact between textured surfaces will be shown. The contacting
surfaces are assumed to be deformable and the accumulation of worn-out debris is considered.
The lubrication liquid layer is considered to be compressible polyatomic fluid. For studying the
macroscopic behavior of the lubricated surfaces, the friction coefficient has been interpolated
and investigated under the influence of various modeling parameters. The external pressure is
taken as one of the simulation parameters governing the degree of textured surface wetting and,
consequently, the slippage of the fluid on the solid. The relative direction of the flow to the
textured surface affects the apparent friction as well. Comparative studies of the values of the
friction coefficient are performed to assume the conditions leading to longer lifetime of the texture.
S11.6: Waves and Jets Thu, 16:00–18:00
Chair: Holger Marschall S1|03–123
Growth rate and dominant frequency of unstable interfacial waves in air-water mixing
layers
Thomas Otto (TU Ilmenau), Maurice Rossi (Institute d’Alembert, CNRS/University Pierre and
Marie Curie), Thomas Boeck (TU Ilmenau) Schedule
We are interested in the linear instability of growing interfacial waves that appear near the nozzle
or splitter plate in liquid atomization by fast gas streams. Inviscid models have not been able
to explain the growth rates of these waves measured in experiments. We apply viscous stability
analysis to this problem in order to determine if the properties of these waves can be described
within the limitations of the parallel flow assumption.
To this end, we construct a basic velocity distribution with a velocity deficit near the interface.
This modification accounts for the proximity of the splitter plate, where the liquid and gas have
zero velocity. It leads to an additional parameter describing the velocity deficit at the interface
relative to the free-stream velocities in the liquid and gas phase. For the streamfunction perturbations
we solve the traditional Orr-Sommerfeld problem for two coupled layers in both temporal
and spatial setting.
We apply our stability analysis to two different atomisation model experiments performed
with air and water using a concentric and a planar nozzle configuration. In these experiments
the spatial growth rate and dominant frequency of the unstable waves have been measured for
a range of different air and water velocities. In contrast to purely inviscid stability theory, our
viscous analysis can reproduce the growth rates satisfactorily. Agreement with the experimental
frequencies is less favorable, which may be caused by non-parallel effects. The importance of
different physical instability mechanisms will also be discussed.

Section 11: Interfacial flows 245
High-speed jet formation after solid object impact
Stephan Gekle (TU München), Jose Manuel Gordillo (Universidad de Sevilla), Devaraj van der
Meer, Detlef Lohse (University of Twente) Schedule
A circular disc hitting a water surface creates an impact crater which after collapse leads to
a vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a
single point halfway down the cavity. Two fast sharp-pointed jets are observed shooting up- and
downwards from the closure location, which by then has turned into a stagnation point surrounded
by a locally hyperbolic flow pattern. This flow, however, is not the mechanism feeding the jets.
Using high-speed imaging and numerical simulations we show that jetting is fed by the local flow
around the base of the jet, which is forced by the colliding cavity walls. We show how the wellknown
theory of a collapsing void (using a line of sinks on the symmetry axis) can be continued
beyond pinch-off to obtain a new and quantitative model for jet formation which agrees well with
our numerical and experimental data.
A fully adaptive finite element scheme for the Cahn-Hilliard Navier-Stokes system
Michael Hinze, Christian Kahle (Universität Hamburg) Schedule
We consider the Cahn-Hilliard Navier-Stokes system (CHNSS) in the phasse field approximation
with the double obstacle potential, and apply a semi-implicit scheme to its time discretization.
We relax the variational inequalities appearing in every time step by a penalization approach
and develop reliable and effective residual based a posteriori error estimators for the resulting
PDE system along the lines of [1]. Several numerical experiments show the performance of our
approach. The work presented extends the investigations of [1] on adaptivity for the Cahn Hilliard
system to the CHNSS.
[1] An adaptive finite element Moreau-Yosida-based solver for a non-smooth Cahn-Hilliard problem,
to appear in OMS.

246 Section 12: Waves and acoustics
Section 12: Waves and acoustics
Organizers: Claus-Dieter Munz (Universität Stuttgart), Wolfgang Schröder (RWTH Aachen)
S12.1: Aeroacoustic Tue, 13:30–15:30
Chair: Wolfgang Schröder S2|02–C120
Computational aeroacoustics - Advanced finite element scheme for acoustic perturbation
equations
Manfred Kaltenbacher, Andreas Hüppe (Universität Klagenfurt), Aaron Reppenhagen (Virtual Vehicle
Research and Test Center Graz), Barbara Wohlmuth (TU München) Schedule
Since the beginning of computational aeroacoustics (CAA) several numerical methodologies have
been proposed. Due to practical advantages provided by the separate treatment of fluid and
acoustic computations, hybrid methodologies still remain the most commonly used. Therewith, a
splitting of the unknowns velocity �u, pressure p and density ρ into mean (denoted by an overline)
and fluctuating (denoted by the superscript a) parts is performed. Such an ansatz results, e.g., in
the acoustic perturbation equations [1]
∂pa ∂t + c2ρ ∇ · �u a + �u · ∇p a = qc ; ρ ∂�ua
∂t + ρ(�u · ∇)�u a + ∇p a = �qm
with c the speed of sound and qc, �qm acoustic source terms. Its variational formulation is then
given as follows (for simplification we use homogeneous Dirichlet boundary conditions): Find
(�u a , pa ) ∈ V × W such that
�
∂
∂t
p a ϕdx − c 2 �
ρ �u a �
· ∇ϕ dx +
�
�u · ∇p a� �
ϕ dx = qcϕ dx (1)
ρ ∂
∂t
�
�v a · � �
ψ dx +
Ω
Ω
∇p a · � �
ψ dx + ρ
Ω
Ω
�
�u · ∇�u a� · � �
ψ dx =
Ω
Ω
�qm · � ψ dx (2)
for all ( � ψ , ϕ) ∈ V × W .
Following [2] we apply a mixed formulation and apply spectral finite elements. In order to
stabilize our formulation, we use similar techniques as for DG-approaches and reformulate the
third term in (2) as a special flux term (upwinding) and furthermore add a jump-term in the
acoustic particle velocity �u a along common element interfaces.
Within our talk, we will present the efficiency of the proposed numerical scheme and demonstrate
its applicability to industrial relevant applications.
[1] R. Ewert and W. Schröder. Acoustic perturbation equations based on flow decomposition via
source filtering. Journal of Comp. Phys., 188:365398, 2003.
[2] G. Cohen and S. Fauqueux. Mixed finite elements with mass-lumping for the transient wave
equation. Journal of Comp. Acoustics, 8:171188, 2000.
Simulation of a Nozzle-Jet Configuration including the Acoustic Near-Field
Stefan Bühler, Leonhard Kleiser (ETH Zürich) Schedule
A numerical setup is presented which allows to study a circular jet flow configuration in which
the nozzle is included in the simulation domain. Direct Numerical Simulations (DNS) are performed
using up to 10 th order compact finite-difference schemes which are stabilized by applying

Section 12: Waves and acoustics 247
a mild low-pass filter. A parallelization approach has been implemented which shows good weak
and strong scaling behavior. At the inflow the Synthetic Eddy Method is employed to generate
turbulent fluctuations in the nozzle boundary layer with prescribed statistics, which are imposed
by a sponge (forcing) layer technique. A comparison of the flow field within the nozzle and in the
vicinity of the trailing edge is made to a recent DNS study in which a fully developed turbulent
pipe flow serves as a model for the upstream unsteadiness of the subsequent jet. Simulation results
for the jet flow field obtained at Reynolds number ReR = 9050 and a Mach number Ma = 0.9
as well as for the acoustic near-field are found to be in good agreement with recent nozzle-jet
simulation results at higher Reynolds number.
Airframe noise prediction on unstructured grids
Marcus Bauer (DLR Braunschweig) Schedule
Airframe noise is an important contributor to the overall noise generated by modern airliners with
quiet engines, especially during the approach and landing phase of flight. Then, main airframe
noise sources are geometrically complex objects like the landing gear or the airfoils’ deployed
slats and flaps. The goal of this work is to efficiently predict such kinds of noise. Therefore, the
acoustic perturbation equations (APE) are solved, a discontinuous Galerkin (DG) method with
nodal shape functions given in terms of Lagrange polynomials providing their spatial discretization
on flexible, unstructured meshes. The unsteady, turbulent source term of the APE is efficiently
modelled via the FRPM (fast random particle mesh) method based on statistical turbulence information
from a RANS (Reynolds-Averaged Navier-Stokes) solution. Slat noise of various high-lift
airfoil configurations is computed in two space dimensions. Computations are indeed cheap and
deliver good agreement with wind tunnel measurements and expensive scale-resolving approaches
like large eddy simulation (LES). Future work aims at the application of the DG-APE-FRPM
approach to predict flap side edge noise. To this end, a three-dimensional DG-APE solver is
currently under development at German Aerospace Center (DLR).
On the impact of thermal sources on noise generation
A. Hahnenkamm, M. Münsch, H. Lienhart, R. Masood, E. Lopez, L. Zhou, A. Delgado (Universität
Erlangen-Nürnberg) Schedule
Sound emission is nowadays considered as a major environmental issue. The sound emission is
generated, amongst other sources, due to an increasing amount of traffic and transport, i.e. road
transport, rail and air traffic. Here, sound emission presents a significant risk to public health and
a major cause of stress, especially in industrial countries. In this framework the present work is
addressed to the topic of active noise control with the target of noise reduction.
The investigated method is based on the idea of noise control due to thermal sources which
are assumed to have an impact on the flow field due to weakly compressible effects of the flowing
media. For that purpose two benchmark test cases were developed to investigate the effects of
thermal sources. In detail the flow over a forward facing step and flow around a circular cylinder
with heated walls was investigated. In the first test case the step itself and some part up- and
downstream of the step was heated to affect the re-circulating flow downstream of the step and
the base vortex in front of the step. The cylinder was heated entirely. Wall temperatures up to
550 K were obtained for both benchmarks. Measurements of sound emission conducted in an
aero-acoustic wind tunnel showed an only limited effect of the heating on the sound emission for
the test cases and not in all the cases sound reduction was achieved.
For the cylinder test case the sound emission was reduced due to heating effects, specially the
tonal emission connected with the Strouhal frequency was reduced up to 10 dB depending on the
flow velocity. LDA measurements of the flow in the wake of the cylinder indicated an expansion of

248 Section 12: Waves and acoustics
the wake in crosswise direction, a reduction of velocity gradients and also a decrease of turbulence
intensity in the shear layer of about 30 Percent was observed.
For the forward facing step an increasing wall temperature caused a broadband amplification
of sound emission within the whole frequency spectrum. In contrast to the cylinder test case the
velocity field was just slightly influenced due to the heating. In the vicinity of the step and up
to one step height above the step, turbulence intensity increased perceptibly whereas turbulence
intensity was reduced in the outer region.
In addition to the experimental investigations, also numerical simulations of the test cases were
conducted for detailed source term analyses. Preliminary results showed the expected relation
between heating, source term generation and sound emission.
Experimental and numerical findings of the impact of thermal sources on sound emission on
the background of two benchmark test cases will be presented in the talk.
Aerodynamic sound generation by turbulence in plane shear flows
G.Khujadze, G.Chagelishvili (E. Kharadze Georgian Astrophysical Observatory), M.Oberlack (TU
Darmstadt), A.Tevzadze (Iv. Javakhishvili University Tbilisi), J.Hau (TU Darmstadt), G.Bodo
(Osservatorio Astronomico di Torino) Schedule
The nonlinear aerodynamic sound generation by turbulence has been long analyzed since the
foundation of the theory of aerodynamic sound in pioneering papers by Lighthill [1,2]. He noted
that velocity shear can increase the acoustic wave emission in the aerodynamic situation due to the
existence of linear terms in the inhomogeneous part of the analogy equations. In the paper [3] it
was described a mechanism of linear aerodynamic sound generation. Therein it was shown that the
linear phenomenon of the conversion of vortex mode into the acoustic wave mode induced by the
non-normality of the flow is the only contributor to the acoustic wave production of the unbounded
shear flows and the potential vorticity was identified as the linear source of acoustic waves. The
results of comparative analysis of linear and nonlinear aerodynamic sound generation by turbulent
perturbations in these flows, especially in plane Couette flow and jets are presented. Numerical
study of the generation of acoustic waves by stochastic/turbulent perturbations embedded in
these flows are performed. The spectrum has a peak at some steamwise wave-number k0 in the
form
Vx ′ (x, y) = Be −y2 /L2 �
cos(2πζ1(y))
+∞
−∞
dkx
� kx
k0
� 6
e −
�
kx
k0
� 6
e ikxx+i2πζ2(kx) , (1)
where ζ1(y) and ζ2(kx) are random numbers in the range [0, 1] varying with y and kx respectively,
L denotes the localization scale in the cross-stream direction. The half-width of the spectrum of
the inserted perturbation meets the condition ∆k0 ≪ k0, that allows to discriminate linearly
and nonlinearly generated acoustic waves and to carry out comparative analysis of linear and
nonlinear aerodynamic sound generation by turbulent perturbation.
According to our study the linear aerodynamic sound generation dominates over the nonlinear
one at moderate and high shear rates up to large amplitudes (B ∼ 1000) of the turbulent
perturbations. The mean flow vorticity is larger than the perturbation potential vorticity.
[1] Lighthill M. J.: Proc. R. Soc. London, Ser. A 211, 564 (1952).
[2] Lighthill M. J.: Proc. R. Soc. London, Ser. A 222, 1 (1954).
[3] Chagelishvili G., Tevzadze A. et al.: Phys.Rev.Lett. 79, 3178 (1997).

Section 12: Waves and acoustics 249
S12.2: Waves in Structures Tue, 16:00–18:00
Chair: Claus-Dieter Munz S2|02–C120
Study of mode conversion at defects in rope structures using ultrasonic waves
Stefan Bischoff, Lothar Gaul (Universität Stuttgart) Schedule
Ultrasonic waves travel in rope structures over long distances as guided waves (see lamb waves in
plates), allowing for effective monitoring. In order to localize and characterize defects, an exact
knowledge of the propagation, reflection and transmission properties of the ultrasonic waves is
required. These properties can be obtained using the Finite Element Method by modeling a
segment of the periodic wave guide with a periodicity condition. The solution of the corresponding
eigenvalue problem leads to all propagating modes of the waveguide as well as locally generated
evanescent modes.
The Boundary Element Method is used in combination with the Finite Element Method for
the characterization of the wave propagation. The mode conversion at discontinuities, such as
cracks or notches, can be subsequently described by reflection and transmission coefficients. The
reliability and numerical accuracy of the simulation results are verfied by comparison with experimental
findings.
Numerical computation of dispersion relations in wave guides
Hauke Gravenkamp (BAM Berlin), Chongmin Song (University of New South Wales, Sydney),
Jens Prager (BAM Berlin) Schedule
Guided waves in thin-walled structures, such as plates or pipes, are widely used for non-destructive
testing and structural health monitoring applications. For high frequencies, a large number of
propagating modes can be excited. As in general all modes are strongly dispersive, the accurate
calculation of the dispersion relations is essential. Analytical models, which are used for homogeneous
or simply layered structures, fail to give sufficient results, if the geometries become more
complex or if the material parameters vary continuously on the specimen’s cross section.
In the present work, a numerical approach is presented for the computation of the frequencydependent
wave numbers and group velocities of the propagating modes in wave guides. The
formulation is based on the Scaled Boundary Finite Element Method. The cross section of the wave
guide is discretized in the Finite Element sense. The governing equations of general elastodynamics
are applied. A standard eigenvalue problem is then derived for the calculation of wave numbers.
The group velocities can directly be obtained as the eigenvalue derivatives. For the discretization
of the boundary, higher-order elements have been employed as they have shown to drastically
improve the accuracy and efficiency of the computation. Polynomials up to 14th order have been
applied as the element shape functions.
This approach is not limited to homogeneous materials. Complex wave guides consisting of
an arbitrary number of layers or materials with continuously varying elastic parameters can
accurately be described.
Simulation of Lamb wave interaction with defects in laminated plates by SFEM.
Andreas Asmus, Bianca Hennings, Rolf Lammering (Universität der Bundeswehr Hamburg) Schedule
A variety of online structural health monitoring systems are based on the use of Lamb-Waves
which are guided waves that propagate in thin plate or shell structures, [1]. The main problems in
the numerical analysis of high frequency elastic waves are related to spatial and time discretization.
A huge number of degrees of freedom and small time steps are needed in order to guarantee a
sufficient accurate solution. In the context of Finite Elements (FEM) a fully populated mass-

250 Section 12: Waves and acoustics
matrix is a drawback in respect to the computational cost of the analysis.
A solution of this problem is the Spectral Finite Element Method (SFEM) which is a masslumping
technique and consists in using the Gauss-Lobatto quadrature formula for computing
the mass-matrix which is then diagonal. Thus, an algorithm based on an explicit time scheme is
truly explicit and a noticeable decrease of computational cost can be expected, [2].
The presentation deals with the implementation of Spectral Finite Elements for a first-order
laminated plate. Related numerical results concerning the wave interaction with defects are presented
and compared with the Literature and calculations which are based on a plane strain plate
Spectral Finite Element.
[1] Zhongqing Su, Lin Ye, Identification of damage using lamb waves, Lecture Notes in Applied
and Computational Mechanics Vol. 48, 2009.
[2] Cohen, Gary C., Higher-order numerical methods for transient wave equations, Springer,
2002.
Inter-wire Coupling Model Development for Health Monitoring of Cable Structures
Natalie Higgins, Christoph Schaal (Universität Stuttgart) Schedule
Structural Health Monitoring (SHM) allows the integrity of a system to be monitored in situ,
detecting weaknesses as they form. Due to the waveguide nature of cylindrical structures, ultrasonic
waves can be used to detect defects in cables over large distances. Common power line cables
consist of numerous individual wires, making modeling of the energy interactions within the entire
multi-wire cable very complex. Moreover, handling the multi-modal and dispersive nature of the
guided wave propagation itself is already a challenge.
Considering the mathematical complexity each additional wire brings, a straightforward energybased
model is chosen to describe inter-wire coupling in the entire cable. This model takes into
account wave propagation energy as well as energy losses due to damping and friction.
While detecting cracks in two-wire cables has proven to be successful, in order to detect defects
in cables with several wires, inter-wire coupling must be well understood. The purpose of this
investigation is to better qualify inter-wire coupling and extend the current coupling model to include
more wires. This goal is achieved through theoretical model development and experimental
verification.
Dispersion in Cylindrical Waveguides with Uncertain Parameters
Christoph Schaal, Miriam Krautter, Michael Hanss (Universität Stuttgart) Schedule
Current wave-based Structural Health Monitoring (SHM) methods of cylindrical structures rely
on the accurate description of the wave numbers as a function of frequency, called dispersion. An
efficient algorithm to calculate dispersion for propagating and non-propagating waves in cylindrical
waveguides of a specific material has been recently developed. Using the Waveguide Finite
Element method, only a segment of the waveguide is modeled with a common FEM package. By
introducing a periodicity condition, the wave numbers follow directly from the eigensolutions of
the resulting transfer matrix.
In this work, a new approach is presented where the calculations of the wave numbers and
the according phase and group velocities are based on uncertain parameters, describing real-world
applications more adequately. Modeling of uncertainties in parameters can be accomplished by representing
the parameters as fuzzy numbers; a special kind of fuzzy sets. With the Transformation
Method, which is an increasingly evolving strategy in the field of advanced fuzzy arithmetic, the

Section 12: Waves and acoustics 251
effects of uncertain model parameters are investigated by simulating their propagation towards
the system’s outputs.
In addition to tracking the uncertain parameters to the wave numbers and velocities, overall
imprecision of the results as well as measures of influence are also discussed to identify further
possibilities to improve performance and robustness of SHM algorithms for cylindrical structures.
Numerical simulations of pile integity tests using a coupled FEM SBFEM approach
Marco Schauer, Sabine Langer (TU Braunschweig) Schedule
Piles are widely-used to build a proper foundation for various buildings. The pile’s quality in
soil can be tested by a so called pile integrity test. In order to apply this test, an acceleration
sensor has to be attached to the pile’s head to which an impulse is sent afterwards. Due to this
impulse a p-wave runs through the pile. The major part of this wave is reflected on the pile’s toe
and can be measured by the attached acceleration sensor on top of the pile. This yields to an
acceleration-time plot which has to be analysed to determine the pile’s condition.
Sometimes the interpretation of these plots is difficult, specially when the cross-section of the
pile is changing or influenced by the surrounding soil. For a better understanding of these kind
of measurements, numerical simulations can be performed. For these simulations a coupled finite
element method (FEM) and scaled boundary finite element method (SBFEM) approach is used.
This approach satisfies the Sommerfeld radiation condition and allows the simulations of an
infinite half-space. This ensures that the applied impulse is not going to be reflected at the
artificial boundary which is intoduced by the numerical discretization and hence the discretised
domain can be smaller than the approach which uses FEM only.
S12.3: Wave Propagation Wed, 13:30–15:30
Chair: Claus-Dieter Munz S2|02–C120
Microscale Investigations of Highfrequency Wave Propagation Through Highly Porous
Media
David Uribe (Universidad EAFIT, Medellin, Colombia/Universität Bochum), Erik Saenger (ETH
Zürich), Ralf Jänicke, Holger Steeb (Universität Bochum), Oscar Ruiz (Universidad EAFIT, Medellin,
Colombia) Schedule
Wave propagation in highly porous materials has a well established theoretical background, still
there are parameters which require complex laboratory experimentation in order to find numerical
values. This paper presents an effective method to calculate the tortuosity of aluminum foam
using numerical simulations. Additionally, the interaction mechanisms between fluid and foam
phases was determined. The work flow begins with the acquisition of the foam geometry by
means of a micro-ct machine and further image segmentation and analysis. The elastodynamic
wave propagation equation is solved using a displacement-stress rotated staggered finite-difference
technique. The effective wave velocities are calculated and using the fluid and aluminum effective
properties, the tortuosity is determined. The numerical simulations closely match the results from
our experimental data.
Experiments on Peregrine soliton type deep water gravity waves
Hoffmann, N.P., Chabchoub, A. (TU Hamburg-Harburg) Schedule
The Peregrine soliton solution of the Nonlinear Schrödinger equation is often regarded as the
prototype of oceanic rogue waves. We present measurements of laboratory realizations obtained
in a water wave tank for first and higher order solutions. The experimental data is compared with

252 Section 12: Waves and acoustics
theoretical predictions based on Peregrine and Peregrine-Akhmediev solutions of the Nonlinear
Schrödinger Equation. For small steepness of the underlying carrier wave, excellent agreement
can be observed.
Internal Flow And Pressure Waves In Reciprocating Compressors
Thomas Müllner (TU Wien) Schedule
In reciprocating compressors gas is compressed from the pressure level in the suction chamber to
a higher pressure in the discharge chamber using the driving power from a moving piston. The gas
flow is controlled by self-acting valves. In a first approach a simple valve model is considered. The
suction valves open if the in-cylinder pressure is lower then the suction pressure and close if the
pressure is higher, while the discharge valves open when the pressure inside the cylinder exceeds
the discharge pressure. Valve opening and closing cause internal pressure waves. The 3D-flow and
the waves inside the compressor are computed using the unsteady Euler-equations. Results for
the flow and the pressure waves will be presented.
Studies on material properties used for noise barriers
Alin-Cosmin Tot, Calin Lumei, Mariana Arghir (Technical University of Cluj-Napoca) Schedule
Noise barriers are typically used to reduce noise near to the highway or near to the building
construction. Factors that characterize the barrier effectiveness are the position and geometry of
the barrier, its height and materials which is made from. Considering the interaction of noise with
the surface of the barrier we can distinguish three principles: reflection, resonance and absorption
of the waves. The phenomenon of reflection is met in special on barriers made of rigid material
and a surface roughness which does not contribute to noise mitigation. Resonant element consists
of a cavity which communicates with the outside environment through of a hole or a membrane.
Under the action of wave sound that penetrates through the hole or the membrane, the volume
of air in the cavity resonators running alternative movements of oscillation, sound energy will be
dissipated due to the phenomena of inertia and viscosity. Areas with barriers absorbent coverings
materials contain porous elements attenuate of airborne noise intensity. The main feature is
that the phonon absorbent materials have a porous structure, with intercommunicating canals
communicating through channels or openings in the material. Thus, attenuation and absorption
of sound is produced by multiple reflections of sound waves in the material and wave refractions
inside it. The structure of porous materials can be cellular, fibrous or granular. Determination of
sound-absorbing nature of these materials is one of the most important acoustic characteristics.
Measurement of sound absorption coefficients in an impedance tube is achieved by two different
methods: Wave ratio method [1] and transfer function method [2]. In conclusion, this paper may
be considered as guidance in choosing a proper absorbing material using an impedance tube.
[1] ISO 10534-1:1996, Acoustics - Determination of sound absorption coefficient and impedance
in impedance tubes - Part 1: Method using standing wave ratio
[2] ISO 10534-2:1998, Acoustics determination of sound absorption coefficient and impedance
in impedance tubes. Part 2: transfer function method.
Anti-plane shear waves in a structurally-nonlinear fibrous composite material
Igor V. Andrianov (RWTH Aachen), Vladyslav V. Danishevskyy, Olexandr I. Ryzhkov (Prydniprovska
State Academy of Civil Engineering and Architecture, Ukraine), Dieter Weichert (RW-
TH Aachen) Schedule

Section 12: Waves and acoustics 253
Elastic waves propagating in heterogeneous solids can undergo the effects of nonlinearity and
dispersion. The types of nonlinearity can be classified as geometrical, physical, and structural.
Dispersion is caused by successive reflections and refractions of local waves at the interfaces
between the components. The balance state between nonlinearity and dispersion results in the
formation of stationary nonlinear waves. Increase in nonlinearity leads to the appearance of localized
nonlinear modes that accumulates all the mechanical energy and can propagate for long
distances keeping stable the shape and velocity. We study 2D anti-plane shear waves propagating
in a structurally-nonlinear fibrous composite material with an imperfect interface between
the matrix and fibres. The macroscopic wave equation is obtained by the method of asymptotic
homogenization. Explicit analytical expressions for the effective linear and nonlinear elastic
moduli are obtained. Magnitude of the coefficient at the dispersive term is determined by the
Floquet-Bloch approach. For stationary plane waves, analytical solutions are derived in terms
of elliptic functions. A number of nonlinear phenomena are detected, such as (i) dependence of
the wave shape, velocity and attenuation upon the amplitude and (ii) development of localized
solitary and kink (shock) waves. Obtained results can be practically important for the purposes
of non-destructive testing in Materials Science as well as for design of new acoustic devices in
Engineering (such as wave-guides, acoustic filters, ultrasonic transducers, etc.)
Acoustical performance of concreted wood fiber materials
Calin Lumei, Alin-Cosmin Tot, Mariana Arghir (Technical University of Cluj-Napoca) Schedule
The paper presents the acoustical properties of a material which is made from a mixture of wood
and concrete. Its composed of recycled waste wood which is first chipped in wood fiber and then
is mineralized and bonded with Portland cement. Measurements on small specimens were performed
in an impedance tube [1] to find the absorption coefficient. A mathematical model [2] is
also presented in order to determine the absorption coefficient analytically. It is then optimized
to fit the data results. Originally, this model was proposed to describe the impact of porous asphalt
on highway noise levels. The model consists of three parameters: flow resistivity, porosity
and structure factor or tortuosity. These parameters can be independently determined. For the
optimization of the model, a simple approximation of these three parameters to data results is
made. Knowing the acoustic performance of concreted wood fiber materials is important as it is
100% recyclable that can used for building constructions or noise barriers.
[1] ISO 10534-2:1998, Acoustics determination of sound absorption coefficient and impedance in
impedance tubes. Part 2: transfer function method.
[2] Bérengier, M., M. Stinson, et al. (1997), Porous road pavements: Acoustical characterization
and propagation effects. Journal of the Acoustical Society of America 101(1): 155-162.
S12.4: Elastic Waves Wed, 16:00–18:00
Chair: Claus-Dieter Munz S2|02–C120
Nonlinear Rayleigh elastic surface waves:new wave equations, solutions, and effects
J.J. Rushchitsky, O.O. Khotenko (P Timoshenko Institute of Mechanics, Kyiv, Ukraine) Schedule
The presented results can be thought as next to the publication, in which a row of new nonlinear
wave equations is obtained for the two-dimensional case of elastic quadratic nonlinear deformation
within the framework of Murnaghan model. It should be noted that the Rayleigh wave theory
is no the complete fragment of classical theory, it is still developing. In the classical statement

254 Section 12: Waves and acoustics
of the problem on Rayleigh surface waves, the wave along the plane x3 = 0 is studied, when the
elastic medium occupies the upper half-space. It is assumed further that the problem is the twodimensional
one (the plane problem in the plane Ox1x3 ). The direction of motion is choosing along
the axis Ox1. The motion equations are then transforming into two non-linear wave equations.
These equations are the basic ones in analysis of nonlinear elastic waves propagating in the
plane Ox1x3, including the waves localized near the boundary surface. One of such waves is the
classical Rayleigh wave. The new nonlinear wave equations are solved by the method of successive
approximations.
Main observations: 1. The corresponding to the 2nd approximation wave picture is described
by the wave parameters of the 1 st (linear) approximation. 2. The 2 nd approximation is characteristic
by the 2 nd harmonic in contrast to the 1 st approximation characteristic by the 1 st harmonic
- the 2 nd harmonic relative to the propagating in direction of the horizontal coordinate wave and
the 2 nd harmonic relative to the exponential delay of wave along the vertical coordinate. These
harmonics amplitudes depend nonlinearly on coordinates and then increase with increasing of
time of the Rayleigh wave propagation. As a result, the 1 st harmonic will distort. 3. The dependence
of the 2 nd harmonics amplitudes on the squared 1 st harmonics amplitudes is the standard
situation for the method of successive approximations and has some consequences relative to the
1 st harmonic distortion. In particular, because the amplitudes in engineering materials and the
earth’s crust have very distinguishing orders (they are measured in millimeters-microns in the
first case and centimeters in the second case), then to detect the effect of distortion, a smallness
of the squared amplitudes must be compensated by the larger values of wave numbers (larger
values of frequencies). 4. The second approximation is zeroth for the pure surface wave, but this
approximation can intro-duce the essential contribution in to the wave picture for the near-thesurface
wave. 5. The derived new nonlinear equation for determination of the wave number shows
the new factor of an initial wave profile distortion - distortion owing the wave length changing
with unchanging frequency.
On the geometric transformations and new materials
Veturia Chiroiu (Institute of Solid Mechanics of Romanian Academy) Schedule
In this paper, yet another idea of designing new materials is investigated. The property of Helmholtz
equation to be invariant under geometric transformations is exploited to obtain new materials
with inhomogeneous and anisotropic distribution of elastic properties. This approach opens
up the possibility to configure new materials that might be useful in the design of elastic cloaking
devices. As an example, the conventional foam which occupies a given domain is transformed into
an auxetic material which fills another domain. The new material is inhomogeneous and anisotropic
and exhibits new interesting properties. All computations are performed in the framework of
the Cosserat theory of elasticity which admits degrees of freedom not present in classical elasticity,
i.e. rotation of points in the material and couple stresses
Conservation laws and implectic operators of two-dimensional Zakharov-Kuznetsov
nonlinear dynamical system
Arkadii Kindybaliuk, Mykola Prytula (Ivan Franko National University in Lviv, Ukraine) Schedule
Following two-dimensional nonlinear dynamical system is considered in this paper:
ut = uxxx + uxxy + uxyy + uyyy − uux − uuy = K[u], (1)
where K[u] - smooth by Frechét functionally polynomial vector field [1].
System (1) has been derived as a sum of two nonlinear models describing wave propagation

Section 12: Waves and acoustics 255
in x-direction [2]: ut = uxxx + uxyy − uux and y-direction: ut = uyyy + uxxy − uuy . Derived system
(1) is isotropic, since it describes wave propagation in x and y direction simultaneously.
Conserved quantities and implectic operators are fundamental conceptions in theory of dynamical
systems [1].
Infinite hierarchy of conservation laws has been found. First three of them are presented below:
��
γ0 =
Ω
��
u dxdy, γ1 =
Ω
u 2 dxdy, γ2 = − 1
2
Also implectic operators for system (1) have been found:
η = − (∂x + ∂y) ,
��
Ω
�
u 2 x + u 2 y + u3
�
dxdy.
3
ϑ = ∂xxx + ∂xxy + ∂xyy + ∂yyy − 1
3 (u∂x + ∂xu + u∂y + ∂yu) .
In our case correspondal Hamiltonians are:
Hη = γ2, Hϑ = γ1
Obtained results are useful for investigating complete integrability of dynamical system and verification
of numeric schemes for their solving.
[1] Prykarpatsky A.K., Mykytiuk I. V., Algebraic integrability of nonlinear dynamical systems
on manifolds: classical and quantum aspects. - Netherlands: Kluwer, - 1999. - 560p.
[2] Zakharov V.E., Kuznetsov E. A., On three dimensional solitons, Sov. Phys. JETP, 39 (1974)
285-286 pp.

256 Section 13: Flow control
Section 13: Flow control
Organizers: Christian O. Paschereit (TU Berlin), Cameron Tropea (TU Darmstadt)
S13.1: Flow Control - Boundary Layers Tue, 13:30–15:30
Chair: Elfriede Friedmann S1|01–A04
Variation of friction drag via spanwise transversal surface waves
P. Meysonnat, S. Klumpp, M. Meinke , W. Schröder (RWTH Aachen) Schedule
Introducing spanwise motion into the near-wall flow field of turbulent boundary layer has proven
to be an effective mean of active flow control aiming at the reduction of wall shear stress [1]. The
skin-friction is responsible for about 50% of the total drag of an aircraft, making this approach
very attractive for the increasing demand in greener transportation.
Miscellaneous approaches for introducing spanwise motions have been studied in several experimental
and numerical investigations in order to reduce the wall shear stress. Du et al. [2] used
spanwise traveling excitations, realized by near wall volume forces, in a channel flow yielding a
reduction in friction of up to 30%. Itoh et al.[3] experimentally investigated the drag reduction via
a spanwise traveling transversal sinusoidal wall oscillation achieving a drag reduction of 7.5% in a
turbulent boundary layer. Klumpp et al. [4] set-up an LES with the same mechanism to investigate
the near wall features of the flow. Whereas over the unactuated wall a streaky structure is evident,
for the actuated case a ribbon-like structure is formed corresponding to the excitation, affecting
the friction drag [5]. They found a drag reduction of 9% compared to an unactuated wall for a
particular combination of amplitude, wavelength and period, whereas other combinations even led
to drag increase. In the present study two set-ups of traveling wall oscillations are investigated via
LES. The first set-up (ˆy + = 30, λ + = 870, T + = 50) which matches the case in [4] possesses a higher
amplitude, wavelength and period than the second case (ˆy + = 10, λ + = 174, T + = 10) which
yields a drag increase of 8%. The comparison between the two set-ups evidences the existence of
a key feature of drag reduction with spanwise traveling wave excitation. A detailed analysis of
the flow field, fluctuating vorticity components, and energy balance in the system of the different
configurations will be given at the conference.
[1] G. E. Karniadakis and K.-S., Choi Mechanisms on transverse motions in turbulent wall flows,
Annu. Rev. Fluid Mech., 35:45–62, 2003.
[2] Y. Du, V. Symeonidis, and G. E. Karniadakis, Drag reduction in wall-bounded turbulence
via a transverse travelling wave, J. Fluid Mech., 457:1–34, Apr. 2002.
[3] M. Itoh, S. Tamano, K. Yokota, and S. Taniguchi, Drag reduction in a turbulent boundary
layer on a flexible sheet undergoing a spanwise traveling wave motion, J. Turbulence, 7:1–17,
2006.
[4] S. Klumpp, M. Meinke and W. Schröder, Drag Reduction by Spanwise Transversal Surface
Waves, J. Turbulence,22:1–13 ,2010.
[5] A.-T. Le, G. N. Coleman and J. Kim., Near-wall turbulence in three-dimensional boundary
layers, Int. J. Heat Fluid Flow, 21:480–488,2000.
Turbulent drag reduction at moderate Reynolds numbers via spanwise velocity waves
Davide Gatti (TU Darmstadt), Maurizio Quadrio (Politecnico di Milano) Schedule

Section 13: Flow control 257
Several techniques are currently under investigation to decrease the friction drag in turbulent wall
flows. Among the most promising ones, the streamwise-traveling waves of spanwise wall velocity
have been recently shown (Quadrio et al., JFM 2009) to be simple and open-loop, to relaminarize
low-Re turbulent flows and yield large reductions of drag at higher Re, and to require little energy
to operate.
Of course, the question whether such large drag reductions can be obtained at the high values of
Re typical of applications remains to be answered. Answering such question, either by experiments
or DNS, is obviously challenging. For DNS, the problem lies in the tremendous increase of the
computational cost with Re, that has to be appreciated in view of the need of carrying out
an entire parametric study at every Re, owing to the unknown location of the optimal forcing
parameters.
In this paper we investigate the behaviour of the streamwise-traveling waves at relatively high
Re. We use DNS of a turbulent plane channel flow with Re up to 73, 000 (or Reτ = 2, 000).
To achieve high Re while keeping the computational cost affordable, computational domains of
reduced size are employed. Though much larger than the Minimal Flow Unit that guarantees a
self-sustained turbulence (Jiménez & Moin, JFM 1991), their limited size requires special care to
interpret results that are indeed still box-size dependent. Space-averaged quantities (like friction)
show large temporal fluctuations when the domain size is small, and thus require longer averaging
times to converge: a suitable compromise between space- and time-average is required. We
instrument the DNS results with an error bar, related to the finite averaging time, which helps
setting such a compromise.
We focus on friction drag reduction rate R, as well as the net savings S that result from
accounting for the power input Pin of the control. The effects of Re on the energetic budget and
on the optimal parameters of the wall forcing are both studied.
Our results indicate that up to R = 0.29 can be obtained at Reτ = 2, 000. The maximum R is
found to decrease as R ∼ Re−0.22 τ in the Reynolds range investigated. This seems to confirm the
trend suggested by J.I.Choi et al. (AIAA J, 2002) on the basis of a numerical study carried out
up to Reτ = 400 and for the oscillating wall alone. By extrapolation we infer that R = 0.1 could
be achieved at Reτ ≈ 3 × 105 . Moreover, we find that the sensitivity of R to Re becomes smaller
when far from the low-Re optimum parameters: in this region, we suggest R ∼ Re−0.05 τ .
Boundary behavior of viscous fluids: Influence of wall roughness and friction-driven
boundary conditions
Dorin Bucur (Universite de Savoie), Eduard Feireisl, Sarka Necasova (Czech Academy of
Sciences) Schedule
We consider a family of solutions to the evolutionary Navier-Stokes system supplemented with
the complete slip boundary conditions on domains with rough boundaries. We give a complete
description of the asymptotic limit by means of Γ−convergence arguments, and identify a general
class of boundary conditions.
[1] Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka Boundary behavior of viscous fluids: influence
of wall roughness and friction-driven boundary conditions. Arch. Ration. Mech. Anal. 197
(2010), no. 1, 117-138.
Non-sinusoidal wall oscillation for drag reduction
A. Cimarelli (University of Bologna), B. Frohnapfel (TU Darmstadt), Y. Hasegawa (TU Darmstadt;
University of Tokyo), E. De Angelis (University of Bologna), M. Quadrio (Politecnico di
Milano) Schedule

258 Section 13: Flow control
The control of wall-bounded turbulent flows with the aim of reducing the wall-shear stress is an
important and challenging topic in modern fluid mechanics. Indeed, such a reduction has very
important beneficial effects for engineering flow systems. One prominent control technique which
allows to achieve a significant reduction of turbulent drag is based on the modification of wall
turbulence by the cyclic spanwise movement of the wall, [1]. Despite the studies available in the
literature, there are a number of issues related to drag reduction properties of the oscillating wall
that have not yet received a definite answer. For example, it is well known that the frequency and
the amplitude of the oscillation play a first-order role in determining the amount of the turbulent
drag reduction rate but the effects of the shapes of the wall oscillations are still not determined.
Indeed, all the attemps carried out towards achieving a reduction of turbulent friction have used
a sinusoidal shape for the spanwise oscillation of the wall. For that reasons, we investigate the
drag reducing properties of non-sinusoidal wall oscillations. The present work aims at answering
two related questions:
• How do deviations from the sinusoidal wave shape - which might occur when trying to
realize an oscillating wall in practice - influence the control performance?
• Is it possible to obtain flow control performance superior to the sinusoidal wall oscillations
with other oscillations shapes?
The analysis of the non-sinusoidal wall oscillations is performed using direct numerical simulation
data of a turbulent channel flow. The simulations are carried out with an highly accurate
numerical code. The friction Reynolds number of the reference simulation without wall oscillation
is Reτ = 200 and the computational domain is 6.67h×2h×3.33h. All simulations for the different
boundary conditions of spanwise velocity at the walls are performed starting from the same initial
condition of fully developed channel flow without wall oscillation.
The obtained results illustrate the dependency of the drag reduction rate, R, and of the power
spent to move the walls, Pin, with respect the shape of the wall motion. An analytical model
based on the generalization of the laminar solution of the Stokes layer is derived which allows
the a priori prediction of R and Pin for different wall motions in turbulent flows under certain
constraints.
[1] M. Quadrio, Drag reduction in turbulent boundary layers by in-plane wall motion, Phil.
Trans. R. Soc. A 369 (2011), 1428 – 1442.
On the effect of superhydrophobic surfaces in turbulent channel flow
Sebastian Türk, Gerti Daschiel, Yosuke Hasegawa, Bettina Frohnapfel (TU Darmstadt) Schedule
From experimental and numerical investigations it is known that superhydrophobic surfaces lead
to a decrease in skin friction drag in laminar and turbulent channel flow [2]. For turbulent channel
flow, a drag reduction up to 50% can be achieved. This reduction in skin friction drag is achieved
by providing an alternating gas-liquid solid-liquid interface that results in an alternating no-slip
no-shear boundary condition. For laminar flow an analytic solution for calculating the effective
slip length in the Stokes limit exists for certain geometries, namely for ribs oriented parallel and
perpendicular to the flow [3]. The effective slip length is a parameter for quantifying the benefit
of a superhydrophobic surface. For turbulent flow, no analytic solution or correlation functions
are available.
Within the present investigation, the impact of a superhydrophobic surface pattern oriented
parallel to the main flow direction on turbulent channel flow is shown using direct numerical

Section 13: Flow control 259
simulation (DNS). The predictions are carried out with a constant pressure gradient, respectively
uτ = const. The friction Reynolds number is chosen to be Reτ = 180. It is shown, that for
short-wave surface structures, the effective slip length in turbulent channel flow is in good agreement
to the corresponding Stokes solution. However, for an increase in the wave-length of the
alternating boundary conditions a deviation in effective slip length occurs. In order to identify
the mechanism responsible for the observed phenomenon, the FIK-Identity [1] is used. In doing
so, the resulting bulk mean velocity can be decomposed into a slip contribution, a laminar contribution
and a turbulent contribution. Special attention is given to the influence of the modified
surface on the turbulent quantities. In addition a critical assessment of the potential benefit of
using superhydrophobic surfaces in laminar and turbulent channel flows is presented.
[1] Koji Fukagata, Kaoru Iwamoto, and Nobuhide Kasagi. Contribution on reynolds stress distribution
to the skin friction in wall-bounded flows. Physics of Fluids, 14(11):L73, 2002.
[2] Jonathan P. Rothstein. Slip on superhydrophobic surfaces. Annual Review of Fluid Mechanics,
42(1):89-109, January 2010.
[3] Christophe Ybert, Catherine Barentin, Cecile Cottin-Bizonne, Pierre Joseph, and Lyderic
Bocquet. Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries.
Physics of Fluids, 19(12):123601, 2007.
Using the γ-Reθ-model for simulating, quantifying and delaying transition on dolphin
geometries
Donald Riedeberger, Dina-Marie Zimmermann, Ulrich Rist (Universität Stuttgart) Schedule
Simulation of laminar to turbulent transition in finite volume CFD codes has recently seen some
interesting new approaches regarding modelling the underlying process. The set of the Reynolds
Averaged Navier-Stokes equations has been extended by two transport equations of the γ-Reθmodel
[1] that uses empirical correlations to determine transition onset and blends in an underlying
eddy viscosity turbulence model. This local modelling approach offers possibilities to manipulate
the underlying transition onset - for example to indirectly account for damping mechanisms at
the wall.
In the present project the flow around a geometry of a common dolphin [2] was simulated
in a low to moderate turbulence environment at varying free stream velocities. Although Gray’s
paradox that suggested laminarization techniques on the dolphin skin was solved and compliant
walls do not necessarily need to be present on the dolphin [3] studies on the dolphin flow remain
of interest in regard to transition location and correlation with dermal structures [2]. Results
are presented and evaluated regarding overall flow topology and transition location depending on
Reynolds number and turbulence level.
In a second step the empirical correlation for transition onset was manipulated to shift transition
location downstream to assess possible benefits of turbulence damping capabilites in the
dolphin skin - i.e. accounting for flow control mechanisms of a compliant wall. The results show,
that the model is very much capable to support this kind of simulations. Comparing results at
moderate turbulence intensities with and without a modified (i.e. delayed) transition location one
can see that drag reduction potential is as high as 40 percent - mostly coming from skin friction
reduction in the parts where flow is sustained laminar for a longer amount of body surface.
Summarizing this talk will highlight the possibilities of the empirical transition model and its
potential in accounting for effects influencing the transition process.

260 Section 13: Flow control
[1] R. B. Langtry and F. R. Menter. Correlation-based transition modeling for unstructured parallelized
computational fluid dynamics codes. AIAA JOURNAL, 47(12):28942906, (2009).
[2] V. V. Pavlov, Dolphin skin as a natural anisotropic compliant wall. Institute of Physics
Publishing: Bioinspiration & Biomimetics 1 3140, (2006).
[3] F. E. Fish, The myth and reality of grays paradox: implication of dolphin drag reduction for
technology. Bioinspiration & Biomimetics, 1(2):R17 R25, (2006).
S13.2: Flow Control II Wed, 13:30–15:30
Chair: Andre Thess S1|01–A04
Turbulent Flow with Embedded Vortical Structures Induced by Vortex Generators
in a Cascade
Natalie Souckova, Vaclav Uruba (Czech Academy of Sciences) Schedule
Vortex generators (VGs) are passive flow control devices that are widely used in both internal
and external flow. VGs occur in many different configurations. The choice of the optimal VGs
configuration for a particular case is still quite obscure. The way to make the selection of suitable
actuators arrangement easier can lead through the comprehension of generated vortices behaviour.
The vortical structures produced by several configurations of vortex generators cascade have
been studied to better understand the influence of spacing between pairs of VGs and vortex generator
shape on the generated vortices behaviour. The used vane type VGs were integrated in
straight channel so that they were submerged in the boundary layer. The turbulent flow affected
by VGs has been examined by means of Stereoscopic Particle Image Velocimetry technique in
several cross-sections downstream of VGs.
Reactive control of spatially developing turbulent boundary layer
Alexander Stroh, René Simon, George Khujadze (TU Darmstadt), Yosuke Hasegawa (TU Darmstadt;
University of Tokyo), Bettina Frohnapfel, Martin Oberlack (TU Darmstadt) Schedule
Reduction of losses caused by turbulent skin friction drag is of great economical and ecological
interest. One of the promising turbulence control strategies is a reactive control, where instantaneous
flow field information captured by sensors is used in order to determine actuator operation.
Such control schemes exhibit high energy gain due to low power consumption. Although most
previous control schemes have been assessed in fully developed turbulent channel flows, their
applicability in spatially developing turbulent flows are not fully investigated.
We focus on opposition control proposed by [1] as a representative reactive control scheme.
The investigation is performed using direct numerical simulations of a turbulent boundary layer
with zero pressure gradient in a Reynolds number range of ReΘ = 400 − 750. Opposition control
is applied partially in the middle of domain between x ∗ = 250 and 350 covering 16.6% of the total
domain length.
The total drag reduction is estimated as 13.8% with net energy saving rate of 13.2% and
local energy gain up to 23. It is found that the reduction of skin friction is mainly caused by the
reduction of the turbulent term and the spatial development term appearing in the FIK-Identity
[2]. Whereas the turbulent term is decreased due to a decrease of Reynolds shear stress, the
spatial development term is mainly affected by the streamwise gradient of the streamwise velocity
fluctuations, ∂u ′ u ′ /∂x, and streamwise gradient of streamwise mean velocity product, ∂UU/∂x.
While ∂u ′ u ′ /∂x demonstrates essential deviations from the uncontrolled state in the beginning
and at the end of the control area, ∂UU/∂x shows a decrease over the entire control area.

Section 13: Flow control 261
In the presentation we will report the influence of control area length on the control performance
and on the flow state in the recovery region.
[1] Choi, H., Moin, P. & Kim, J., Active turbulence control for drag reduction in wall-bounded
flows. J. Fluid Mech. 262, (1994), 75 - 110.
[2] Fukagata, K., Iwamoto, K. & Kasagi, N., Contribution of Reynolds stress distribution to the
skin friction in wall-bounded flows. Phys. Fluids 14, (2002) L73 - L76.
Rotation-Symmetric Reference Geometries for Energyefficient Flow Around Bodies
Michael Quarti, Andreas Gottlieb, Karl Bühler, Gerhard Kachel (Hochschule Offenburg) Schedule
Topology optimization is used to optimize problems of flow around bodies and problems of guided
flow. Within the context of research, optimization criteria are developed to increase the energy
efficiency of these problems [1,2,3,4]. In order to evaluate the new criteria in respect to the
increasing of energy efficiency, reference bodies for different Reynolds numbers in combination
with given design space limitations are needed. Therefore, an optimal body at Reynolds number
against 0 was analytically determined by Bourot [5]. At higher Reynolds numbers, in the range
of laminar and turbulent flows, no analytical solution is known. Accordingly, reference bodies are
calculated on the basis of CFD calculations at three technical relevant Reynolds numbers (1.000,
32.000, 100.000) in combination with parameter optimization. The cross section of the bodies is
described by a parameterized model.
To get the optimal body, a parameter optimization, is used to optimize with regard to the friction
loss and pressure loss in order to minimize the total loss (cw-value). The result is an optimal
parameter constellation, depending on the Reynolds number. Within the results, it is possible to
generate the optimal geometries. The identified characteristics of the flow field around the bodies
are used as base for new optimization criterias.
[1] K. Bühler, G. Kachel, and A. Gottlieb, Von der umströmten Scheibe zur optimierten Körperform,
in: FB HS Offenburg. - 2010, 75-77 (2011).
[2] A. Gottlieb, A. Strobel, and M. Stephan, Anwendung der Topologieoptimierung für strömungsführende
Bauteile im Fahrzeugentwicklungsprozess, in: VDI-Tagungsband 2107: SIMVEC
Berechnung und Simulation im Fahrzeugbau, (2010).
[3] C. Hinterberger and M. Olesen, Automatic Geometry Optimization of Exhaust Systems
Based on Sensitivities Computed by a Continuous Adjoint CFD Method in OpenFOAM,
in: General emissions, (SAE International, Warrendale and PA, 2010).
[4] F. Klimetzek, J. Paterson, and O. Moos, AutoDuct: topology optimization for fluid flow, in: 1.
Konferenz für Angewandte Optimierung in der Virtuellen Produktentwicklung, (FE-Design
GmbH, Karlsruhe, 2006).
[5] J. M. Bourot, Journal of Fluid Mechanics 65(03), 513-515 (1974).
Boundary layer simulations of turbulent flow over drag reducing surfaces
Elfriede Friedmann (Universität Heidelberg) Schedule
We are interested in passive turbulent flow control by manipulating the boundary layer of turbulent
flow using tiny microstructures. Direct Numerical Simulations (DNS) of fully developed

262 Section 13: Flow control
turbulent flows are very time consuming if one would like to resolve both: the turbulence and the
microstructures. The focus of our work lies on model reduction and on high quality numerical
methods needed for precise drag calculations. Following the boundary layer theory of Prandtl and
Schlichting, we will present a model for the viscous sublayer (steady Navier-Stokes equations) and
for the buffer layer (unsteady Navier-Stokes equations) which we use for drag predictions. In the
steady case flow characteristics can be calculated with less numerical effort using homogenization
theory. Applying the results of [6], we can replace the boundary layer model on rough surfaces
(microscopic model) by the so-called homogenized model (macroscopic model) with smooth surface.
The solution of the effective equations can be given analytically and the influence of the
roughness are calculated from an auxiliary problem resulting from the homogenization process.
The complexity of this auxiliary problem depends on the shape of the roughness. For universal
structures a three-dimensional Stokes problem with an additional jump condition on the interface
must be solved in a periodic cell domain. For riblets, only a two-dimensional Laplace problem
with this jump condition in the solution must be solved. We will validate the drag prediction with
this reduced model with the drag resulting from the microscopic model on non-optimal riblets and
pimpels. In [3], where an optimization problem for such structures was solved, we find shapes with
higher contribution to drag reduction. In general, the contribution here is small because the steady
situation deals with small structures within the viscous sublayer. An unsteady model reaching
inside the buffer layer of the turbulent boundary layer was developed to consider the higher and
more relevant structures for drag reduction. Initial and boundary conditions were provided here
from turbulent smooth channel flow simulations (Center of Smart Interfaces, Darmstadt, [9]. We
will present DNS of the boundary layer models over riblets and pimpels which are performed with
the software Gascoigne [5] developed in Rolf Rannachers group based on Finite Elements. With
the high quality numerical methods implemented in this software like adaptive mesh refinement,
multigrid algorithms and error control [2], [8] and by using isoparametric elements for the boundary
approximation [3], we can resolve the rough boundary well and provide drag calculations
with an accuracy per mill [7]. Our research will allow us a small contribution to the boundary
layer theory concerning the comparability of the different (but non-optimal) microstructures.
Mathematics Subject Classification 2000 (MSC 2000): 76D05, 76D10, 35B27
[1] Bechert, D.W. and Bruse, M. and Hage, W., Experiments with three-dimensional riblets as
an idealized model of shark skin, Experiments in Fluids, 28:403-412, 2000.
[2] Becker, R., Rannacher, R., An optimal control approach to a posteriori error estimation in
finite element methods, Acta Numerica 10, 1102, 2001.
[3] Friedmann, E., Richter, T., Optimal microstructures. Drag reducing mechanism of riblets, J.
of Math. Fluid Mech., 13 (3), 429-447, 2010.
[4] Friedmann, E., The optimal shape of riblets in the viscous sublayer, J. of Math. Fluid Mech.,
12(2), 243-265, 2010.
[5] GASCOIGNE, High Performance Adaptive Finite Element Toolkit, URL: http://www.
numerik.uni-kiel.de/~mabr/gascoigne/.
[6] Jäger, W. and Mikelić, A., Couette flows over a rough boundary and drag reduction, Communications
in Mathematical Physics, Springer, 232(3), 429-455, 2003.
[7] Maier M., Simulation von Grenzschichtströmungen über Ribletstrukturen, diploma thesis,
Heidelberg University, 2011.

Section 13: Flow control 263
[8] Rannacher, R., Adaptive finite element discretization of flow problems for goal-oriented model
reduction, Computational Fluid Dynamics Review 2010, (M. M. Hafez, K. Oshima, D. Kwak,
eds), 51-70, World Scientific, 2010.
[9] Stroh, A., Frohnapfel, B., Hasegawa, Y., Kasagi, N., Tropea, C., The influence of frequencylimited
and noise-contaminated sensing on reactive turbulence control schemes, The Seventh
International Symposium on Turbulence and Shear Flow Phenomena, Ottawa, Canada,
2011.
On the flow resistance of wide surface structures
Gerti Daschiel, Tobias Baier, Jürgen Saal, Bettina Frohnapfel (TU Darmstadt) Schedule
It has been shown that riblet-mounted surfaces can reduce the skin-friction drag by up to 10%
compared to flat surfaces in turbulent channel flows [3]. In the laminar regime, however, the use
of these surface geometries was found to result in drag increase [2]. Using a variational principle
for the surface shape, Pironneau et al. [4] were able to show analytically that in the laminar case
benefits can only be expected if the surface structures are wide enough compared to the channel
height, in particular if the ratio obeys the condition l/L > π/z where z ≈ 1.2 is the root of
1 − x tanh x (2l: width of the structure, 2L: mean channel height).
In the present investigation the curved optimum surface shape found numerically by Pironneau
et al. is analysed further. Using an analogy between structural mechanics and fluid mechanics,
namely the analogy between torsion of beams and fully developed laminar flow in ducts (the governing
equation in both cases is Poissons equation), the pressure drop, and thus the skin-friction
drag, arising from various curved structures can be calculated using Saint Venants principle [1].
In this respect the analysis concentrates on surface modifications described by a trigonometric
function of the form x2 = ± ((a/2)cos(πx3/l) + 2b) with b + a/2 = L. Based on this approach
the impact on flow resistance for the variation of all parameters determining the trigonometric
structure is taken into account. Drag is found to be reduced up to about 50% compared to the
flow through a rectangular channel of the same cross section and the same width (here: 2l) for
a certain range of parameters. In addition, numerical simulations of the flow in the structured
channels are performed. Currently, these simulations are extended to higher Reynolds numbers
in order to also study the drag reduction potential of these wide surface structures in turbulent
flows.
[1] M. Bahrami, M. Yovanovich, J. Culham, A novel solution for pressure drop in singly connected
microchannels of arbitrary cross-section, International Journal of Heat and Mass Transfer
50 (2007), 2492 – 2502.
[2] H. Choi, P. Moin, and J. Kim, On the effect of riblets in fully developed laminar channel
flows, Physics of Fluids3 (1991), 1892 – 1896.
[3] H. Choi, P. Moin, J. Kim, Direct numerical simulation of turbulent flow over riblets, Journal
of Fluid Mechanics 225 (1993), 503 – 539.
[4] O. Pironneau, G. Arumugam, On riblets in laminar flow, Control of boundaries and stabilization
(1989), 51 – 65.

264 Section 13: Flow control
Assessment of Flow Control Techniques in Terms of Time and Energy Savings
Bettina Frohnapfel, Yosuke Hasegawa (TU Darmstadt), Maurizio Quadrio (Politecnico di Milano)
Schedule
The performance of drag reducing flow control techniques for internal flows is customarily evaluated
by either measuring the flow rate achieved with a fixed pressure drop or determining the
pressure drop needed to drive the flow at a fixed flow rate. The obtained results are typically
presented in a plot of skin friction drag (i.e. pressure drop) versus bulk Reynolds number (i.e.
flow rate) where either the reduction of skin friction drag at fixed Reynolds number or the increase
of Reynolds number at a fixed skin friction drag represent successful control. In this conventional
cf − Re−plot the two key aspects of practical fluid transport systems, namely the time required
to transport a given amount of fluid over a certain distance and the energy required to realize
this transport, cannot be viewed independently. This mainly stems from the fact that the energy
consumption is directly related to the product of flow rate and pressure drop. Based on the idea
to put potential energy and time savings in the focus of flow control evaluation we derive two
dimensionless parameters which quantify the energy consumption and the transportation time for
flows through an arbitrary duct independently. These parameters span a novel evaluation plane
that allows reevaluating the performance of passive and active drag reduction techniques in one
framework also including the energy expenditure to run active control. This novel evaluation plane
allows including application-dependent cost functions such that the optimal control strategy
for a given application can be determined.
S13.3: Flow Control III Wed, 16:00–18:00
Chair: Stefan Odenbach S1|01–A04
Experimental Investigation of magnetoactive composites
Thomas Gundermann, Dmitry Borin, Stefan Günther, Stefan Odenbach (TU Dresden) Schedule
Magneto-switchable composite materials consisting of a polymer matrix and magnetizable components
offer enormous potential for innovation. Such material systems enable a targeted response
to external loads and can be used advantageously as adaptive structures. By applying a magnetic
field, the viscoelastic and dynamic mechanical properties can be active and reversible changed.
The main goal of this study was to investigate the mechanical properties of these composites
under the influence of an external magnetic field using a compression test unit. For this purpose
a dynamic table-top test machine with a servopneumatic drive has been equipped with a
fixture based on electromagnets combined with permanent magnets. Furthermore, studies were
undertaken with a micro-computed tomography system which provides information about the
internal structure under the influence of a magnetic field. For the experimental investigations
samples based on the carbonyl iron particles have been used. The particles were dispersed in
a polymeric matrix and after the cross-linking procedure they were limited in their movement,
but stable towards sedimentation, forming the elastic magnetoactive composite. Combinations of
the mechanical tests with microstructural observations represent the fundamental basis for the
understanding of the behavior of magneto-switchable composite materials.
This project is funded by the European Union (ERDF) and the Free State of Saxony.
Thermal conductivity measurements in magnetic fluids
Martin Krichler, Stefan Odenbach (TU Dresden) Schedule
Material properties like viscosity and sound propagation in magnetic fluids are known to depend
on external magnetic fields due to structure formation of the magnetic particles. In this experimental
study thermal transport behaviour is investigated on the basis of thermal conductivity

Section 13: Flow control 265
measurements. Therefore an improved measuring technique - a plane heat source method - is used
for thermal conductivity measurements in magnetic fluids. Initially four magnetic fluid samples
varying in particle interaction and Brownian motion behaviour are selected for the fundamental
investigation of the effect of chain-like structure formation on thermal behaviour. Thermal
conductivity is measured as a function of strength and direction of an external magnetic field
relative to heat flux. Unlike former experimental investigations our results show consistency with
theoretical predictions.
The anisotropy of the magnetoviscous effect in ferrofluids with interparticle interactions
J. Linke, M. Gerth-Noritzsch, D. Y. Borin, S. Odenbach (TU Dresden) Schedule
Ferrofluids are colloidal suspensions of coated magnetic nanoparticles in a carrier liquid. The viscosity
and the flow behaviour of ferrofluids may be tuned by an externally applied magnetic field
which opens a range of interesting technical applications. The change of the viscosity is caused
by two effects. In highly dilute ferrofluids, the free rotation of the magnetic particles in the flow is
slowed down by their magnetic torque. This causes a raise in the viscosity, the so called rotational
viscosity. In concentrated ferrofluids on the other hand, the dipole-dipole interaction between the
particles supports chain-like microstructures that obstruct the flow and increase the viscosity.
This effect is known as the magnetoviscous effect (MVE) [1]. Both effects are anisotropic; however,
the majority of experimental investigations of the MVE have been carried out with only one
fixed orientation of the magnetic field.
In the present work, pressure flow viscometers with a capillary and a slit geometry have been
used to access the viscosity coefficients for three orientations of the magnetic field, i.e. parallel
and perpendicular to the direction of flow, as well as parallel to the vorticity of the flow. The MVE
has been measured in cobalt-based ferrofluids with strong interparticle interactions [2]. In these
ferrofluids the change in viscosity is more than a magnitude higher than the maximum rotational
viscosity. This supports the theory of structure formation due to dipole-dipole interactions. The
MVE for the field direction perpendicular to the flow is lower than the MVE for the parallel direction
due to shear-induced disintegration of the chain-like structures. Furthermore, it has been
investigated how this anisotropy of the MVE, together with the flow profile, changes by varying
the strength of the applied magnetic field, and the results are compared with microstructural
simulations.
We gratefully acknowledge the financial support of our research by the Deutsche Forschungsgemeinschaft
(DFG grant Od18-18).
[1] S. Odenbach, Magnetoviscous Effects in Ferrofluids, Lecture Notes in Physics (2002), Springer.
[2] M. Gerth-Noritzsch, D. Y. Borin, S. Odenbach, Anisotropy of the magnetoviscous effect in ferrofluids
containing nanoparticles exhibiting magnetic dipole interaction, J. Phys.: Condens.
Matt. 23 (2011), 346002.
Investigations on a branched tube model in magnetic drug targeting systematic
measurements and simulation
K. Gitter, S. Odenbach (TU Dresden) Schedule
Magnetic drug targeting has been established as a promising technique for tumour treatment. Due
to its high targeting efficiency unwanted side effects are considerably reduced, since drug-loaded

266 Section 13: Flow control
nanoparticles are concentrated within a target region due to the influence of a magnetic field. In
order to contribute to the understanding of basic phenomena experiments on a half-Y-branched
glass tube model as a model-system for a blood vessel supplying a tumour were performed. As
a result of measurements, novel drug targeting maps, combining e.g. the magnetic volume force,
the position of the magnet and the net amount of targeted nanoparticles were presented. In a first
targeting-map, which summarizes results for 63 magnet positions, the concentration of the injected
ferrofluid is 2.95vol. Up to 97 of the nanoparticles were successfully targeted into the chosen
branch; however, the region where yield was considerable is rather small. A high concentration
of injected ferrofluid brings the danger of accretion in the tube. It is shown that an increase in
magnetic volume force does not necessarily lead to a higher amount of targeted nanoparticles. In
a second targeting-map the concentration of injected ferrofluid is reduced to 0.14vol. At a first
glance the result with low concentration is promising, since the danger of accretion is avoided.
Nevertheless, one has to consider, that, unless the magnetic volume force in the branch-point
was provided in the necessary strength, an application would not be successful. The current
focus is a finite-element simulation based on the considered setup and artery-model. The fluid
flow is described by the Navier-Stokes equations, the magnetic field is derived from Maxwells
equations and mass flux is given by the diffusion equation. The magnetic volume force acting on
a volume of magnetic fluid combines the magnet and the ferrofluid data and is proportional to
the field dependent magnetisation and the gradient of the field strength. The diffusion equation
allows the implementation of concentration-dependent magnetic volume force and viscosity. In
the experiments, the model, the injection-procedure and the ferrofluid were chosen close to the
parameters of a medical application in order to allow a transfer of the results to future medical
investigations.
Creep experiments on ferrofluids with clustered nanoparticles
Dmitry Borin (TU Dresden), Andrey Zubarev (Ural State Univeristy Ekaterinburg), Stefan Odenbach
(TU Dresden) Schedule
Even a small amount of magnetite nanoparticles larger than 12 nm gives rise to a variety of
interesting changes of the rheological behavior of ferrofluids in applied magnetic elds [1]. Recently
[2], we observed the effect of the slow relaxation of the rheological properties of a ferrouid with
clustered iron nanoparticles under joint action of shear ow and magnetic eld. In the present study
we invistigate the inverse creep for this ferrofluid experimentally as well as from a theoretical point
of view. With a magnetic field applied to the fluid, the shear force has been suddenly removed
and the subsequent relaxation of the shear stress has been measured. The relaxation time can
reach several minutes analogous to [2] and depends on magnetic field strength and initial shear
rate. Furthermore, an offset in the shear stress after removing the shear force is observed and
can be attributed to the yield stress in ferrofluids [3]. The proposed theoretical model tries to
explain the observed effects on the basis of the formation of long chains of magnetic particles in
the ferrofluid under action of the magnetic field.
[1] S. Odenbach, Magntoviscous effect in ferrofluids, Springer Lecture Note in Physics m71,
Berlin, Heidelberg, Springer-Verlag (2002)
[2] D. Borin et al, Ferrouid with clustered iron nanoparticles: slow relaxation of rheological
properties under joint action of shear ow and magnetic eld, J. Magn. Magn. Mater. 323
(2011), 1273–1277
[3] H. Shahnazian and S. Odenbach, Rheological investigations of ferrofluids with a shear stress
controlled rheometer, J. Phys.: Condens. Matter 20 (2008), 204137

Section 13: Flow control 267
Determining of Velocity Fields During Real and Experimental Simulated Beer Fermentations
by UDV and LDA
Kai Böttcher, Heiko Meironke (Fachhochschule Stralsund) Schedule
Beer fermentation is a very complex process, especially in the fluid-mechanical and the biochemical
point of view. Our aim is to optimize the fermentation by flow control, which requires
quantities of data. The applied velocity measuring techniques should be non-invasive to ensure
that neither the flow nor the fermentation in the green beer gets influenced. Therefore, an Ultrasonic
Doppler Velocimetry (UDV) system is used to determine velocity fields with 128 measuring
points. It works in the turbid fluid with the existing yeast cells as tracer particles and can be
applied easily to the industrial scale.
For the validation of CFD-codes and the better understanding of measurements and flow processes,
model fluids are used. They can be adapted to real fluid properties like density and viscosity
and allow measurements with Laser Doppler Anemometry (LDA). Another advantage over the
real fluid is their fixed composition, which leads to negligible natural variations.
All experiments are performed in a 270 liter fermenter. Besides the real process, measurements
through optical access points and the simulation of fermentations with CO2 and heat emission
are enabled. Eight individually controllable cooling zones are used as thermal actors. Resulting
changes in boundary conditions induce temperature gradients and hence allow to control the flow
inside the tank.
This work deals with the experimental setup and the results on the one hand and a comparison
between real and simulated fermentations on the other hand. Special attention is given to investigations
of the multi-phase flow inside the vessel and the effects of changing constraints. The
usability of UDV measurement techniques is the key benefit in that case, because it can be used
in green beer and model fluids and does not influence the flow.
S13.4: Flow Control IV Thu, 13:30–15:30
Chair: Bettina Frohnapfel S1|01–A04
Non-sinusoidal wall oscillation for drag reduction
A. Cimarelli (University of Bologna), B. Frohnapfel (TU Darmstadt), Y. Hasegawa (TU Darmstadt;
University of Tokyo), E. De Angelis (University of Bologna), M. Quadrio (Politecnico di
Milano) Schedule
The control of wall-bounded turbulent flows with the aim of reducing the wall-shear stress is an
important and challenging topic in modern fluid mechanics. Indeed, such a reduction has very
important beneficial effects for engineering flow systems. One prominent control technique which
allows to achieve a significant reduction of turbulent drag is based on the modification of wall
turbulence by the cyclic spanwise movement of the wall, [1]. Despite the studies available in the
literature, there are a number of issues related to drag reduction properties of the oscillating wall
that have not yet received a definite answer. For example, it is well known that the frequency and
the amplitude of the oscillation play a first-order role in determining the amount of the turbulent
drag reduction rate but the effects of the shapes of the wall oscillations are still not determined.
Indeed, all the attemps carried out towards achieving a reduction of turbulent friction have used
a sinusoidal shape for the spanwise oscillation of the wall. For that reasons, we investigate the
drag reducing properties of non-sinusoidal wall oscillations. The present work aims at answering
two related questions:
• How do deviations from the sinusoidal wave shape - which might occur when trying to

268 Section 13: Flow control
realize an oscillating wall in practice - influence the control performance?
• Is it possible to obtain flow control performance superior to the sinusoidal wall oscillations
with other oscillations shapes?
The analysis of the non-sinusoidal wall oscillations is performed using direct numerical simulation
data of a turbulent channel flow. The simulations are carried out with an highly accurate
numerical code. The friction Reynolds number of the reference simulation without wall oscillation
is Reτ = 200 and the computational domain is 6.67h×2h×3.33h. All simulations for the different
boundary conditions of spanwise velocity at the walls are performed starting from the same initial
condition of fully developed channel flow without wall oscillation.
The obtained results illustrate the dependency of the drag reduction rate, R, and of the power
spent to move the walls, Pin, with respect the shape of the wall motion. An analytical model
based on the generalization of the laminar solution of the Stokes layer is derived which allows
the a priori prediction of R and Pin for different wall motions in turbulent flows under certain
constraints.
[1] M. Quadrio, Drag reduction in turbulent boundary layers by in-plane wall motion, Phil.
Trans. R. Soc. A 369 (2011), 1428 – 1442.
Numerical Investigation of Vortex Generator Jets On The Trailing Edge Shroud of
Improved High-Lift Configuration
Saqib Mahmood, Marcus Casper, Ingmar Hartung, Peter Scholz (TU Braunschweig) Schedule
This paper focuses on numerical simulation of active flow control devices by means of vortex
generator jets on the trailing edge shroud of improved high-lift configurations. The test case used
for the numerical work is the DLR F-15 two-element high lift airfoil. The vortex generator jets
produce longitudinal vortices within the boundary layer which suppresses the stalling of an airfoil.
The numerical work has been carried out using the TAU-Code developed by German Aerospace
Centre (DLR), which is a Compressible Finite Volume based unstructured solver. The effect of grid
refinement is described in detail. Numerical results without active flow control are compared with
experiments conducted at the Institute of Fluid Mechanics, Technische Universität Braunschweig.
The numerical results agree well with experimental data by predicting trailing edge type stall.
Stabilization of Laminar Boundary-Layer Flow using Dielectric Barrier Discharges
Alexander Duchmann, Debora Gleice da Silva Del Rio Vieira, Sven Grundmann, Cameron Tropea
(TU Darmstadt) Schedule
Drag reduction of immersed bodies is of major importance to the aeronautical industry and is an
expanding field of research. In this contribution the development of active flow control techniques
is examined with the aim to retain the laminar flow state, and hence a reduction of skin friction
drag.
Dielectric Barrier Discharges (DBD) are used to delay laminar-turbulent transition initiated
by Tollmien-Schlichting instabilities. An electric potential of several thousand Volts between two
electrodes separated by a dielectric material leads to ionization of the surrounding air. Interaction
between the resulting weakly ionized plasma and the electric force field causes an acceleration of
the fluid molecules close to the surface. This effect can be used to change the stability properties
of the laminar boundary-layer flow and postpone the turbulent breakdown.

Section 13: Flow control 269
The present study demonstrates that DBD actuators cannot only delay transition triggered
by controlled disturbances, as shown by Grundmann et. al. [1], but are also effective in delaying
natural transition. Transitional boundary-layer flow along a flat plate inside an open-circuit
wind tunnel is experimentally investigated. A combination of hot-wire measurements and particle
image velocimetry provides the time-resolved velocity distribution in wall normal and tangential
direction. Integral boundary-layer quantities and statistical data enable an analysis of the transition
process which is affected by the discharges. Linear stability theory is considered to analyze
the stability characteristics of the boundary-layer flow with and without flow control [2]. Direct
numerical simulations enable a close-up view of momentum coupling in the immediate vicinity of
the discharge and the impact on the flow stability.
[1] S. Grundmann, C. Tropea, Experimental Damping of Boundary-Layer Oscillations using
DBD Plasma Actuators, International Journal of Heat and Fluid Flow 30, (2009), 394–402.
[2] A. Duchmann, A. Reeh, R. Quadros, J. Kriegseis, C. Tropea, Linear Stability Analysis for Manipulated
Boundary-Layer Flows using Plasma Actuators, In: Seventh IUTAM Symposium
on Laminar-Turbulent Transition, ISBN 978-90-481-3723-7.
Phase-avaraged vortex train flow generated by plasma DBD actuator
Pavel Procházka, Václav Uruba (Czech Academy of Sciences) Schedule
The way how plasma actuator can generate wall-jet-like flow or train of periodical vortices depending
on the generator setting will be shown. The high-frequency high-voltage AC is used for
generation. Low-frequency modulation of the supply voltage is required to generate vortices. Data
acquisition will be performed using time-resolved PIV technique. Phase-avaraging will be studied
from two different perspectives. Firstly, sampling of phases will be ensured using trigger that is
contained in the PIV software and, secondly, phase-avaraged flow will be computed from two main
modes of POD analysis. The generated flow patterns are to be applied for control of a boundary
layer.
Feedback-control of Tollmien-Schlichting waves and laminar-turbulent transition in
a Blasius boundary layer
Ulrich Rist (Universität Stuttgart) Schedule
In a low-disturbances environment, laminar-turbulent transition starts with the amplification of
small-amplitude disturbances. Any disturbance can then be decomposed into a sum of Tollmien-
Schlichting waves such that the initial (linear) development becomes predictable using linear
stability theory (LST). The present talk will relate results of LST to features occurring in the
flow field and thus try to clarify some misconceptions about Tollmien-Schlichting waves that exist
in literature.
Control of boundary-layer transition in the early stage relies on controlling either the amplitude
or the growth of linear Tollmien-Schlichting waves. The present talk will address both paths: The
wave-superposition principle for amplitude reduction, and feedback control for growth reduction.
Here, feedback control connects actuation at the wall with the time-derivative of the wall shear
(here I wanted to show a figure). 1
Results of LST and direct numerical simulations (DNS) will be used to illustrate the basic
mechanisms, the relative merits of each method and their limits. The wave-superposition principle
1 The complete abstract with figure is here:
http://www.iag.uni-stuttgart.de/people/ulrich.rist/GAMM2012.pdf

270 Section 13: Flow control
is shown to be very sensitive to phase differences between the target wave and the control wave.
Since it is by definition based on linear superposition it can only work in the linear regime. In the
non-linear regime where finite-amplitude effects come into play and where different disturbance
modes interact with each other it is better to use the feedback control scheme. The underlying
mechanisms which have been identified by LST and DNS for both, the linear and the non-linear,
regimes will be discussed.
Advancing active wave cancellation using plasma actuators for in-flight transition
control
A. Kurz, S. Grundmann, C. Tropea (TU Darmstadt), Nikolas Goldin, Rudibert King (TU Berlin)
Schedule
Active flow control has increasingly attracted attention over the past years and has led to improvements
in aerodynamic performance, like enhanced lift or reduced drag.
Transition to turbulence in low Reynolds number flows is usually triggered by two-dimensional,
wave like velocity fluctuations, commonly known as Tollmien-Schlichting (TS) waves. Once initiated,
the amplitude of the TS waves grows until breakdown to turbulence occurs. If the amplitude
of these initial waves can be lowered at an early stage, it is possible to delay the transition, and,
for example, lower the drag of the aerodynamic surface.
In an attempt to advance active wave cancellation (AWC) using plasma actuators one step
closer to real aerodynamic applications, an existing experimental setup has been adapted to
a testing platform capable of examining the feasibility of free-flight operation. It consists of a
wing glove that can be used as a sleeve on the wing of a full-sized Grob G109 motorized glider,
available at the Technische Universität Darmstadt. The hollow carbon-fiber composite design
allows for the installation of measurement equipment, sensors and actuators inside the wing
glove, without altering the structural integrity of the aircraft. Several further constraints have to
be addressed in order to achieve the goal of sucessful in-flight AWC experiments. This includes not
only the development of lightweight high-voltage power supplies, which allow for a precise control
of the force production, but also the application of more sophisticated, fast closed-loop control
algorithms. In collaboration with the Technische Universität Berlin a robust extremum-seeking
controller and in addition, a FIR-Model, which is adapted online by a filtered-xLMS approach,
has been implemented on a dSPACE system and tested in the wind tunnel. Both controllers were
applied sucessfully for the first time in combination with plasma actuators on a full size airfoil
geometry.
Another set of experiments has been conducted using an amplitude modulation for the body
force originating directly from the high frequency carrier wave driving the plasma actuator. This
approach exploits the fact that the force production is highly unsteady at the actuator driving
frequency and opens up the possibility to operate the plasma actuator directly at TS wave frequency.
The results demonstrate that a substantial increase of the achievable forcing frequency,
and with it of the flight Reynolds number, will be possible.
S13.5: Flow Control V Thu, 16:00–18:00
Chair: Ulrich Rist S1|01–A04
Flow rate measurements in turbulent liquid metal channel flow using time-of-flight
Lorentz force velocimetry
Dandan Jian, Christian Karcher (TU Ilmenau) Schedule
Non-contact flow control and flow measurements in hot and aggressive metal melts are big challenges
in metallurgical applications. For instance, during the production of secondary aluminum,

Section 13: Flow control 271
the primary melt flows in a channel from a melting furnace to a holding furnace. To determine
both the scrap yield rate during the melting process and the exact amount of alloying elements to
be put into the holding furnace during charge makeup, exact measurement of global flow rate in
the channel is crucial for process control. Lorentz force velocimetry (LFV) is an electromagnetic
measurement technique to meet these challenges. It is based on measuring the Lorentz force acting
on a magnet system when liquid metal flow is crossing the field lines that are stretched by the magnet
system. The respective measurement device, called Lorentz force flow meter, mainly consists
of such a magnet system equipped with a digital force sensor. According to the basic principles
of magnetohydrodynamics, the recorded force is proportional to the flow rate, the square of the
characteristic amplitude of the applied magnetic field, and the electrical conductivity of the melt.
However, in application the conductivity is often unknown or changes in time due to its strong
dependence on both temperature and composition of the melt. In the present paper we describe
an extended method called time-of-flight Lorentz force velocimetry (tof LFV). Here, two identical
flow meters are arranged in a certain distance D one behind the other. In this case, flow rate can
be determined by just cross-correlating the two force signals recorded by the flow meters. In more
detail, we measure the transit time τ of a tagging signal that is transported by the flow with a
certain velocity U between the flowmeters. In this case the flow rate can easily be determined
using the simple relation Q = cUA = cAD/τ, where A is the cross-section of channel and c is a
calibration constant. Hence the measurement becomes independent of any fluid property data or
magnetic field characteristics.
Within this context we study experimentally and numerically turbulent liquid metal channel
flow affected by two localized magnetic fields. The flow rate measurements are conducted in the
model test stand EFCO (electromagnetic flow control channel) using the low-melting test melt
GaInSn as a test melt. EFCO is a closed channel with rectangular cross section of height and width
equal to H ×W = 80×10mm 2 . The overall length and breadth of the test stand are L×B = 860×
350mm 2 . The channel walls consist of electrically insulating plexiglass. The channel is equipped
with two Lorentz force flow meters each of which consisting of two permanent magnets that
generate a localized spanwise magnetic field. Attached to the magnetic field is a digital strain gage
that records the Lorentz force acting in the streamwise direction. Tagging signals are produced
by a cylindrical obstacle submerged into the flow. The flow is driven by an electromagnetic pump
(EMP) on basis of rotating permanent magnets mounted on two disks. The disks are put into
rotation by a frequency-controlled electrical motor. Upon controlling the rotation frequency f of
the pump, we adjust the Reynolds number of the flow. At the highest achievable frequency of
f = 25Hz, the corresponding Reynolds number is Re = 1.6e4. Hence, we are in the regime of
turbulent liquid metal channel flow. During the model experiments we additionally measure the
pressure produced by the EMP, velocity profiles using Ultrasonic Doppler Velocimetry (UDV), and
local velocity using Vives probe. The latter two techniques serve to calibrate the time-of-flight flow
meter. Moreover, the motor is equipped with a switch to allow changing of the flow direction from
the counterclockwise mode into the clockwise mode. Hence, using UDV we are able to measure
both purely hydrodynamic flow profiles and magnetohydrodynamic flow profiles, respectively.
Finally, a water-based heat exchanger is integrated in the loop to guarantee isothermal conditions
during the experimental runs. Melt temperature is measured using a submerged thermocouple.
Our experimental results demonstrate that time-of-flight LFV is a suitable method to measure
flow rate in turbulent liquid metal channel flow. We find a linear dependence of the measured
characteristic vortex transportation velocity U and the mean velocity of the flow. Moreover, the
measured flow profiles are in very good agreement with predictions of numerical simulations using
the commercial program Package FLUENT MHD.
We are greatful to the Deutsche Forschungsgemeinschaft (DFG) and the Bundesministerium

272 Section 13: Flow control
für Bildung und Forschung (BMBF) for financial support. We have benefited from discussions
with Dr. Ch. Resagk, and form the technical help by students J. Schumacher and S. Badtke.
Electromagnetic interaction of a conducting cylinder with a magnetic dipole caused
by steady translation and rotation
Sonja Engert, Thomas Boeck, André Thess (TU Ilmenau) Schedule
The electromagnetic interaction between a translating respectively rotating solid cylinder and
the magnetic field of a point dipole is studied by numerical simulation and asymptotic analysis.
The cylinder has finite electric conductivity and is assumed to be much longer than the distance
between dipole and cylinder. Our investigation is motivated by the novel, non-invasive techniques
named Lorentz force velocimetry and the Lorentz force eddy current testing. Both techniques
are based on Lenz rule of electromagnetic induction and utilize the force on a magnet system
produced by the movement of a conducting body. They allow one to measure integral and local
velocities in conducting liquids and to detect deep-lying flaws in solid conductors.
Our model problem has the advantage of conceptual simplicity, which allows us to compare
analytical and numerical results in the limiting cases when the distances between the dipole and
the cylinder are small and large compared to the cylinder radius. The governing equations are
the induction equations for a prescribed velocity field. They are simplified by assuming that the
magnetic Reynolds number is small, and that the induced eddy currents are stationary. In this
so-called quasistatic approximation one only has to compute the electric potential from a Poisson
equation with the scalar product of magnetic field and vorticity as right hand side. The Lorentz
force and torque are then obtained from Ohm’s law for a moving conductor. At small distances
h, our numerical computations for the Lorentz force agree with the h −3 behavior for a translating
infinite conducting plate. At large separation, the force shows a h −6 decay for the rotating cylinder,
and h −7 for the translating case, which is in agreement with the asymptotic analysis.
Oscillating flow driven by a rotating magnetic field in liquid metal with an upper
free surface
V. Travnikov, K. Eckert, S. Odenbach (TU Dresden), T. Vogt, S. Eckert (Helmholtz-Zentrum
Dresden-Rossendorf) Schedule
The oscillatory flow instability in a liquid metal cylinder with a free upper surface, exposed
to a rotating magnetic field (RMF), is analysed by numerical simulations of the axisymmetric
Navier-Stokes equations [1]. The critical Taylor number designating the onset of the oscillatory
flow regime is lower than that for the development of Taylor-Görtler vortices and decreases with
increasing aspect ratio A = H . The instability sets in as a Hopf bifurcation and is initiated
2R
near the free surface, where an oscillatory variation of both the size and the position of the
upper vortex in the secondary flow can be observed accompanied by horizontal oscillations of
the azimuthal velocity maximum at the free surface. We found that the flow frequency depends
linear on the Taylor-number for all A investigated. Moreover, the Taylor-number interval, where
the flow oscillations occur, becomes narrower. The predicted flow regime has been observed in
corresponding model experiments with GaInSn using Ultrasound Doppler Velocimetry (UDV) for
flow field measurements. The occurrence of the oscillatory flow regime depends sensitively on the
cleanliness of the liquid metal surface.
[1] V. Travnikov, K. Eckert, P. A. Nikrityuk, S. Odenbach, T. Vogt, S. Eckert, J. Crystal Growth
(in press)

Section 13: Flow control 273
Thermomagnetic convection under the influence of thermodiffusion
Lisa Sprenger, Adrian Lange, Stefan Odenbach (TU Dresden) Schedule
Thermomagnetic convection denotes a transport phenomenon induced by a temperature gradient
and a magnetic field applied to a layer of a magnetisable fluid [1]. The onset of the convective
motion is thereby described by a critical value of the sum of the Rayleigh and magnetic Rayleigh
number
Ra + Ram = (βT d 3 g∆T )/(νκ) + (K 2 ∆T 2 d 2 µ0)/(ηκ), (1)
where K denotes the pyromagnetic coefficient, ∆T the temperature difference over the layer,
d the layers height, g the acceleration due to gravity, βT the coefficient of thermal expansion,
µ0 the magnetic permeability of vacuum, ν (η) the kinematic (dynamic) viscosity, and κ the
heat coefficient. Considering the magnetic fluid as a binary fluid thermodiffusion may have to be
considered if a temperature gradient is present. Former experiments carried out with a magnetic
fluid revealed a dependence of the direction of thermodiffusion on the magnetic field. The direction
is predicted to be in favor of the onset of convection for small magnetic field strengths and
hindering it for large magnetic fields [2].
The actual influence of thermodiffusive transport processes on the onset of convection is investigated
with a linear stability analysis of the relevant hydrodynamic equations [1, 3]. The set
of equations is composed of the continuity equation, the diffusion equation, the heat equation,
and the Navier-Stokes equation, including the magnetic volume force as well as thermodiffusive
terms.
Experimental and numerical investigations on thermodiffusion complement the theoretical
analyses aiming at a more detailed understanding of thermodiffusion. The experiments are set
up in a horizontal diffusion cell based on a design presented in [2]. The change in concentration
due to thermodiffusion is measured by sensor coils wrapped around the separation reservoirs of
the setup. The inductivities change of these coils is measured by a precision LCR meter. The
measured concentrations are compared with numerical results obtained by a finite differences
code in three dimensions for the relevant partial differential equation of the ferrofluid-dynamics
theory [4].
[1] B. A. Finlayson, J. Fluid Mech. 40, 753-767 (1970)
[2] T. Völker, S. Odenbach, Phys. Fluids 17, 037104 (2005)
[3] A. Ryskin et al., Phys. Rev. E 67, 046302 (2003)
[4] A. Lange, Phys. Rev. E 70, 046308 (2004)
Flow distortion of liquid metal in a square duct due to a magnetic point dipole
Saskia Tympel, Thomas Boeck, Dmitry Krasnov, Jörg Schumacher (TU Ilmenau) Schedule
Lorentz force velocimetry is a new contactless technique to measure the velocities of hot and
agressive conductiong liquids. The Lorentz force on the magnet is highly sensitive to the velocity
profile that is influenced by the magnetic field. Thus the knowlegde of the flow transformation
and the influence of an inhomogeneous local magnetic field on liquid metal flow is essential for
obtaining velocity information from the measured forces.
We consider liquid metal flow in a square duct with electrically insulating walls under the
influence of a magnetic point dipole using three-dimensional direct numerical simulations with

274 Section 13: Flow control
a finite-difference method. The dipole acts as a magnetic obstacle. A wide range of parameters
affects the created wake. In this canonical setting, we study the modification of the flow for
different Hartmann and Reynolds numbers. We observe a strong dependence of the magnetic
obstacle effect and the corresponding Lorentz force on the orientation of the dipole as well as on
its position.
Secondary Flow Effects as Physical Mechanism of Molecular Species Transport in
Highly Oscillating Generic-Trachea Flows
Markus Rütten, Lars Krenkel, Roland Kessler (DLR) Schedule
The high frequency oscillation artificial respiration technique is often the last hope for patients
to survive highly damaged lung tissue. The mortality can significantly be reduced. In comparison
to conventional artificial respiration the applied volume flow rate and pressure is significantly
lowered in order to avoid further damaging of lung tissue and remaining intact alveolae. However,
the physical mechanism of transport of oxygen to the aeriols under high frequency oscillation
is not well understood. In the upper part of the lung convection is dominant, in contrast, the
gas exchange in the lower parts of the lung is mainly driven by diffusion. It is not clear how
associated gradients of concentrations of different molecular species are then achieved. Highly
oscillating fluid flows has been a long research topic in fluid dynamics. It is known that oscillating
pressure fluctuations are able to induce secondary flows, in particular, in curved ducts and pipes.
The question is, whether the trachea enforces the generation of secondary flow by its kidney like
cross section geometry. The influence of molecular species of different densities onto the formation
of secondary flows and the convectional transport within the trachea is investigated. In order to
clarify the physical mechanisms behind flow simulations have been conducted by using state of the
art CFD techniques. We concentrate on a generic trachea configuration with a smoothed kidney
like cross sections [3]. Thereto, we have reduced the complexity of the real trachea in order to
clearly separate mechanism inducing secondary flows. In our numerical experiment the trachea has
been filled with a mixture of oxygen and solcane, a tracer gas often used in clinical applications [1].
A well known method in analytical fluid dynamics is the transformation of boundary conditions,
see [2]. In this work we will discuss our numerical simulation results, special attention is given
to the formation of the secondary flow structures and their impact on the netto transport of the
different species.
[1] Chang HK.: Flow dynamics in the respiratory tract. In: Respiratory Physiology: An Analytical
Approach, edited by Chang HK and Paiva M. Dekker: New York, 1989, p. 57 - 138.
[2] Lacor C., Jayaraju S. T., Brouns M., Verbanck S.: Simulation of the Airflow in the Upper Airways
with Applications to Aerosols Coupled Methods in Numerical Dynamics (eds: Zdravko
Terze and Chris Lacor), SBN-ISSN: 978-953-6313-88-4, 2007.
[3] Landau L. D., Lifschitz J. M.: Lehrbuch der theoretischen Physik in 10 Bänden, Akademie-
Verlag Berlin, neu: Harri Deutsch-Verlag Frankfurt/Main

Section 14: Applied analysis 275
Section 14: Applied analysis
Organizers: Robert Denk (Universität Konstanz), Friedemann Schuricht (TU Dresden)
S14.1: Applied analysis, Session A Tue, 13:30–15:30
Chair: Friedemann Schuricht S1|03–113
Linearized elastoplasticity is the evolutionary Γ-limit of finite elastoplasticity
Alexander Mielke (WIAS Berlin), Ulisse Stefanelli (IMATI, Pavia) Schedule
We provide a rigorous justification of the classical linearization approach in plasticity. By taking
the small-deformations limit, we prove via Γ-convergence for rate-independent processes that
energetic solutions of the quasi-static finite-strain elastoplasticity system converge to the unique
strong solution of linearized elastoplasticity.
The work combines the static approach of [DNP02] with the abstract Γ-convergence result for
energetic rate-independent system developed in [MRS08]. The crucial step is the construction of
a suitable mutual recovery sequence that transforms the additive split of the strain tensor in the
linearized theory into a carefully chosen multiplicative decomposition of the strain tensor as is
needed in the setting of finite-strain elastoplasticity.
[DNP02] G. Dal Maso, M. Negri, and D. Percivale. Linearized elasticity as Γ-limit of finite
elasticity. Set-Valued Anal., 10(2-3):165–183, 2002.
[MRS08] A. Mielke, T. Roubíček, and U. Stefanelli. Γ-limits and relaxations for rate-independent
evolutionary problems. Calc. Var. Partial Differential Equations, 31(3):387–416, 2008.
On the passage from atomistic systems to nonlinear elasticity theory
Julian Braun, Bernd Schmidt (Universität Augsburg) Schedule
The main aim of our work in [1] is to provide a rigorous derivation of nonlinear elasticity functionals
from atomistic models. A fundamental contribution towards this aim has been made by
Alicandro and Cicalese in [2], where they prove a general integral representation result for continuum
limits of atomistic pair interaction potentials. It is our main aim, departing from this result,
to derive a continuum theory for more general interaction potentials which, in particular, can also
incorporate bond-angle dependent potentials. Such an extension is desirable in applications, as
many atomistic models such as, e.g., the Stillinger-Weber potential, cannot be written as a pure
pair potential. In fact, the class of potentials our theory applies to is rich enough to model any
continuum energy density, even if the Cauchy-relations are violated.
The limiting density is described in terms of a sequence of cell problems. This is related to
standard homogenization results of nonconvex integral functionals. Using the results in [3], we
prove, that under appropriate conditions, this limiting density is given by the Cauchy-Born-rule
for small (but finite) strains.
In order to prove our main representation result we resort to abstract integral representation
results for functionals on Sobolev spaces and thus follow the scheme set forth in [2], which is
dictated by verifying the hypotheses of that abstract theorem. There are, however, some major
differences as compared to the pair interaction case treated by Alicandro and Cicalese. While these
authors use slicing arguments in order to obtain energy estimates on the usual d × d deformation
gradients in the direction of interacting pairs, we will have to estimate the much higher dimensional
d × 2 d discrete deformation gradients. In fact, as in general our discrete energies cannot be

276 Section 14: Applied analysis
recovered by slicing techniques, we will instead work with very carefully chosen interpolations of
the discrete deformations which encode the full discrete gradient on lattice cells.
[1] Julian Braun, Bernd Schmidt, On the passage from atomistic systems to nonlinear elasticity
theory, preprint, arXiv:1107.4155 (2011).
[2] Roberto Alicandro and Marco Cicalese, A General Integral Representation Result for Continuum
Limits of Discrete Energies with Superlinear Growth, SIAM J. Math. Anal. 36(1)
(2004), 1 – 37.
[3] Sergia Conti, Georg Dolzmann, Bernd Kirchheim, Stefan Müller, Sufficient conditions for the
validity of the Cauchy-Born rule close to SO(n), J. Eur. Math. Soc. (JEMS) 8 (2006), 515
– 539.
Global spatial regularity for elastic fields with cracks and contact
Dorothee Knees (WIAS Berlin) Schedule
A global higher differentiability result in Besov spaces is proved for the displacement fields of
linear elastic models with self contact. In particular, domains with cracks are studied, where
nonpenetration conditions/Signorini conditions are imposed on the crack faces. It is shown that
in a neighborhood of crack tips (in 2d) or crack fronts (3d) the displacement fields are B 3
2
2,∞regular.
The proof relies on a difference quotient argument for the directions tangential to the
crack. In order to obtain the regularity estimates also in the normal direction, an argument due
to Ebmeyer/Frehse/Kassmann is modified. The methods used here will also be applied to further
examples like contact problems with nonsmooth rigid foundations or to energies with nonsmooth
constraints as they occur for instance in the modeling of shape memory alloys. Numerical examples
will illustrate the proved results.
This is joint work with Andreas Schröder (HU Berlin).
The Loves problem for hyperbolic thermoelasticity.
Jerzy Gawinecki, Józef Rafa, Jarosław Łazuka (Military University of Technology, Warsaw) Schedule
In our presentation we investigated the initial-boundary value problem for elastic layer situated
on half space of another elastic medium. In this medium the thermomechanical interactions were
taken into consideration. The system of equations with initial-boundary conditions describes the
phenomenon of wave propagation with finite speed. In our problem there are two surfaces i.e.
free surface and contact surface between layer and half space. On the free surface are setting
boundary conditions for normal and tangential surface force. We consider two types of contact
between layer and half space: rigid contact and slip contact. The initial-boundary value problem
was solved by using integral transformation and Cagniard- de Hoope methods. From the solution
of this problem follows that in layer and half space exist some kind of thermoelastic waves. We
investigated moreover the conditions which should be fullfiled for propagation of Raylaighs and
Loves type waves on the contact surface between layers and half space. Our results can be used
in technical applications especially engineering design and diagnostics of roads and airfields.
Delamination in visco-elastic materials with thermal effects
Marita Thomas (WIAS Berlin), Riccarda Rossi (Università di Brescia) Schedule
This contribution deals with the analysis of a model describing a rate-independent delamination
process along a prescribed interface. The material properties in the bulk are considered to be viscoelastic
and temperature-dependent. In the spirit of continuum damage mechanics the delamination

Section 14: Applied analysis 277
process is modeled with the aid of an internal delamination variable z. The related PDE system,
which couples the displacements, the absolute temperature and the delamination variable, has
a highly nonlinear character and features nonpenetration conditions. The goal is to obtain the
existence of weak solutions in the setting of brittle delamination, where the delamination variable
takes the values 0 or 1, only, and where the crack is described in terms of a transmission condition
being a local, nonconvex constraint, which links the displacements and the delamination variable
in a very rigid manner. In order to deduce this existence result the brittle model is consecutively
approximated by suitably regularized problems: On the one hand, the brittle constraint z ∈
{0, 1} is gained from a Modica-Mortola functional; on the other hand, the brittle transmission
condition is approximated by a surface energy term for so-called adhesive contact, which penalizes
displacement jumps outside the crack set but does not rigidly exclude them.
S14.2: Applied analysis, Session A Tue, 16:00–18:00
Chair: Alexander Mielke S1|03–113
Analytical model for deformable roll coating with nip feed
Bettina Willinger (Universität Erlangen-Nürnberg), Philipp Epple (Hochschule Coburg), Antonio
Delgado (Universität Erlangen-Nürnberg) Schedule
Nowadays roll coating is a common technique for applying thin coating films on continuous
substrates, e.g. paper and foils. Roll coating are operated either with co-rotating or counterrotating
rolls and the field of applications ranges from printable solar cells via composites to
adhesive labels. Key advantages are the comparatively simple technology and the possibility of
coating thin films using highly viscous fluids. On the other hand, the probably most important
disadvantage of roll coating systems compared to other coating technologies like curtain, spray or
slot coating is the self-metered coating process. A lot of experience and experiments are necessary
to find the proper parameters to coat a defined film thickness. Analytical solutions offer a good
possibility to find predictions for the necessary set-up parameters.
The presented work deals therefore with an analytical solution for a roll coater with deformable
rolls, as commonly used in industry. In this coating technique often a pair of a rigid (steel) roll
and a deformable roll is used. The deformable roll is in most cases a steel roll wrapped with an
elastic rubber layer. The focus is on the calculation of the nip feed system in a forward coating
mode.
The calculation is done with thin film theory, as it is an useful simplification of Navier-Stokes-
Equations for the presented case. For including the elasticity of the deformable roll Hooks law
for elasticity of the deformable roll are used. Pressure boundary conditions are introduced in the
calculation for getting a closed solution. The film splitting of the coating film is described by
a commonly used relation based on the calculations of Landau and Levich and experimentally
validated in literature.
The new model has been validated by experiments with an industrial roll coater. The analytical
prediction and the experimental data are in good agreement.
Estimations on Thermo-mechanical Dynamics of Vibration Elastomeric Isolators
Silviu Nastac, Carmen Debeleac (Dunarea de Jos University of Galati, Braila) Schedule
This analysis deals with one of the basic problem category of vibratory systems, means the complete
and complex characterization of elastic and viscous isolators behaviour under dynamic loads
such as vibrations, seismic waves, shocks, etc. Usually, the dynamic characteristics of vibration
isolators made by elastomeric materials are considered to have a constant shape for a certain
practical case. It is ignored the thermal phenomenon inside the isolator block during the exploita-

278 Section 14: Applied analysis
tion cycles and its influences on the proper characteristic parameters. This usual approximation
leads to more or less significant differences between simulation and practical evolution of a vibration
isolator subjected to the same dynamic load. Continuous changes of rigidity modulus and/or
dissipative characteristics due to internal thermal effects imply aleatory evolution of the isolated
system, unstable movements and resonance imminence danger. The partial results of this analysis
dignify the linkage between thermal effects into the elastomeric isolator and its essential dynamic
parameters. Using of these correlations frames the seismic shock and vibration protective devices
designing and deployment areas.
On Non-linear Characteristics Evaluation of Vibratory Tool and Terrain Interaction
for Embankment Works
Carmen Debeleac, Silviu Nastac (Dunarea de Jos University of Galati, Braila) Schedule
The complete and correct identification and evaluation of proper characteristics of terrain for embankment
works is the frame idea of this analysis. The study began from the necessity of vibratory
working tools utilization for different construction jobs. Mainly, the simple dynamic calculus is
used for estimation of proper parameters values for this kind of works. It supposes a linear characteristic
of the material in interaction with vibrating tool and it estimates the domain of working
parameters. But instrumental tests reveal that the terrain has a non-linear characteristic and the
dynamic behaviour acquires deviation from theoretical estimations. An identification procedure
followed by a correct and complete evaluation of the non-linear parameters gives the necessary
information for a practical case. Available mathematical models require a lot of initial values
for characteristic parameters, but changing the case changes the values. A complex model which
needs only initial tuning offers a proper solution to simulate, estimate, evaluate and analyze the
interactions between the vibratory tools of construction equipments and the terrain. Non-linear
static and dynamic characteristics are the basic model defined properties. Elastic, dissipative and
plastic rheological components were included into the main model. Partial concluding remarks
have shown a good approximation between numerical results and experiments. The results of
this study are very useful for vibratory equipment designing and correct exploitation, check of
Regulations conformity for construction technologies, and oldies equipments maintenance.
On the modeling of slender heat sources
Thomas Martin Cibis, Nicole Marheineke (Universität Erlangen-Nürnberg), Raimund Wegener
(Fraunhofer-ITWM Kaiserslautern) Schedule
In the production process of nonwoven materials thousands of long slender fibers are spun and
entangled by fast air streams before they are fall down onto a conveyor belt where they form
a nonwoven texture (web). The quality of the fabric is crucially determined by the fiber-flowinteractions.
Since the direct numerical simulation of this two-phase multi-scale problem is impossible,
we intend to model the two-way coupling on basis of slender-body theory and drag
sources that satisfy the actio-reactio principle in the balance laws of momentum and energy with
respect to flow and fibers. In this talk, we focus on the aspect of heat exchange treating the
fibers as long and slender heat sources. We introduce an asymptotic surrogate model in which
the three-dimensional objects are replaced by line sources. To evaluate this approach, a simplified
model scenario is investigated and solved analytically.
S14.3: Applied analysis, Session B Wed, 13:30–15:30
Chair: Robert Denk S1|03–113

Section 14: Applied analysis 279
A free boundary problem related to the spin-coating process
Matthias Geissert (TU Darmstart) Schedule
We consider the spin-coating process which is described by the Navier-Stokes equations in a layerlike
domain in 3 in the rotating setting. Our model takes into account Coriolis forces, centrifugal
forces as well as surface tension on the free boundary. On the fixed boundary we prescribe Robin
boundary conditions.
Our aim is to show local existence and uniqueness of strong solutions. In order to do so, we
transform this problem to a fixed layer by the Hanzawa transform and show maximal regularity
estimates for a suitable linearized problem.
Helically symmetric flows: Conservation laws using Lie symmetries
Olga Kelbin (TU Darmstadt), Alexei F. Cheviakov (University of Saskatchewan, Saskatoon), Martin
Oberlack (TU Darmstadt) Schedule
A new theoretical approach for helical flows using Lie symmetries is presented. By introducing
the helical variable ξ = az + bϕ, in which ϕ, z are cylindrical coordinates, we are able to derive
the Euler and Navier-Stokes equations for helically symmetrical flows in primitive variables as
well as in vorticity formulation. The obtained systems of equations unify the equations of planar
and axially symmetrical flows as being the natural limits characterized by two parameters a and
b.
Conservation laws are constructed using the direct method [1] . This method is based on the idea to
use the Euler operator to obtain the divergence expressions that comes originally from the ideas
related to famous Noether’s theorem, but is applicalbe to a much wider class of PDE systems.
In addition to classical well known conservation laws like conservation of mass, momentum, energy,
new infinite families of conservation laws are discovered.
[1] S. Anco, G. Bluman, A.F. Cheviakov. Applications of Symmetry Methods to Partial Differential
Equations, vol. 168. Springer: Applied Mathematical Sciences, 2010
On the ultra relativistic Euler equations
Mahmoud Abdelrahman, Matthias Kunik, Gerald Warnecke (Universität Magdeburg) Schedule
In this paper we study the relativistic Euler equations in isentropic fluids with the equation of
state p = ρ
, which is the ultra-relativistic limit. We first analyze the single shocks and rarefaction
3
curves. Then the Riemann problem is solved constructively. We derive sharp estimates for the
strength of the waves in the Riemann solution and prove uniqueness for the Riemann problem.
Finally we study explicit examples for the irreversibilty of the ultra relativistic Euler equations.
The exterior Dirichlet and the interior Neumann boundary value problems for the
scalar Oseen equation
Emma Skopin (Universität Kassel) Schedule
The scalar Oseen equation represents a linearized form of the Navier Stokes equations. We present
an explicit potential theory for this equation and solve the exterior Dirichlet and interior Neumann
boundary value problems via a boundary integral equations method in spaces of continuous
functions on a C 2 -boundary, extending the classical approach for the isotropic selfadjoint Laplace
operator to the anisotropic non-selfadjoint scalar Oseen operator.

280 Section 14: Applied analysis
Sufficient conditions for second order L 2 -convergence of the fractional step theta
method
Florian Zanger (Universität Kassel) Schedule
We consider the fractional step theta time stepping procedure for the non-stationary incompressible
linear Stokes equations in a cylindrical domain (0, T ) × G, where G is a bounded domain
in R n . Using energy estimates and assuming a certain degree of regularity for the data, we show
second order L 2 -convergence.
On Sharp Interface Limits of Diffuse Interface Models for Viscous Incompressible
Fluids
Helmut Abels (Universität Regensburg) Schedule
We present recent results on the sharp interface limits of a new diffuse interface model for two
viscous incompressible fluids with different densities. We will discuss how the sharp interface limit
depends on the choice of the mobility. The sharp interface limit is determined with the aid of the
method of formally matched asymptotics. Moreover, in some cases we can perform the limit on
the level of so-called varifold solutions rigorously.
S14.4: Applied analysis, Session B Wed, 16:00–18:00
Chair: Matthias Geissert S1|03–113
Convergence properties of weak solutions of the Boussinesq equations in domains
with rough boundaries
Christian Komo (TU Darmstadt) Schedule
We act on the assumption that the boundary of every ’physical’ domain Ω has microscopic asperities
which influence the boundary behaviour of weak solutions of the Boussinesq equations. Let
(Ωn)n∈N ⊆ R3 be domains with rough boundaries and let Ωn ’converge to’ Ω. Consider a sequence
(un, θn)n∈N of weak solutions of the Boussinesq equations with un fulfilling the impermeability
condition un · N = 0 on ∂Ωn and θn fulfilling the Robin boundary condition ∂θn
∂N + α(θn − h0) = 0
on ∂Ωn. In this talk the boundary conditions and limit equations of weak limits of (un, θn) on Ω
under certain assumptions of the rugosity of the boundaries will be determined.
Exponential stability for a general model in electrophoresis
Jürgen Saal, André Fischer, Dieter Bothe (TU Darmstadt) Schedule
We present a thorough analysis of the Navier-Stokes-Nernst-Planck-Poisson equations. This system
describes the dynamics of charged particles dispersed in an incompressible fluid. In contrast
to existing literature and in view of its physical relevance, we also allow for different diffusion coefficients
of the charged species. In addition, the commonly assumed electro-neutrality condition
is not required by our approach. Our aim is to present results on local and global well-posedness
as well as exponential stability of equilibria. The results are obtained jointly with Dieter Bothe
and Andre Fischer at the Center of Smart Interfaces at TU Darmstadt.
Validity of the Korteweg-de Vries Approximation for the Two-Dimensional Water
Wave Problem in the Arc Length Formulation
Wolf-Patrick Düll Schedule
We consider the two–dimensional water wave problem in an infinite long canal of finite depth both
with and without surface tension. It has been proven by several authors that long–wavelength
solutions to this problem can be approximated over a physically relevant timespan by solutions
of the Korteweg–de Vries equation or, for certain values of the surface tension, by solutions of the

Section 14: Applied analysis 281
Kawahara equation. These proofs are formulated either in Langrangian or in Eulerian coordinates.
In this talk, we provide a new proof, which is simpler, more elementary and shorter. Moreover,
the rigorous justification of the KdV approximation can be given for the cases with and without
surface tension together by one proof. In our proof, we parametrize the free surface by arc length
and use some geometrically and physically motivated variables with good regularity properties.
This formulation of the water wave problem has already been of great usefulness for Ambrose and
Masmoudi to simplify the proof of the local well–posedness of the water wave problem in Sobolev
spaces.
Cosymmetric problems and bifurcations without parameter
Andrey Afendikov (Keldysh Institute of Applied Mathematics, Moscow) Schedule
In the early 1990s V.Yudovich introduced the notion of cosymmetry. He discovered that steady
states are generically non-isolated in such problems and investigated the loss of stability and
the bifurcation of cycle generation. We consider several hydrodynamic problems in unbounded
domains where in a vicinity of the instability threshold the dynamics is governed by generalized
Cahn-Hilliard equation. For the time independent solutions of this equation we recover
Bogdanov-Takens bifurcation without parameter in the 3-dimensional reversible system with a
line of equilibria. This line of equilibria is neither induced by symmetries, nor by first integrals.
At isolated points, normal hyperbolicity of the line fails due to a transverse double eigenvalue
zero. The bi-reversible problem and its small perturbation where only one symmetry is left was
studied in [1],[2]. Our aim is to relate Yudovich theory to our results and to discuss hydrodynamic
problems, where the reversibility breaking perturbation can not be considered as small.
[1] A. Afendikov, B. Fiedler, and S. Liebscher. Plane Kolmogorov flows and Takens-Bogdanov
bifurcation without parameters: The doubly reversible case.Asymptotic Analysis, 60 (3,4),
(2008), 185–211.
[2] A. Afendikov, B. Fiedler, and S. Liebscher. Plane Kolmogorov flows and Takens-Bogdanov
bifurcation without parameters: The singly reversible case. Asymptotic Analysis, 72, n. 1-2
, (2011), 31–76
On a one-dimensional upper-convected Maxwell model for a viscoelastic fiber jet –
asymptotic derivation and numerical simulations
Maike Lorenz (TU Kaiserslautern), Nicole Marheineke (Universität Erlangen-Nürnberg), Raimund
Wegener (Fraunhofer ITWM) Schedule
In this talk we present a strict systematic derivation of a one-dimensional model for the dynamics
of a viscoelastic jet using asymptotic analysis in the slenderness ratio of the jet. The model is
obtained from the three-dimensional free boundary value problem of the upper-convected Maxwell
equations describing the flow of a viscoelastic fluid. It also covers the purely viscous case. The
model system has a hyperbolic character and contains several parameters that determine the
solvability of the equations and hence the applicability range of the model. For a stationary
uniaxial gravitational spinning process we show numerical simulations and investigate the effect
of a die swell, i.e. an increase in the jet diameter which is larger than the diameter of the nozzle
where the fluid is extruded.
S14.5: Applied analysis, Session C Thu, 13:30–15:30
Chair: Helmut Abels S1|03–113

282 Section 14: Applied analysis
On the Riesz minimal energy problem
Wolfgang L. Wendland (Universität Stuttgart) Schedule
This is on joint work with H. Harbrecht, G. Of and N. Zorii.
In Rn ≥ 2, we study the constructive and numerical solution of minimizing the Riesz energy
relative to the Riesz kernel |x − y| α−n , where 1 < α < n, for the Gauss variational problem. which
is considered for two compact, disjoint closed manifolds Γj ⊂ Rn , j = 1, 2, charged with Borel
measures of opposite sign. Since this minimizing problem over an affine cone of Borel measures
with finite Riesz energy can also be formulated as the minimum problem over an affine cone of
ε
− surface distributions belonging to a Sobolev–Slobodetski space H 2 (Γ), 0 < ε = α−1, Γ := Γ1∪Γ2,
the application of simple layer boundary integral operators on Γ can be used. The numerical
approximation is based on a Galerkin–Bubnov discretization with piecewise constant boundary
elements. For n = 3 and n = 2 multipole approximation and for 1 < α < 3 = n wavelet matrix
compression is applied. The minimizing procedure is executed with an active set strategy. We
finally present some numerical results.
Maximum modulus estimates for the linear steady Stokes system
Werner Varnhorn (Universität Kassel) Schedule
In the theory of partial differential equations the classical maximum principle is well-known.
It states that any non-constant harmonic function u takes its maximum (and minimum) values
always at the boundary ∂G of the corresponding domain G. For higher order differential equations
as well as for systems of differential equations such a principle does not hold in general. In these
cases, however, there is some hope for a so-called maximum modulus estimate of the form
max |u(x)| ≤ c max
G ∂G |u(x)|,
where c denotes some constant. We prove the validity of such an estimate for the linear Stokes
system via the method of boundary integral equations. Here G ⊂ R n (n ≥ 2) is some bounded
or unbounded open set having a compact boundary ∂G of class C 1,α (0 < α ≤ 1).
Blow-up of solutions to a p-Laplace equation
Yuliya Gorb (University of Houston) Schedule
The problem considered in this talk describes two perfectly conducting spheres in a homogeneous
medium where the current-electric field relation is the power law. Electric field E blows up in the
L ∞ -norm as δ, the distance between the conductors, tends to zero. A concise rigorous justification
of the rate of this blow-up in terms of δ will be given.
On asymptotic behavior of 1-dimensional functional of Ginzburg-Landau type with
internally-externally created oscillations of minimizers
Andrija Raguz (Zagreb School of Economics and Management, Department of Mathematics and
Statistics, Zagreb) Schedule
In this note we provide a kind of generalization of the well-known notion of internally (externally,
resp.) created oscillations of minimizers of non-convex integrands in the calculus of variations. As
an example, we consider a class of 1-dimensional Ginzburg-Landau functionals (the simplest case
being considered in the paper G. Alberti, S. Muller: A new approach to variational problems with
multiple scales, Comm. Pure Appl. Math. 54, 761-825 (2001)). We describe asymptotic behavior
leading to multiple small scale separation as parameter epsilon tends to zero.

Section 14: Applied analysis 283
Analysis and simulations of data based PDE-models in intracellular signaling
Elfriede Friedmann (Universität Heidelberg) Schedule
Complex biological processes in systems biology are usually reduced to a system of chemical
reactions taking place in a fluid medium. Rate equations link the reaction rate or velocity of
the reaction to the concentration of the reactants according to a specific law. With resulting
differential equations we obtain the evolution of signaling pathways over time and space. They
help to understand underlying mechanisms, explain certain characteristic behavior, or predict
the outcome of experiments. For intracellular systems, such as signaling pathways, most existing
models are based on ordinary differential equations. These models describe temporal processes,
while they neglect spatial aspects. In [9] and [10] experimental evidence was given that cell size
and shape can influence intracellular signaling. Basic theoretical work concerning this aspect can
be found in [2] and [7].
We will compare data-based (non)linear PDE models on the basis of reaction diffusion equations
with the corresponding ODE model of the JAK2/STAT5 and SMAD signaling pathway, to
analyze whether the cell geometry plays a significant role to its fate or not. It is an interesting
biological question, if the diffusion of signaling molecules leads to a roughly homogeneous distribution
or if we can observe a significant gradient of proteins in the cell. Such a gradient might affect
the signaling pathway and constitute a regulatory mechanism. In the cytoplasm, signaling may
be localized to certain areas. In addition, the signal to the nucleus may be delayed or modulated
by diffusive processes.
We present numerical simulations of these data-based models performed with the software
Gascoigne [6] developed in Rolf Rannachers group based on Finite Elements. With the high
quality numerical methods implemented in this software like adaptive mesh refinement, multigrid
algorithms and error control [1], [11], we are able to handle even more complex shapes within a
suitable computing time. We used different diffusion coefficients and calculated the spatial average
of each species’ concentration as the integral over the cytoplasmic domain divided by the volume
of the cytoplasm, i.e. uaverage(t) = 1
�
u(x, t). These average concentrations were plotted as
vcyt
Ωcyt
time courses and compared to the results of the pure ODE system.
Nevertheless, the outcome of our simulations can be significant only if we use as model input
high-quality quantitative data (provided by our collaboration partner from the German Cancer
Research Center [8]), and if we are able to establish some theoretical results to guarantee the
existence and uniqueness of solutions of our differential equation system.
We will present our analytical and numerical results and will show that diffusion in the model
can lead to significant intracellular gradients of signaling molecules and changes the level of
response to the signal transduced by the signaling pathway. In particular, the extend of these
observations will depend on the geometry of the cell.
[1] Becker, R., Rannacher, R., An optimal control approach to a posteriori error estimation in
finite element methods, Acta Numerica 10, 1-102, 2001.
[2] Brown, G. C., Kholodenko, B. N., Spatial gradients of cellular phospho-proteins, FEBS Letters,
457:452-454, 1999.
[3] Friedmann, E., Pfeifer, A. C., Neumann, R., Klingmüller, U., Rannacher, R., Interaction between
Experiment, Modeling and Simulation of Spatial Aspects in the Jak2/Stat5 Signaling
Pathway, Modellgestuetzte Parameterschaetzung - Theorie und Anwendungen, Springer, in
print.

284 Section 14: Applied analysis
[4] Friedmann, E., Neumann, R., Rannacher, R., Well-posedness for a spatio-temporal model of
the JAK2/STAT5 signaling pathway, submitted 2011.
[5] Friedmann, E., Claus, J., Rannacher, R., Spatial aspects in the SMAD signaling pathway,
submitted 2011.
[6] GASCOIGNE, High Performance Adaptive Finite Element Toolkit, URL: http://www.
numerik.uni-kiel.de/~mabr/gascoigne/.
[7] Kholodenko, B. N. Cell signalling dynamics in time and space, Nat. Rev. Mol. Cell Biol.,
7:3:165-176, 2006.
[8] Klingmüller, U., Bauer, A., Bohl, S., Nickel, P. J., Breitkopf, K., Dooley, S., Zellmer, S.,
Kern, C., Merfort, I., Sparna, T., Donauer, J., Walz, G., Geyer, M., Kreutz, C., Hermes,
M., Götschel, F., Hecht, A., Walter, D., Egger, K. Neubert, C. Borner M. Brulport, W.
Schormann, C. Sauer, F. Baumann, R. Preiss, L., MacNelly, S., Godoy, P., Wiercinska,
E., Cuiclan, L., Edelmann, J., Zeilinger, K., Heinrich, M., Zanger, U. M., Gebhardt, R.,
Maiwald, T., Heinrich, R., Timmer, J., von Weizsäcker, F., Hengstler, J. G., Primary mouse
hepatocytes for systems biology approaches: a standardized in vitro system for modelling
of signal transduction pathways, Syst Biol (Stevenage), 153:433-47, 2006.
[9] Meyers, J., Craig, J., Odde, D. J., Potential for Control of Signaling Pathways via Cell Size
and Shape, Current Biology, 16:17:1685-1693, 2006.
[10] Neves, S. R., Tsokas, P., Sarkar, A., Grace, E. A., Rangamani, P., Taubenfeld, S. M., Alberini,
C. M., Schaff, J. C., Blitzer, R. D., Moraru, I. I., Iyengar, R., Cell Shape and Negative Links
in Regulatory Motifs Together Control Spatial Information Flow in Signaling Networks, Cell,
133:4:666-680, 2008.
[11] Rannacher, R., Adaptive finite element discretization of flow problems for goal-oriented
model reduction, Computational Fluid Dynamics Review 2010, (M. M. Hafez, K. Oshima,
D. Kwak, eds), 51-70, World Scientific, 2010.
S14.6: Applied analysis, Session C Thu, 16:00–18:00
Chair: Robert Denk S1|03–113
Homogenization on Nonflat Surfaces and Applications
Sören Dobberschütz (Universität Bremen) Schedule
The notion of periodic unfolding has become a standard tool in the theory of periodic homogenization,
which has been applied to many problems. However, all the results obtained so far deal
only with domains or boundaries of domains in the flat Euclidean space R n for some n ∈ N. In
the talk, we present a generalization of the method of periodic unfolding which is applicable to
certain classes of compact Riemannian manifolds. The method is then applied to a simple elliptic
model-problem for illustration.
Covering Surfaces with Noncommutative Monodromy Groups and their Industrial
Applications
Irina Dmitrieva (Odessa National Academy of Telecommunications, Odessa) Schedule

Section 14: Applied analysis 285
Let an arbitrary algebraic (compact) Riemann surface R be given, and its finite genus ρ ≥ 0. We
are looking for the function f(z, u), (z, u) ∈ R, that is analytic everywhere on R except the finite
set of ramification points, has a finite order at infinity and its values undergo the m-dimensional
permutations when come around these ramification points.
The search of such multi-valued (here is m-valued) function by its monodromy group that
is described by the ramification points and respective permutations, leads to the solution of the
corresponding homogeneous vector Riemann problem with the boundary condition:
F + (t, v) = M(t, v)F − (t, v), (t, v) ∈ L =
M(t, v) =
n�
Miδ(t, v; Li), D −1 |(F ).
i=1
n�
i=1
Li, Lj
� Lk = ∅, (j �= k);
Here: F = F (z, u) = {Fj(z, u)} m j=1 is the class of unknown m-dimensional vector-valued functions
that are analytic everywhere on surface R outside the finite system of open contours L whose
endpoints are the original ramification points; F are bounded at the endpoints of L, extend to
it H-continuously from the left and right, have the finite order at infinity and F ± (t, v) are the
limited values of F at L from the left and right respectively; Mi(i = 1, n) is the so called m × m
permutation matrix that is raised by the appropriate permutation from the aforesaid monodromy
group and δ is the Kronecker symbol; D is the m-dimensional vector-valued divisor of infinities
and F is divisible by it. Each the sought for scalar component Fj(z, u) (j = 1, n) is the jth branch
of the initially wanted multi-valued function f(z, u).
The explicit solution of the given problem generates the construction of the relevant algebraic
equation of the covering with respect to the surface R. The last fact and the corresponding matrix
Riemann problem have the majority of industrial applications in technical electrodynamics, optics,
acoustics, various wave propagation, etc., and are interesting mostly in the noncommutative case
that is studied here.
We suggest also some illustrative examples of the covering surfaces’ construction with noncommutative
monodromy groups, and whose corresponding algebraic equations have direct industrial
applications.
Backscatter data in electric impedance tomography
Stefanie Hollborn, Martin Hanke (Universität Mainz), Nuutti Hyvönen (Aalto University) Schedule
This talk presents the concept of backscatter data in electric impedance tomography. These sparse
data are the analogue to so-called backscattering data in inverse scattering. They arise in practice
if the same single pair of electrodes is used to drive currents and measure voltage differences
subsequently at various locations on the boundary of the object to be imaged. A single insulating
cavity within an otherwise homogeneous object is uniquely determined by its backscatter data.
However, this is in general not true for a perfectly conducting inclusion. The talk presents the
uniqueness proof for an insulating cavity, and it outlines a reconstruction algorithm based thereon.
Furthermore, the non-uniqueness for perfect conductors is illustrated by an example. The
results presented here arise from joint research with Martin Hanke and Nuutti Hyvönen.

286 Section 15: Applied stochastics
Section 15: Applied stochastics
Organizers: Steffen Dereich (Universität Marburg), Hanno Gottschalk (Bergische Universität
Wuppertal)
S15.1: Applied Stochastics Wed, 13:30–15:30
Chair: Hanno Gottschalk S1|02–344
Almost Sure Stability Criterion for Parametric Roll in Random Seas Based on Top
Lyapunov Exponent
Leo Dostal, Edwin Kreuzer (TU Hamburg-Harburg), Navaratnam Sri Namachchivaya (University
of Illinois at Urbana-Champaign) Schedule
A criterion for the stability of the upright position of a ship in random head or following waves
is presented. Such waves lead to parametric excitation of roll motion due to periodic variations
of righting lever. The development of simple criteria for occurrence of parametric induced roll
motion in random seas is of major interest for improvement of the international code on intact
stability provided by the International Maritime Organization. The criterion is based on calculation
of the top Lyapunov exponent using the fact, that a negative top Lyapunov exponent yields
no roll motion. With this criterion, roll motion is excluded for specific sea states.
The Analysis of Stochastic Fiber Lay-Down Models: Geometric Formulation, Operator
Semigroups and Convergence to Equilibrium
Patrik Stilgenbauer, Martin Grothaus (TU Kaiserslautern) Schedule
The so called fiber lay-down models arise in the production process of nonwovens. These new
mathematical models have been developed in recent years and provide an interesting interplay
between functional analysis, stochastics and differential geometry. The models are of stochastic
nature and can precisely be formulated in a geometric language as stochastic differential equations
on manifolds. An important criterion for the quality of the nonwoven material is how the solution
to the associated Fokker-Planck equations converges towards its stationary state. Especially, one
is interested in determining the speed of convergence. Thus the analytic study of the models
yields to the investigation of their corresponding Kolmogorov- and Fokker-Planck operators. To
solve the Cauchy problems we make use of the theory of operator semigroups. Techniques from
the theory of Dirichlet forms as well as hypocoercivity are used for analyzing the convergence
to equilibrium. Summarizing, the models show up a fascinating interaction between applied and
pure mathematics.
A Smooth 3D Model for Fiber Lay-down Processes
Johannes Maringer, Axel Klar, Patrik Stilgenbauer (Technische Universität Kaiserslautern), Raimund
Wegener (Fraunhofer ITWM Kaiserslautern) Schedule
We present an improved three dimensional stochastic model concerning the fiber lay-down in the
production process of nonwoven materials. The model describes the position of the deposited fibers
on a conveyor belt, which is determined by a system of stochastic differential equations. Here
we remove a drawback of a previous 3D model, that is the non-smoothness of the fiber paths.
Besides the derivation of the smooth 3D model we show its connection to the non-smooth model
in a white noise limit.
Brownian Dynamics of Rigid Body by Fluctuating Hydrodynamic Equations
Anamika Pandey, Axel Klar, Sudarshan Tiwari (TU Kaiserslautern) Schedule

Section 15: Applied stochastics 287
The current work focuses on a meshfree simulation for the Brownian dynamics of rigid body in
an incompressible viscous fluid. The Brownian dynamics of rigid body is demonstrated by fluctuating
hydrodynamic equations coupled with the equation of motion for rigid body. The rigid
body accomplishes random motion through the hydrodynamic force acting on its surface from
the surrounding fluid. Fluctuation is incorporated in fluid equation via random stress.
The used meshfree method is a promising numerical approach to simulate multiphase flow and
irregular geometries. Though, it is challenging to work in a meshfree framework with stochastic
partial differential equations(SPDEs) but it has advantage to deal interface boundary in fluid-solid
interaction and in many future application such as study of complex fluid. A successful meshfree
scheme for the simulation of fluctuating hydrodynamic equations in the case of compressible
flow has been presented by Pandey et al. [2]. The previous study by Sharma and Patankar [1]
for investigating Brownian dynamics by fluctuating hydrodynamic equations neglects the inertia
term and focuses on resultant Stokes problem. Furthermore, the fluid-solid domain is considered
to be a fluid and fixed grid method is employed for spatial discretization.
The mathematical formulation in present study can be described as:
• The fluid flow is modeled by Landau-Lifshitz-Navier-Stokes equation.
• No body force was applied either in the particle domain or the fluid domain. However,
the force due to random stress induces fluctuation in fluid, which will lead to Brownian
dynamics of rigid body.
• Compute forces on the surface of rigid body due to surrounding fluid.
• Newton-Euler equations modeled the motion of rigid body.
Unlike the conventional Brownian dynamics type approaches, the random term is incorporated
in fluid equation to capture the Brownian dynamics of rigid body.
[1] N. Sharma and N. A. Patankar. Direct numerical simulation of the Brownian motion of
particles by using fluctuating hydrodynamics equations. J. Comput. Phys. 201(2) : 466-
486, 2004.
[2] A. Pandey, A. Klar and S. Tiwari. Meshfree Method for the Stochastic Landau-Lifshitz
Navier-Stokes Equations. Proc. II International Conference on Particle-based Methods Fundamentals
and Applications (2011).
Strong approximation of the Cox-Ingersoll-Ross process
S. Dereich (Universität Marburg/Universität Münster), A. Neuenkirch (TU Kaiserslautern), L.
Szpruch (Oxford University) Schedule
We analyze strong approximation of the Cox-Ingersoll-Ross (CIR) process in the regime where
the process does not hit zero by a positivity preserving drift-implicit Euler-type method. As an
error criterion we use the p-th mean of the maximum distance between the CIR process and its
approximation on a finite time interval. We show that under mild assumptions on the parameters
of the CIR process the proposed method attains, up to a logarithmic term, convergence of order
1/2.

288 Section 15: Applied stochastics
S15.2: Applied Stochastics Wed, 16:00–18:00
Chair: Steffen Dereich S1|02–344
Fixed design regression estimation based on experimental and artificially generated
data.
Dmytro Furer, Michael Kohler (TU Darmstadt) Schedule
In this article we study least squares estimates based on experimental and artificially generated
data. The artificially generated data comes from already undertaken estimates on the basis of
similar experiments. It is investigated under which condition the rate of convergence of least
squares estimates applied to this data is better then the rate of convergence of least squares
estimates applied to the experimental data.
Estimation of the optimal design of a nonlinear parametric regression problem via
Monte Carlo experiments
Ida Hertel, Michael Kohler (TU Darmstadt) Schedule
A Monte Carlo method for estimation of the optimal design of a nonlinear parametric regression
problem is presented. The basic idea is to produce via Monte Carlo values of the error of a
parametric regression estimate for randomly chosen designs and randomly chosen parameters and
to use nonparametric regression to estimate from this data the design for which the maximal
error with respect to all possible parameter values is minimal. A theoretical result concerning
consistency of this estimate of the optimal design is presented and the method is used to find an
optimal design for an experimental fatigue test.
Keywords and phrases: Optimal design, nonparametric regression, consistency.
On the statistical performance of optimizers applied to random processes and fields
Hanno Gottschalk (Universität Wuppertal) Schedule
As a mean to measure and compare performance and robustness of optimization algorithms, we
apply them to Gaussian random fields in d=1,2.

Section 16: Optimization 289
Section 16: Optimization
Organizers: Florian Jarre (Universität Düsseldorf), Arnd Rösch (Universität Duisburg-Essen)
S16.1: Shape optimization and forming processes Tue, 13:30–15:30
Chair: Arnd Rösch S1|01–A3
A second order approximation technique for robust shape optimization
Adrian Sichau, Stefan Ulbrich (TU Darmstadt) Schedule
We present a second order approximation for the robust counterpart of general uncertain nonlinear
programs with state equation given by a partial differential equation. We show how the approximated
worst-case functions, which are the essential part of the approximated robust counterpart,
can be formulated as trust-region problems that can be solved efficiently. Also, the gradients of
the approximated worst-case functions can be computed efficiently combining a sensitivity and
an adjoint approach. However, there might be points where the approximated worst-case functions
are nondifferentiable. This is referred to as the hard case. Hence, we introduce an equivalent
formulation of the approximated robust counterpart, in which the objective and all constraints
are differentiable functions. This method is applied to shape optimization in structural mechanics
in order to obtain optimal solutions that are robust with respect to uncertainties in acting forces
and other quantities. Numerical results are presented.
Mesh Regularization in parameter-free Shape Optimization
E. Stavropoulou, M. Hojjat, R. Wüchner, K.-U. Bletzinger (TU München) Schedule
In parameter-free shape optimization, no relation between the different degrees of freedom is established
and the design variables are the position of the finite element nodes. This gives a great
flexibility in exploring the design space. However, special care has to be given in preventing the
quality of the surface mesh. For this, an in-plane-regularization method is established. Moreover,
the computed gradients are usually noisy and contain spurious modes which have to be removed
for several reasons such as mesh dependency and manufacturing limits. To remove this problem,
an out of plane regularization method is integrated in the optimization process.
More precisely, the in-plane regularization is a global method which regularizes the finite element
mesh to a desired condition [1],[2]. In this method, an artificial stress field is applied on the surface
or on the volume mesh and a global linear system of equations is solved. The applied stress adapts
each element towards a desired predefined template geometry and at the end a globally smooth
mesh is achieved. In this way both the shape and the size of each element is effectively controlled.
On the other hand, in out of plane regularization the sensitivity field is smoothened with a local
method. Here, non-parametric regression is used and the continuous sensitivity field is established
by convolving the gradients with a kernel function.
The optimization framework as well as the position of these modules in the optimization chain
is presented. Various examples which motivate the use of the aforementioned methods are shown
and the application of the overall methods in fluid and fluid-structure interaction problems is
demonstrated.
[1] K.-U. Bletzinger, R. Wüchner, F. Daoud and N. Camprubi, Computational methods for form
finding and optimization of shells and membranes, Computer Methods in Applied Mechanics
and Engineering 194(30-33) (2005), 3438-3452.
[2] R. Wüchner, K.-U. Bletzinger, Stress-adapted numerical form finding of pre-stressed surfaces
by the updated reference strateg, International journal for numerical methods in engineering

290 Section 16: Optimization
64(2) (2005), 143-166.
Multipoint Aerodynamical Global Shape Optimization of the Flying Configurations
with Spanwise Movable Leading Edge Flaps, in Supersonic Flow
Adriana Nastase (RWTH Aachen) Schedule
The aerodynamical multipoint global optimization (GO) of the shape of a flying configuration
(FC), fitted with leading edge flaps movable in spanwise direction, leads to two enlarged variational
problems at two different cruising Mach numbers.Let us further suppose that the surfaces
of the wing, of the fuselage and of the flaps of FC in open position are approximated in form of
different superpositions of homogeneous polynomes in two variables.The coefficients of these polynomes
and the similarity parameters of the planforms of the FC, flying with movable leading edge
flaps in closed and, respectively, in open position, are the parameters of optimization. Meshless
discontinuous hybrid numerical solutions for the full Navier-Stokes layer (NSL) are used here as
start solutions for the GO shape of FC. These NSL’s solutions use own analytical hyperbolic potential
solutions of the flow over the same FC twice. Firstly, as outer flow, at the NSL’s edge and,
secondly, the velocity’s components are products between the corresponding potential velocities
and polynomial expansions with arbitrary coefficients, which are used to satisfy the NSL’s PDEs.
The first enlarged variational problem consists in the determination of the GO shape of the surface
and of the similarity parameters of the planform of FC, flying with the flaps in retracted position,
which is of minimum drag, at the higher supersonic cruising Mach number. The constraints are:
the lift and the pitching moment coefficients of FC are given, the Kutta condition on the subsonic
leading edges of the wing is fulfilled, the relative volumes of the wing and of the fuselage are given,
the leading edges are sharp and the integration conditions along the junction lines wing/fuselage
are fulfilled (i.e. the wing and the fuselage have same tangent planes along their junction lines).
The second variational problem consists in the determination of the shape of the surface and of
the planform of the leading edge flaps, in such a manner that the entire FC, with the flaps in open
position, is of minimum drag at the second, lower supersonic cruising Mach number. The value
of the lift and pitching moment coefficients of the FC and the relative volume of the flaps are
given. The iterative optimum-optimorum theory of the author is used for the multipoint global
optimization of the FC’s surface and of the similarity parameters of the planforms of the FC with
flaps in open and in retracted position.
Keywords: 76N25 Flow control and optimization, 76D05 Navier-Stokes equations,76J20 Supersonic
flow. (2010 MSC)
Optimal control of hydroforming processes
Daniela Koller, Stefan Ulbrich (TU Darmstadt) Schedule
The sheet metal hydroforming process is a complex forming process, which involves contact, friction
and plasticity to manufacture complex curved sheet metals with bifurcated cross section.
These sheet metals are examined within the framework of the Collaborative Research Centre
(CRC) 666. Mathematically, the sheet metal hydroforming process leads to a quasi-variational
inequality. We seek for optimal controls for typical control variables, e.g. the time dependent
blank holder force and the fluid pressure.
As a first step derivative-free optimization algorithms were used to control the hydroforming
process. The commercial FEM-software ABAQUS is invoked for the simulations. Numerical examples
with appropriate objective functions for this new kind of manufacturing process for sheet
metals will be presented.

Section 16: Optimization 291
To reduce the runtime of the optimization process, algorithms based on reduced models are
under investigation. In this context we want to use a POD Galerkin approach. Preliminary numerical
results for the reduced order model approach will be presented.
Numerical optimization of process parameters for combined quasi-static and impulse
forming
Marco Rozgic (Universität der Bundeswehr Hamburg), Farhad Taebi (TU Dortmund), Marcus
Stiemer (Universität der Bundeswehr Hamburg) Schedule
Recent results in forming technology indicate that forming limits of classical quasi-static forming
processes can be extended by combining them with fast impulse forming. However, in such combined
processes, process parameters have to be chosen carefully, to eventually achieve an increase
in formability. In this work a numerical optimization method is presented to identify process parameters
of combined deep drawing and electromagnetic forming. This leads to an extension of
classical quasi-static forming limits. The parameter space comprises contributions of the triggering
current (e.g. frequency, amplitude, damping, etc.), geometric descriptions of the tool coil as well
as deep drawing parameters (e.g. drawing radii or tribological parameters). The quality of a given
parameter set is determined by computing the distance of the simulated forming result to the
prescribed ideal shape. A finite element simulation of the combined process computes the target
function. To avoid a large number of target function evaluations, a gradient-based optimization
scheme is employed. Forming limits have to be incorporated as constraints to the optimization
process, considering rate dependence and prestrain in the second impulse forming step.
Geometry Optimization of Branched Sheet Metal Products
Thea Göllner, Wolfgang Hess, Stefan Ulbrich (TU Darmstadt) Schedule
We consider the geometry optimization of hydroformed branched sheet metal products, which
can be produced integrally and continuously using the new technologies of linear flow splitting
and linear bend splitting. These are explored within the framework of the Collaborative Research
Centre (CRC) 666.
The geometry of such products can be parameterized by means of free form surfaces whereas their
mechanical behaviour is described by the three dimensional linear elasticity equations.
The associated PDE-constrained problem for optimizing the stiffness of the structure is formulated.
An algorithm for solving this problem using exact constraints and a globalization strategy
based on adaptive cubic regularization is presented. Numerical results for an example are given.
S16.2: Applied optimization Tue, 16:00–18:00
Chair: Arnd Rösch S1|01–A3
Parameter identification based on multiple inhomogeneous experiments of practical
relevance
D. Schellenberg (Deutsches Institut für Kautschuktechnologie), J. Ihlemann (TU Chemnitz),
D. Juhre (Deutsches Institut für Kautschuktechnologie) Schedule
The quality and validity of FEM simulations is limited by the suitability of the used material model
and its related material parameters. Especially in the field of rubber materials high advanced
material models have been developed. Therefore, disadvantages of current standard procedures
to identify material parameters have gained in importance.

292 Section 16: Optimization
Usually, current available procedures are based on experiments with simple test specimens.
Furthermore, the load distribution is approximately homogeneous. Of course, this results in low
computational costs and allows to directly characterize the material behaviour. Unfortunately,
the restriction to homogenous experiments leads to losses in the reliability of the identified parameters.
On the one hand, there are only few feasible experiments, which produce homogeneous
or almost homogeneous load distributions. On the other hand, deviations from homogeneity and
their consequences cannot be avoided and are often ignored.
In this work, we present a solution algorithm, which takes several different experimental results
into account. Thereby, the experiments are performed on specimens which respond with
inhomogeneous distributions of strains and stresses. The restriction to homogeneous loads is not
necessary. Thus, it is possible to use different measurement results of multiple load cases on one
and the same test specimen. The intentional design of the specimen permits to consider the specific
properties of product groups and load types already during the identification process. In
addition, the effect of the manufacturing process on the final material properties can be incorporated.
Reducing the Model-Data Misfit in a Marine Ecosystem Model Using Periodic Parameters
and Linear Quadratic Optimal Control
Mustapha El Jarbi, Thomas Slawig (Universität Kiel), Andreas Oschlies (Leibniz-Institut für
Meereswissenschaften) Schedule
This paper presents the application of the Linear Quadratic Optimal Control (LQOC) method for
a parameter optimization problem in a marine ecosystem model. The ecosystem model simulates
the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column with
temperature and turbulent diffusivity profiles taken from a three-dimensional ocean circulation
model. Marine ecosystem models are coupled systems of partial differential equations (PDEs) consisting
of time-dependent advection-diffusion-reaction equations with nonlinear coupling terms.
The turbulent diffusivity, temperature and salinity fields are either computed simultaneously or
in advance by a physical ocean model. Clearly, the second variant is computationally cheaper but
neglects the biology’s feedback effects via impacts on the absorption of solar radiation, generally
assumed to be small relative to uncertainties in the boundary conditions such as surface heat
fluxes. The model uses the ocean circulation and temperature field in an off-line mode, i.e. these
are used only as forcing, but no feedback on them is modeled. The model simulates one water
column at a given horizontal position, which is motivated by the fact that there have been special
time series studies at fixed locations, one of which was used here. We present a linearization
method which is based on the available observations. The linearization is necessary to apply the
LQOC method on the nonlinear system of state equations. We derive the linearized time-variant
problems and two algebraic Riccati Equations. By using the LQOC method, we are able to introduce
temporally varying periodic model parameters and to significantly improve – compared
to the use of constant parameters – the fit of the model output to given observational data.
An Approach to Incremental Support Vector Machine Learning Algorithm for Classification
Kaboon Thongtha (King Mongkut’s Institute of Technology Ladkrabang, Thailand) Schedule
Incremental learning techniques are important tools to operate information data from internet
updating achieves faster. Support Vector Machine (SVM) duties well for incremental learning
model with impressive performance for its prominent power to summarize the data space in a
short way. This research proposes a heuristic algorithm to incremental learning with SVM taking

Section 16: Optimization 293
the possible effect of new training data to history data into account. The partition different set
has fewer elements, and existing hyperplane is closer to the optimal one is used in the algorithm.
The modified support vectors in the algorithm comprise of existing support vector, partition
difference set of new training data and history data by adding partition difference sets and reduce
the computation process by creating new classification of hyperplane on support vector set. The
examples show that algorithm is effective to develop the classification precision.
Sonofusion: EA optimisation of acoustic resonator
Markus J. Stokmaier, Andreas G. Class, Thomas Schulenberg (KIT), Richard T. Lahey Jr. (Rensselaer
Polytechnic Institute) Schedule
Describing imploding cavitation bubbles in a liquid excited by standing sound waves in terms of
continuum mechanics allows the formation of concentric supersonic shock fronts in the vapourfilled
bubble’s inside and represents a mathematical singularity. This implies extreme pressures
and temperatures when the shock reaches the center. The energy-focussing capability of the
singularity is confirmed through experimental observation of accompanying sonoluminescence
(SL) flashes with spectra corresponding to black body radiation of up to 2 · 10 4 K [1]. However,
due to the plasma’s opaqueness and small mass, experiment-based estimation of peak plasma
conditions is extremely difficult. Estimations from first principles have substantial difficulties in
modeling the extreme equations of state and with simulations of molecular dynamics they share
the problem of quantifying the multi-scale energy transport phenomena based on particle collision
and radiation.
Both, theory and experiment suggest the potential of reaching fusion conditions at the singularity.
That motivated sonofusion experiments, i.e. the attempt to detect 2.45 MeV neutrons
and tritium production accompanying SL in deuterated liquids as tracers of D-D fusion. These
comprise publications by Taleyarkhan et al. [2,3] starting in 2002 claiming successful experimental
sonofusion detection, but they are so far lacking independent verification.
The current work is based on 2D-axisymmetric harmonic structural FE simulations of the
liquid-filled acoustic resonators used for sonofusion experiments. We determine a substantial sensitivity
of the sound pressure amplitude performance of the resonators to a majority of the design
parameters. We claim that sonofusion experiments based on manually manufactured resonators
of the current design are not reproducible. Thus they can neither verify nor falsify Taleyarkhan’s
findings.
Our contribution to make sonofusion experiments reproducible, is the development of novel
resonator designs consisting of CAD-machinable parts. We present the application of evolutionary
algorithms (EA) to the resonator design optimisation problem, which is a high-dimensional multimodal
search task. An own EA approach is presented and compared to the evolution strategy
with covariance matrix adaption (CMA-ES) [4]. For a population size of 80 and for the total
number of evaluation calls limited to less than 10 4 the own algorithm yields acceptable results
with much higher probability.
[1] K.S. Suslick, D.J. Flannigan, Inside a Collapsing Bubble: Sonoluminescence and the Conditions
During Cavitation, Annu. Rev. Phys. Chem. 59 (2008), 659 – 683.
[2] R.P. Taleyarkhan, C.D. West, J.S. Cho, R.T. Lahey Jr., R.I. Nigmatulin, R.C. Block, Evidence
for Nuclear Emissions During Acoustic Cavitation, Science 295 (2002), 1868.
[3] R.P. Taleyarkhan, J.S. Cho, C.D. West, R.T. Lahey Jr., R.I. Nigmatulin, R.C. Block, Additional
evidence of nuclear emissions during acoustic cavitation, Phys. Rev. E 69 (2004),
036109.

294 Section 16: Optimization
[4] N. Hansen, A. Ostermeier, Completely Derandomized Self-Adaptation in Evolution Strategies,
Evolutionary Computation 9 (2001), 159 – 195.
Fuzzy-stochastic models for solving CVRPFD
Yuriy P. Kondratenko, Leonid P. Klymenko, Galyna V. Kondratenko (Petro Mohyla Black Sea
State University, Mykolaiv, Ukraine), Igor P. Atamanyuk (Mykolaiv State Agrarian University,
Mykolaiv, Ukraine) Schedule
In many cases the Vehicle Routing Problem (VRP) can be solved using corresponding mathematical
models, exect optimisation algorithms, operations research methods and mathematical
programming. Problem statement, size of set of nodes, existing restricitions and assumptions are
main factors which have significant impact to a choise of solving heuristic.
The CVRP (Capacitated Vehicle Routing Problem) is considered with focus to VRP for tankerrefuellers
which should provide bunkering operations (BO) for various ships. These ordered ships
may be located in different ports or in different sea points. The efficiency of BO is evaluated
by possibility to serve all ordered ships with minimum total length of tankers routes and with
maximum possible quantity of unloaded fuel.
Comparing modelling results for CVRP with crisp demands based on different heuristic (genetic
algorithm, ant colony models, saving algorithm, sweeping algorithm and other) are under
discussion.
Marine practice shows that very often the information about fuel demands is uncertain. The
fuzzy logic algorithms (FLA) are designed by authors for solving CVRP with fuzzy demands
(CVRPFD) and for special sets of input data. For testing and verification of proposed models
authors use fuzzy-stochastic approach.
Among finding of this research are: classification of conflict situations in CVRPFD, stochastic
simulation models of prognoses and real demands for modeling and optimization in uncertainty;
methods for increasing efficiency of CVRPFD solving by adjusting critical value of satisfaction
level for node-applicant in conflict situations.
Average value of critical parameter (desired satisfaction level or preference level) is determined
as 0.5 based on the 10000 fuzzy-stochastic models of uncertain demands in one program for each
port (CVRPFD with 32 ports and 8 marine bunkering programs).
Modelling results confirm the efficiency of suggested intelligent models and fuzzy-stochastic
approach for solving CVRPFD in marine environment.
The main contribution of this research deals with development of intelligent models and algorithms
for solving CVRPFD and design of fuzzy decision support system (DSS) which suggests
alternative decisions to decision-maker.
Using the Elements of Manufacturing Systems Management in the Calculation of the
Implementation of a Serial-Modular Industrial Robot within a Flexible Work Cell
Designed for Special Applications
Marius Alexandru Rizescu, Silviu Mihai Petrisor (Nicolae Balcescu Land Forces Academy, Sibiu,
Romania) Schedule
Organizing the manufacturing activity with industrial robots is a design activity based on the
synthetic analysis of the type of production, the type of equipments used and the products obtained
within those processes. As part of the flexible work cell (F.W.C.), the technological flow
may maintain a certain feature dictated by the operations plan, a situation in which the part
moves either successively from one equipment to another, or randomly, depending on the type of
parts processed within the cell. The flexibility of the work cell serviced by the robot is not given

Section 16: Optimization 295
by the very presence of the robot within the work cell, but by the type of equipments within the
cell. The flexible work cell stands as a developed manufacturing system, and not only because of
the fact it is the most recent concept in the field of material goods manufacturing, but mostly
because it triggers a significant improvement in the economy of the manufacturing process, given
that it is focused on the needs for real and prevailing goods of the human society, that is, widely
diversified goods in terms of typology which are produced in small quantities. In this paper,
the authors propose a basic design of a flexible work cell with a parallel organization, destined
for the spot welding of AAV carcasses. The cell is serviced by three industrial TTR robots that
perform spot welding operations on the carcasses flowing on the conveyor belt to each of the
robots performing this operation. This paper presents economic issues on the value of the robots
comprised by the system, the calculus of the entire F.W.C. value, the determination of the FWC
static configuration, and evaluates the overall profitability of the cell using elements pertaining
to the mathematical game theory and the graph theory, as well.
S16.3: Semidefinite programs and structural optimization Wed, 13:30–15:30
Chair: Florian Jarre S1|01–A3
Data reduction in magnetic resonance imaging by vector and semidefinite optimization
Gabriele Eichfelder (Universität Erlangen-Nürnberg), Matthias Gebhardt (Siemens Healthcare,
Erlangen) Schedule
In parallel transmission applications in magnetic resonance imaging the supervision of local specific
absorption rate (SAR), which is a measure of the rate at which energy is absorbed by the
body, is crucial. One existing approach is to use electromagnetic simulations including human
anatomical models and to precalculate the electric field distributions of each individual channel.
These can be superposed later with respect to certain combined excitations under investigation,
and the local SAR distribution can be evaluated. Local SAR maxima can be obtained by
exhaustive search over all investigated subvolumes of the body model.
However, optimizing local SAR in radiofrequency pulse design using constraints for each subvolume
is impractical due to the large number of subvolumes (300 000 up to 1 000 000 subvolumes).
We present in this talk a method for reducing this complexity significantly. From a mathematical
point of view the subvolumes are represented by a set of matrices and we are interested in the
maximal elements of this set with respect to the partial ordering defined by the cone of positive
semidefinite matrices, i.e. we have to solve a discrete vector optimization problem.
For a larger effect on the data reduction new matrices are constructed which serve as such
maximal elements and which are then called Virtual Observation Points. For that, the matrices
representing the subvolumes are clustered iteratively by a similarity measure and for each cluster a
new matrix is determined by a linear semidefinite optimization problem. By allowing a predefined
overestimation we reach a significant reduction of the number of matrices which have to be
considered for a supervision of the local SAR maxima.
On the solution of the Roothaan equations by nonlinear semidefinite programming
Michael Stingl, Tim Clark (Universität Erlangen-Nürnberg), Michal Kocvara (University of Birmingham)
Schedule
The Roothaan equations are finite dimensional representations of the Hartree-Fock equation, a
well established approximation of the time-independent electric Schrödinger equation. It is shown

296 Section 16: Optimization
that introducing the so called density matrix P ∈ S n + with properties
P 2 = 2P, tr(P ) = N
for a given integer N < n, the Roothaan equation can be turned into a nonlinear program of the
type
min E(P ) (1)
P ∈Sn tr(P ) = N
P 2 = 2P
where E : S n → R is a non-convex quadratic energy function of P . The projection type constraint
P 2 = 2P forces the eigenvalues of P to 0 or 2. In order to get rid of this integer character of
the problem, the projection constraint is relaxed and one obtains the nonlinear (non-convex)
semidefinite program
min E(P ) (2)
P ∈Sn tr(P ) = N
0 � P � 2P
which can be solved efficiently by the nonlinear SDP algorithm Pennon. It is shown that due to
properties of the energy function E the relaxation (2) is exact under reasonable assumptions and
further that each KKT-point of (2) is indeed a solution of the Roothaan equations.
The presentation is concluded by discussing a series of numerical experiments. It is demonstrated
that instances of the Roothaan equations can be successfully treated by the nonlinear SDP
approach, which due to the best knowledge of the authors have not been solved in the literature
before by the ’standard’ SCF approach.
Robust Design of active trusses via Mixed Integer Semidefinite Programming
Kai Habermehl, Stefan Ulbrich (TU Darmstadt) Schedule
This work is an extension of Ben-Tal and Nemirovskis approach on Robust Truss Topology Design
to active trusses. Active trusses may use active components (e.g. piezo-actuators) to react on
uncertain loads. We present the implementation of optimal positioning of active components
within a truss.
The approach is based on a semidefinite programming problem, which is a well-known optimization
approach for robust truss topology design. By introducing actors into the model, it
becomes a nonlinear semidefinite program with binary variables. Discrete-continuous mathematical
optimization problems arise and no state-of-the-art solver is known that delivers an efficient
solution method to solve these problems. We use a sequential semidefinite programming approach
within a branch-and-bound-framework to solve the problems.
Different uncertainty sets are analyzed for the robust optimization approach mainly polyhedral
and ellipsoidal uncertainty sets. These different approaches have their specific advantages and
disadvantages. A combined approach seems to be the best way to deal with active elements in
robust truss topology design.
Several solution methods (e.g. Cascading techniques, projection approaches) and numerical
results will be presented.

Section 16: Optimization 297
Improvement of classical first-order adjoint sensitivity relations
Daniel Materna, Franz-Joseph Barthold (TU Dortmund) Schedule
Sensitivity analysis plays an important role in structural optimization. Of interest are the changes
in the state variable and a chosen objective functional due to perturbations in the design variables.
In the most cases, only first-order sensitivity relations are considered and higher-order terms are
ignored. Such sensitivity relations yield for large design perturbations just a rough approximation
of the true change in the state and objective functionals.
This contribution is concerned with a novel approach for the improvement of classical firstorder
sensitivity relations of general objective functionals or quantities of interest. The improvement
approach is based on an exact variational formulation for the change in the quantity of
interest due to finite design perturbations. The exact change in the quantity of interest can be
expressed in a closed variational form. This formulation is used in order to predict the change in
the quantity of interest and yields an improved solution in comparison to the results of classical
first-order approximations. We consider a general variational framework and present the application
of the proposed approach to shape sensitivity for the model problem of nonlinear elasticity.
The capability of the proposed framework is demonstrated by means of selected computational
examples.
S16.4: Modifications of Newton’s method Wed, 16:00–18:00
Chair: Florian Jarre S1|01–A3
On limited memory BFGS with cubic overestimation
Andreas Griewank, Jonathan Fischer, Torsten Bosse (HU Berlin) Schedule
We consider the classical problem of minimizing a smooth objective by gradient based variable
metric methods. Assuming Lipschitz-continuity of the Hessian on an open neighborhood of a
bounded level set we employ the cubic overestimation approach recently (re)developed by Toint
and his collaborators. We establish local and global convergence results. The linear algebra implementation
is based on an iteratively updated eigenvalue decomposition of variable rank.
On a two-step method for solving nonlinear equations with nondifferentiable operator
Stepan Shakhno, Halyna Yarmola (Ivan Franko National University of L’viv, Ukraine ) Schedule
We consider the problem of finding an approximation solution of the nonlinear equation
H(x) = F (x) + G(x) = 0, (1)
where F, G : D ⊆ X → Y , F is a Fréchet differentiable operator and G is a continuous operator.
In works [1, 2] the authors considered the one-step iterative method for solving (1) given by
xn+1 = xn − A(xn−1, xn) −1 H(xn), x−1, x0 ∈ D, n = 0, 1, . . . .
Here A(xn−1, xn) = F ′ (xn), A(xn−1, xn) = F ′ (xn) + [xn−1, xn; G], A(xn−1, xn) = [xn−1, xn; H].
In this work we propose the two-step method based on methods with order of convergence
1 + √ 2 [3, 4]
xn+1 = xn − A(xn, yn) −1 H(xn),
yn+1 = xn+1 − A(xn, yn) −1 H(xn+1), n = 0, 1, . . . ,
where A(xn, yn) = F ′
� �
xn + yn
+ [xn, yn; G]. A local and semilocal convergence of the method
2
(2) in Banach spaces is investigated and an order of convergence is obtained. In the semilocal case
(2)

298 Section 16: Optimization
we assume that the divided difference of the first order of the operator G and the first Frećhetderivative
of the operator F satisfy Lipschitz conditions. Additionally, we assume that the second
Fréchet-derivative is Lipschitz continuous in the local case.
[1] I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point
Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004), 374 – 397.
[2] M.A. Hernandez, M.J. Rubio, The secant method for nondifferentiable operators, Appl. Math.
Lett. 15 (2002), 395 – 399.
[3] S.M. Shakhno, On an iterative algorithm with superquadratic convergence for solving nonlinear
operator equations, J. Comp. Appl. Math. 231 (2009), 222 – 235.
[4] W. Werner, Über ein Verfarhren der Ordnung 1 + √ 2 zur Nullstellenbestimmung, Numer.
Math. 32 (1979), 333 - 342.
An Optimisation Method for Nonsmooth Ojective Functions based on Algorithmic
Differentiation
Sabrina Fiege (Universität Paderborn), Andreas Griewank (HU Berlin), Andrea Walther (Universität
Paderborn) Schedule
Nonsmoothness is a typical characteristic of numerous objective function in optimisation that arises
from various applications. The standard approach in algorithmic or automatic differentiation
(AD) is to consider only differentiable functions that are defined by an evaluation program. We
extend this functionality by allowing also the functions abs(), min() and max() during the function
evaluation yielding piecewise differential nonlinear functions. It is shown how these functions
can be approximated locally by a piecewise-linear models. These models will have at most a finite
number of kinks between open polyhedra decomposing the function domain. The piecewise linear
model can easily be generated by minor modification of the ADOL-C and other standard AD
tools. We will employ it in an adapted gradient based optimisation method was adjusted to the
special properties. This talk presents this nonsmooth optimisation method and first numerical
results.

Section 17: Applied and numerical linear algebra 299
Section 17: Applied and numerical linear algebra
Organizers: Thomas Huckle (TU München), Miroslav Rozloznik (Czech Academy of Sciences,
Prague)
S17.1: Tensor methods Tue, 13:30–15:30
Chair: Huckle S1|01–A5
Tensor Network States for the study of quantum many-body systems: ground states
and time evolution
Maria Carmen Banuls (MPI Garching) Schedule
The term Tensor Network States has become common in the context of numerical studies of quantum
many-body problems. It refers to a number of families that represent different ansatzes for the
efficient description of the state of a quantum many-body system. The first of these families, Matrix
Product States (MPS), lies at the basis of Density Matrix Renormalization Group methods,
which have become the most precise tool for the study of one dimensional quantum many-body
systems. Their natural generalization to two or higher dimensions, the Projected Entanglement
Pair States (PEPS) are good candidates to describe the physics of higher dimensional lattices.
Other families, like Tree Tensor States can also be understood in terms of renormalization procedures.
Quantum information gives us some tools to understand why these families are expected to
be good ansatzes for the physically relevant states, and some of the limitations connected to the
simulation algorithms.
In this talk I will introduce some of these families from the physical point of view. I will also
describe the existing algorithms that make use them to study quantum many-body problems.
Low-rank tensor structure of elliptic operators in the TT and QTT formats
Vladimir Kazeev, Oleg Reichmann, Christoph Schwab (ETH Zürich) Schedule
We present recent results on the low-rank tensor structure of discretized elliptic operators in the
Tensor Train (TT) and Quantized Tensor Train (QTT) representations. These formats have been
proposed recently for the low-parametric structured representation of large-scale tensors. In a
remarkable number of problems involving d-dimensional n × . . . × n-vectors they have already
demonstrated the reduction of the computational complexity to O � d α n β log γ n � and O � d α log δ n �
with sufficiently small exponents α, β, γ and δ.
We consider a linear elliptic second-order differential operator of the form
L = −∇ ⊤ a∇ + b ⊤ ∇ + c,
where a is a diffusion tensor, b is a velocity field and c is a reaction coefficient, in a d-dimensional
hypercube with the homogeneous Dirichlet boundary conditions. We discretize L with the use
of the standard multi-linear finite elements with n degrees of freedom in each dimension and
study the TT and QTT structure of the obtained n d × n d -matrix Lh. For this matrix, under
certain reasonable requirements on coefficients a, b and c, we construct explicit TT and QTT
representations of ranks which grow linearly with respect to d and, in some important cases,
are also independent of n. This implies that the storage cost of Lh is respectively O (d 3 n 2 ) and
O (d 3 log n) in the TT and QTT formats.
The result can be applied to the tensor-structured spatial discretization of high-dimensional
problems, such as the Fokker-Planck equation or the Black-Scholes equation in finance.

300 Section 17: Applied and numerical linear algebra
Numerical Methods in Tensor Format Representations
Mike Espig (MPI Leipzig) Schedule
We discuss numerical methods and there convergence in tensor representations with a special
focus on tensor networks. The survey provides all necessary ingredients for applying minimization
methods in a general setting. The important cases of target functionals which are linear and
quadratic with respect to the tensor product are discussed in detail. As an example, we consider
the representation rank compression in tensor networks. For the numerical treatment, we use
nonlinear block Gauss-Seidel methods and demonstrate the rate of convergence in numerical
tests.
Tensor calculus of the Fock operator and associated integrals
Venera Khoromskaia (MPI Leipzig) Schedule
The Hartree-Fock equation is one of the basic ab initio models is electronic structure calculations.
Traditional approximation of the Fock operator is based on a rigorous analytical precomputation
of the two-electron convolution integrals in R 3 in a naturally separable Gaussian orbital basis.
We discuss the novel tensor-structured methods for the numerical solution of the Hartree-Fock
equation [3], which can be used as well in other quantum chemistry simulations. These methods
include efficient algorithms for separable representation and calculation of the discretized functions
and integral operators in R 3 using the canonical, Tucker and mixed tensor formats. The core of our
“black-box” solver is the rank-structured computation of the Laplace, nuclear potential, nonlinear
Hartree and the (nonlocal) exchange parts of the Fock operator in R 3 , discretized on a sequence
of n × n × n Cartesian grids [1,2,5]. The arising 3D and 6D convolution integrals are replaced
by 1D algebraic operations implemented with O(n log n) complexity. The robust rank reduction
algorithm [1] enables usage of fine Cartesian grids, yielding high resolution in tensor calculations
which allows arbitrary location of atoms in a molecule as in the conventional mesh-free analyticalbased
solution of the Hartree-Fock equation.
We demonstrate that tensor methods are as well advantageous in calculation of the two-electron
integrals, giving a choice to use the generic set of basis functions, including even simple combinations
of Slater-type and local finite element basis functions [5]. Based on the quantized tensor
multilinear algebra, our approach reduces the numerical costs to O(N 2 log N) with the storage
size O(N 2 ). Thus, the complexity of the calculation of the two-electron integrals and of the Hartree
and exchange operators is bounded only by the unreducible number of coupling parameters,
that is, by the entanglement of a molecular system [4]. Numerical results for several moderate
size molecules demonstrate efficiency of the tensor-structured methods in electronic structure
calculations.
[1] B.N. Khoromskij and V. Khoromskaia. Multigrid Tensor Approximation of Function Related
Arrays. SIAM J Sci. Comp., 31(4), 3002-3026 (2009).
[2] V. Khoromskaia. Computation of the Hartree-Fock Exchange in the Tensor-structured Format.
Comp. Meth. in Appl. Math., Vol. 10(2010), No 2, pp.204-218.
[3] B.N. Khoromskij, V. Khoromskaia and H.-J. Flad. Numerical solution of the Hartree-Fock
equation in multilevel tensor-structured format. SIAM J Sci. Comp., 33(1), 45-65 (2011).
[4] V. Khoromskaia, B.N. Khoromskij and R. Schneider. Grid-based tensor calculus of the twoelectron
integrals with entanglement based complexity, in preparation, 2012.
[5] V. Khoromskaia, D Andrae and B.N. Khoromskij. Tensor Representation of the Fock Operator
in a General Basis, in preparation, 2011.

Section 17: Applied and numerical linear algebra 301
Dynamical low rank approximation in hierarchical tensor formats
Reinhold Schneider, Thorsten Rohwedder (TU Berlin) Schedule
Already known in many body quantum physics the introduction of hierarchical tensor formats
as the HT (hierarchical Tucker) format and TT (tensor train) format can be considered as a
significant progress in tensor product approximation and the numerical treatment of high dimensional
problems. We will present an analytical framework of dynamical low rank approximation
in these formats. This can be directly turned into numerical schemes. We emphasize further on
the space �d i=1 C2 which covers e.g. many body Schrödinger equations and numerical homogenization.
Examples for the computation of open shell molecules and high dimensional PDE’s e.g.
Focker Planck equations will be presented.
S17.2: Tensor methods/ Eigenvalues Tue, 16:00–18:00
Chair: Kressner S1|01–A5
Tensorization and Multiscale Problems
Lars Grasedyck (RWTH Aachen) Schedule
We will present our recent findings on the relation between hierarchical tensor representations —
which is basically a multilinear data model — and the multiscale nature of problems. As it turns
out, the tensorization of a periodic multiscale problem leads trivially to a data-sparse low rank
representation and thus efficient computational techniques. However, even in the non-periodic setting
the model still works and thus gives an algebraic generalisation of the periodic case to other,
entirely non-periodic cases. However, the low rank condition — which makes the computations in
the hierarchical format efficient — restricts the applicability to special multiscale problems. It is
thus a technique between the periodic and the non-periodic case. Due to black-box approximation
techniques being available for tensors in the hierarchical format, one can exploit the structure also
in cases where it is not directly visible and analytically hard to derive.
Subspace iteration methods in terms of MPS
Konrad Waldherr, Thomas Huckle (TU München) Schedule
In the simulation of quantum many-body systems an important task is the computation of ground
states (i.e. the eigenvector related to the smallest eigenvalue) As the dimension of the underlying
vector space grows exponentially in the number of physical sites, one has to consider appropriate
subsets promising both convenient approximation properties and efficient computations. For
1D systems, Matrix Product States (MPS) are in use. Algorithms based on MPS only scale polynomially
in the size of the physical system, but still guarantee to approximate ground states
faithfully.
In this talk we consider Krylov-based subspace iteration methods for finding ground states.
These methods are formulated in terms of MPS. As the set of Matrix product states is not closed
under linear combinations, we need techniques that allow us to project a sum of MPS back onto
the MPS space, a highly nonlinear approximation problem. We will show and analyze techniques
to solve such projection problems and apply them to construct iteration methods working on the
MPS space.
Solving nonlinear eigenvalue problems via contour integrals
Wolf-Jürgen Beyn (Universität Bielefeld) Schedule
In this talk we report on a numerical method that allows to compute eigenvalues (and associated

302 Section 17: Applied and numerical linear algebra
eigenvectors) of a nonlinear eigenvalue problem
A(λ)v = 0, v ∈ C m ,
where the matrix family A(λ) ∈ Cm×m depends analytically on the eigenvalue parameter λ in
some domain Ω ⊂ C.
The method determines all eigenvalues inside a prescribed contour Γ in Ω by evaluating two
integrals
�
1
λ
2πi Γ
j A(λ) −1 rdλ, j = 0, 1
for a number of right hand sides r ∈ Cm that exceeds the number of eigenvalues inside the contour.
The idea of the method results from an application of Keldysh’s theorem.
We show how the errors of the method depend on the number of quadrature points and on
the distance of the contour to the spectrum. Several applications are presented to the stability
analysis of nonlinear waves in PDEs, where the typical problem is to separate a few isolated
eigenvalues from large eigenvalue clusters related to essential spectrum.
Hierarchically enhanced adaptive finite element methods for PDE eigenvalue/eigenvector
approximations
Agnieszka Miedlar (TU Berlin), Luka Grubišić (University of Zagreb), Jeffrey S. Ovall (University
of Kentucky ) Schedule
Although adaptive approximation methods have gained a recognition and are well-established,
they frequently do not meet the needs of real world applications. In this talk we present a hierarchically
enhanced adaptive finite element method for PDE eigenvalue problems. Starting from the
results of Grubišić and Ovall on the reliable and efficient asymptotically exact a posteriori hierarchical
error estimators in the self-adjoint case, we explore the possibility to use the enhanced Ritz
values and vectors to restart the iterative algebraic procedures within the adaptive algorithm.
Using higher order hierarchical polynomial finite element bases, as indicated by Bank and by
Ovall and Le Borne, our method generates discretization matrices whose compressions onto the
complement of piecewise linear finite element subspace (in the higher order finite element space)
are almost diagonal. This construction can be repeated for the complements of higher (even)
order polynomials and yields a structure which is particularly suitable for designing computational
algorithms with low complexity. We present some preliminary numerical results for both the
symmetric as well as the nonsymmetric eigenvalue problems.
Preconditioning for Allen-Cahn variational inequalities with non-local constraints
Martin Stoll (MPI Magdeburg), Luise Blank (Universität Regensburg), Lavinia Sarbu (University
of Sussex) Schedule
The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many
applications. This problem can be solved both in its scalar and vector-valued form as a PDEconstrained
optimization problem by means of a primal-dual active set method. At the heart of
this method lies the solution of linear systems in saddle point form. In this talk we propose the use
of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical
results illustrate the competitiveness of this approach.
Subspace acceleration for pseudospectral computations
Daniel Kressner (EPF Lausanne) Schedule
The computation of pseudospectra and associated quantities (pseudospectral abscissa, H∞ norm)
for large-scale matrices is a computationally challenging task. In this talk, we present a new class

Section 17: Applied and numerical linear algebra 303
of algorithms, which employ reduced basis techniques to reduce the computational cost, sometimes
dramatically. If time permits, an application of these techniques to parameter-dependent
eigenvalue problems is given.
S17.3: HPC / General Wed, 13:30–15:30
Chair: Rozloznik S1|01–A5
An introduction to Compressed Sensing with an application to low-rank matrix recovery
Massimo Fornasier (TU München), Holger Rauhut (Universität Bonn), Rachel Ward (University
of Texas, Austin) Schedule
In this talk we illustrate the main principles of Compressed Sensing by presenting an iteratively
reweighted least squares algorithm for low-rank matrix recovery from few linear measurements.
Calculation of invariant subspaces of general matrices using a modified Newton method
Ute Kandler (TU Berlin), Prof. Hubert Schwetlick (TU Dresden) Schedule
We consider a modified Block Newton Method for approximating an invariant subspace X and
the corresponding eigenvalues of an arbitrary complex matrix A ∈ C n×n . The method generates
a sequence of bases Uk of the subspaces (Uk), which approximate the target subspace X . We
show that for a sufficiently good initial approximation U0 the method converges in the sense
that sin(ξk), with ξk = ∡((Uk), X ), converges Q-quadratically to zero under the condition that
the subspace X is simple, i.e., that the eigenvalues which belong to it are separated from the
rest of the spectrum. In contrast to the established approach by Beyn, Kless and Thümmler
[2001] we only use the U-update from the Newton method but approximate the eigenvalues by a
generalized Rayleigh quotient matrix so the method can be considered as a Block Rayleigh Quotient
Iteration. Moreover we are able to proof the convergence results direct and without using
standard Newton convergence results by using the angles between the corresponding subspaces
instead of their norm differences analogously to the real symmetric case considered in Lösche,
Schwetlick and Timmermann [1998].
On the stability of neural networks
Vladimir Kostic, Ljiljana Cvetkovic (University Novi Sad) Schedule
Neural networks relevant to biology represent large and multi-time-scale nonlinear dynamical
systems that contain both the activity and synaptic changes. Such systems form the foundation
for every cognitive task and their complex dynamical behavior has to be very thoroughly
mathematically analyzed.
Inherently, biological networks undergo many parametric perturbations. Thus, it is of high importance
to understand their dynamical behavior which, due to activation functions and synaptic
weights, has instabilities.
In this talk we will address the stability conditions that applicable to such large scale problems
that can be obtained through the theory of diagonally dominant matrices.
Generalized Least-Squares for Genome-Wide Association Studies
Diego Fabregat-Traver, Paolo Bientinesi (RWTH-Aachen) Schedule
In recent years, genome-wide association studies (GWAS) have become ubiquitous in genomics
and medical genetics. A common approach to perform such studies is the use of mixed-effects
models, which involve the solution of very large sequences of generalized least-squares (GLS)

304 Section 17: Applied and numerical linear algebra
problems. This method requires processing from terabytes up to petabytes of data; it is therefore
imperative to design routines capable of processing very large sets of data while attaining the
highest possible performance.
For multi-core systems, generalized least-squares problems may, for instance, be directly solved
using MATLAB or reduced to a form accepted by LAPACK. Unfortunately, in the context of
GWAS, these approaches present two critical limitations: 1) they do not exploit the specific
structure of GWAS; and 2) they are in-core routines, i.e., they expect data to fit in main memory,
being therefore constrained by the amount of available memory. To address the first limitation,
there is the need to carefully design algorithms that exploit the domain-specific properties of the
problem; while to overcome the second limitation, a common approach for multi-core systems is
to develop out-of-core routines, i.e., routines capable of dealing with data stored in disk while still
delivering high performance.
We introduce an algorithm, and the corresponding out-of-core routine, that address both shortcomings.
On the one hand, the algorithm takes advantage of the specific structure of GWAS, a
parametric sequence of GLS problems, and doing so it greatly reduces redundant computations.
On the other hand, the out-of-core routine is able to deal with very large sets of data residing
on disk. As a result, our implementation outperforms existing naive approaches by a factor of 5,
being able to sustain such high performance for data sets up to the hard-drive size.
Parallel Computing for Long-Time Simulations of Calcium Waves in a Heart Cell
Matthias K. Gobbert (University of Maryland, Baltimore) Schedule
The flow of calcium ions in a heart cell is modeled by a system of time-dependent reaction-diffusion
equations. The highly non-smooth nature of the source terms, the large number of calcium release
sites requiring high-resolution meshes, and the need for long-time simulations up to large final
times are among the challenges for convergent and efficient numerical methods for this problem.
We will describe the techniques used for long-time simulations of this model using sophisticated
time-stepping and a Jacobian-Free Newton-Krylov method. Recent work provides a rigorous
proof for the convergence of the finite element method used and demonstrates that the simulator
can produce physiologically correct behavior such as experimentally observed spontaneous spiral
waves. To further improve the ability of the simulator, we are leveraging the GPGPUs in each
hybrid node for the Newton-Krylov method in the computational kernel of the simulator. GPG-
PUs are ideally suited for this type of application, since they can dramatically speed up studies
for long-time simulations, which would take the parallelism of several compute nodes to achieve
the same run times.
Parallel Fast Computation of Coulomb Interactions Based on Nonequispaced Fourier
Methods
Michael Pippig (TU Chemnitz) Schedule
The evolution of charged particle systems is determined by classical Coulomb interactions. Since
the Coulomb potential is long ranged, the number of interactions increases quadratically with
the number of particles. This makes it impossible to use the direct calculation for large particle
numbers.
Instead, an acceleration can be achieved using fast Fourier transforms at nonequispaced nodes.
For periodic boundary conditions the resulting algorithm is identically to the widely known
particle-particle particle-mesh (P3M) algorithm. Nevertheless, reasonable particle simulations are
still a computationally demanding problem, which can only be tackled with the computing power
of massively parallel architectures. Therefore, the algorithm of choice must not only be fast but
also massively parallel.

Section 17: Applied and numerical linear algebra 305
During this talk, we give an overview of the Fourier based fast calculation of Coulomb interactions.
We introduce a software library for the massively parallel computation of fast Fourier
transforms at nonequispaced nodes. This library forms the key component of our algorithm for
the fast and parallel computation of Coulomb interactions in particle systems.
S17.4: Matrix Functions / General Wed, 16:00–18:00
Chair: Frommer S1|01–A5
On optimality of interpolation-based low-rank approximations of large-scale matrix
equations
Tobias Breiten, Peter Benner (MPI Magdeburg) Schedule
In this talk, we will discuss projection-based approximations for the solution of Lyapunov equations
of the form
AXE T + EXA T + BB T = 0,
with A = A T , E = E T ∈ R n×n and B ∈ R n×m . Recently, in [1] a relation between minimizing the
objective function
f : M → R, X ↦→ XAXE + BB T
on the manifold M of symmetric positive semi-definite matrices of rank k and the L−norm defined
by the operator
L := E ⊗ A + A ⊗ E
together with the inner product 〈u, v〉L = 〈u, Lv〉 has been shown. While there the minimization
problem was solved by means of a Riemannian optimization approach, here we will discuss an
interpolation-based method which leads to the same results but relies on projecting the original
Lyapunov equation onto a smaller subspace. It will turn out that this can be achieved by the
iterative rational Krylov algorithm (IRKA) or, alternatively, by the alternating direction implicit
iteration (ADI) if appropriate shifts are used. Besides a generalization for the case of A �= A T , we
will also discuss an extension for more general Sylvester equations of the form
AXE + F XB + CD = 0,
with A = A T , F = F T ∈ R n×n , B = B T , E = E T ∈ R m×m , C ∈ R n×p and D ∈ R p×m .
[1] B. Vandereycken and S. Vandewalle, A Riemannian optimization approach for computing
low-rank solutions of Lyapunov equations, SIAM J. Matrix Anal. Appl. 31(5) (2010), 2553–
2579.
A completely real way of dealing efficiently with complex shifts in the low-rank ADI
method
Patrick Kürschner, Peter Benner, Jens Saak (MPI Magdeburg) Schedule
Solving large-scale Lyapunov equations defined by an unsymmetric matrix with the low-rank ADI
method might require complex shift parameters to achieve fast convergence. One of our recent
contributions to the low-rank ADI method proposed an efficient way for handling these complex

306 Section 17: Applied and numerical linear algebra
shift parameters. There, the amount of complex arithmetic operations corresponding to pairs of
complex conjugate shift parameters is roughly halved, which also leads to a drastic reduction of
the required complex storage. The solution of onecomplex linear system per complex pair of shifts
is the essential remaining task requiring complex computations. This is the starting point of this
work, where we investigate an approach to get rid of all of these remaining complex arithmetic
operations. This makes the method applicable on computing environments where complex computations
and storage are not supported or not efficiently available.
ADI for Tensor Structured Equation
Thomas Mach (MPI Magdeburg ), Jens Saak (MPI Magdeburg and TU Chemnitz) Schedule
We will present an extension of the well known ADI method for the solution of Lyapunov equations
F X + XF T = −GG T
to higher dimensional problems. The vectorized form of the Lyapunov equation is
(I ⊗ F + F ⊗ I)vec(X) = vec(B).
We consider the generalization of this equation of the form
Avec(X) = (I ⊗ · · · ⊗ I ⊗ A1 + . . . + Ad ⊗ I ⊗ · · · ⊗ I) vec(X) = vec(B).
The tensor train structure is one possible generalization of the low rank factorization we find in
the right hand side of (1). Therefore we assume B to be of tensor train structure. We show that in
analogy to the low rank ADI case the solution X can be generated in tensor train structure, too.
Further we provide an algorithm that computes X using a generalization of the ADI method.
FFT-based Finite Element Method for homogenization
Jaroslav Vondřejc, Jan Zeman, Ivo Marek (Czech Technical University Prague) Schedule
We present a mathematical analysis on an FFT-based homogenization algorithm introduced by
Moulinec and Suquet in [1]. This approach is based on the Lippmann-Schwinger type of integral
equation including the Green function for some reference homogeneous conductivity being
a parameter of the method. We show that this equation is equivalent to weak formulation of
the unit cell problem in the sense that the solution of both formulations is identical. Moreover,
we describe the discretization using Galerkin approximation and numerical integration with the
trigonometric polynomials used as basis functions. The convergence of discrete solutions to the
solution of weak formulation is presented. The solution of resulting non-symmetric linear system
by conjugate gradients is discussed, and it is shown that it results in substantial acceleration of
the original Moulinec-Suquet scheme, cf. [2].
[1] H. Moulinec and P. Suquet, A fast numerical method for computing the linear and nonlinear
mechanical properties of composites, Comptes rendus de l’Académie des sciences. Série II,
Mécanique, physique, chimie, astronomie 318 (1994), no. 11, 1417–1423.
[2] J. Zeman, J. Vondřejc, J. Novák, and I. Marek, Accelerating a FFT-based solver for numerical
homogenization of periodic media by conjugate gradients, Journal of Computational Physics
229 (2010), no. 21, 8065–8071.
Application of Buckingham Pi-theorem to asymmetric plate rolling processes
Tobias Münker, Denis Anders, Kerstin Weinberg (Universität Siegen) Schedule
(1)

Section 17: Applied and numerical linear algebra 307
Rolling under asymmetrical conditions such as temperature gradients within the material, difference
of the circumferential velocity of the rolls and different friction coefficients cause the
rolled slab to bend towards the direction of one of the rolls. In general this effect is undesired,
since it hinders the further material transport and is a potential danger for the machine components
in the proceeding processes. Unfortunately the essential mechanisms and the sensitivity
of the influencing parameters in asymmetric rolling are still not comprehended sufficiently. Here
a novel approach is presented in order to gain an enhanced insight into the front-end bending
phenomenon. To this end Buckingham Pi-theorem is applied to recover dimensionless coefficients
describing the state of the roll gap and enable a reduction of the number of calculations in the
required parametric studies. These parametric studies have been performed applying a finite element
model considering elasto-plastic material behaviour and the boundary conditions applied to
the slab in the roll gap. The dimensionless quantity considering the slab’s curvature is thoroughly
investigated in terms of the other dimensionless system parameters.
Error bounds for functions of matrices
Andreas Frommer, Karsten Kahl, H. Rittich (Universität Wuppertal) Schedule
We consider the task of computing f(A)b, where A is a (complex) n × n matrix, f a sufficiently
smooth function defined on an open set containing the spectrum of A and b a vector. As it is
common in applications, we assume that A is large and sparse, so that f(A) cannot be computed
directly. Instead we consider the approach to approximate f with a rational function r and to
then use the Lanczos process to iteratively approximate r(A)b. This is a computationally viable
approach, since it relies on short recurrencies.
An important aspect is to obtain reliable stopping criteria for this Lanczos iteration. We show
how to obtain precise stopping criteria, often yielding to upper bounds on the exact error, by
running a secondary, restarted Lanczos process which can be retrieved very efficiently from the
primary Lanczos iteration. We illustrate the quality of our approach with a number of examples,
including the matrix exponential and the matrix sign function.
S17.5: Iterative Solvers Thu, 13:30–15:30
Chair: Huckle S1|01–A5
A Deflated Conjugate Gradient Method for Multiple Right Hand Sides and Multiple
Shifts
Sebastian Birk, Andreas Frommer (Universität Wuppertal) Schedule
Computations in QCD simulations often require the solution of linear systems that only differ by a
shift with the identity matrix as well as solutions for several different right hand sides. In the past
Krylov subspace methods have been developed which try to exploit either the need for solutions
to multiple right hand sides (e.g. deflation type methods and block methods) or multiple shifts
(e.g. shifted CG) with some success. Though, in some instances (e.g. the Rational Hybrid Monte
Carlo algorithm) the computations even require solutions to linear systems for both multiple
right hand sides and multiple shifts at the same time. In this talk we present a Krylov subspace
method DSBlockCG that, based on a block Lanczos process, exploits both features at once. We
give numerical evidence that our method is superior to applying other iterative methods to each
of the systems individually as well as in some cases to shifted or block Krylov subspace methods.
Recycling Krylov subspace information in sequences of linear systems
Nemanja Božović (Universität Wuppertal) Schedule

308 Section 17: Applied and numerical linear algebra
Many problems in numerical simulations in physics require the solution of long sequences of slowly
changing linear systems. One problem that is of interest to us arises in Lattice QCD simulations,
e.g., while computing masses of elementary particles. In each time step, we have to solve a linear
system with a Dirac operator which changes slightly from time step to time step. Based on the
work of M. Parks and E. de Sturler [1] we will show how the cost of solving subsequent systems
is reduced by recycling selected subspaces generated for previous systems. Furthermore, we have
investigated how the algorithm behaves when we use the solution of the previous system as an
initial guess and also, when we use different kinds of extrapolations of the previous solutions as
an initial guess. We will show these results and the effectiveness of the algorithm in comparison
to the algorithm that solves each system separately.
[1] Michael L. Parks, Eric de Sturler, Greg Mackey, Duane D. Johnson and Spandan Maiti,
Recycling Krylov subspaces for sequences of linear systems, SIAM Journal on Scientific
Computing, 28(2006), 1651 − 1674
Deflation and Projector Preconditioning in iterative substructuring methods:
Connections and new results
Axel Klawonn, Oliver Rheinbach (Universität Duisburg-Essen) Schedule
In this talk, projector preconditioning, also known as the deflation method, is applied to the
FETI-DP iterative substructuring method in order to create a second, independent coarse problem.
This may help to extend the parallel scalability of classical FETI-DP methods without
the use of inexact solvers and may also be used to improve the robustness, e.g., for almost incompressible
elasticity problems. Connections of FETI-DP methods applying a transformation of
basis using a larger coarse space with a corresponding FETI-DP method using projector preconditioning
are pointed out. It can be shown that the methods have essentially the same spectrum.
Numerical results confirming our theoretical findings are provided.
Exact and Block Factorized Sparse Approximate Inverses based on Kaporin functional
minimization
Matous Sedlacek, Thomas Huckle, Jürgen Bräckle (TU München) Schedule
The talk is concerned with the factorized sparse approximate inverse (FSPAI) preconditioning
technique for symmetric positive definite systems Ax = b. Based on an arbitrary sparsity pattern,
FSPAI automatically captures most profitable indices to improve on a current approximation
L which satisfies L T L ≈ A −1 . The computation of the preconditioner is favorable for high performance
clusters as it can be done column-wise in parallel. A detailed analysis of the FSPAI
provides theoretical properties and makes it possible to derive the Exact FSPAI (EFSPAI). This
exact version of FSPAI updates its sparsity pattern by indices yielding optimal improvement for
the current approximation. In the second part of the talk, we derive the block version of FSPAI
(BFSPAI) which allows parallel preconditioning of block SPD systems. The presented modifications
inherit the main advantages of FSPAI: the computation of the preconditioner remains
inherently parallel and no a priori knowledge on the (block) sparsity pattern is required. Finally,
we present a first scalable implementation of FSPAI which forms the basis for a future parallel
EFSPAI and BFSPAI implementation.
A GPU implementation of the SPAI preconditioner for cardiovascular simulation
William Sawyer, Gilles Fourestey (Swiss National Supercomputing Centre), Radu Popescu (EPL
Lausanne), Carlo Vanini (University of Lugano) Schedule

Section 17: Applied and numerical linear algebra 309
It is well known that the sparse approximate inverse preconditioner (SPAI) [1] has particular potential
for high performance computing. Briefly, given a large, sparse system of equations Ax = b,
this technique minimizes the Frobenius norm,
�
�
�
�AM − I�F = � n �
�(AM − I)k�2 , (1)
which entails solving n decoupled least squares minimization problems,
k=1
min �
ˆmk
 ˆmk − êk�, (2)
where  is formed by taking only the non-zero entries of a A which are relevant for a given
sparsity pattern of M. The solution to this minimization is:
ˆmk = R −1 ˜ Q T êk,
with  = QR, the QR decomposition.
We have ported this calculation to graphical processing units (GPUs) within NVIDIA’s CUSP
library [2] for sparse linear algebra. GPUs perform well on dense problems such as QR where data
resides for long periods on the device. Since the minimization problems (2) are independent, they
are mapped to separate thread-blocks. A highly optimized QR algorithm from the MAGMA
library [3] is employed on each.
Traditionally the challenge has been to determine a sparsity pattern for M which reduces the
norm to a degree where M can be successfully applied in an iterative solver such as GMRES.
Due to the extremely high performance of the GPU, it is possible to consider initially sparsity
patterns for M much denser than have been previously considered.
Utilizing techniques discussed in [4], we evaluate the resulting preconditioner on Stokes problems
arising from the LifeV software [5] for cardiovascular research, and present results for the
time to solution compared with existing preconditioners, as well as the absolute performance in
GFlop/s.
[1] M. J. Grote, T. Huckle, Parallel Preconditioning with Sparse Approximate Inverses, SIAM
Journal on Scientific Computing, 18 (1997), 838–853.
[2] W. N. Bell, M. J. Garland, CUSP: CUDA Sparse linear algebra,
http://code.google.com/p/cusp-library/, 2011.
[3] A. Tomov, J. Dongarra, MAGMA: Matrix Algebra on GPU and Multicore Architectures
http://icl.cs.utk.edu/magma/, 2011.
[4] T. Huckle, A. Kallischko, Frobenius Norm Minimization and Probing for Preconditioning Int.
J. Comp. Math 84(8) (2007), 1225–1248.
[5] A. Crosetto, S. Deparis, G. Fourestey, A. Quarteroni, Parallel Algorithms for Fluid-Structure
Interaction Problems, SIAM Journal on Scientific Computing 33(4) (2011), 1598–1622.
Constructing Sparse Approximate Inverse Block Preconditioner
Thomas Huckle (TU München) Schedule

310 Section 17: Applied and numerical linear algebra
In many applications the matrices related to a linear system of equations exhibit a - maybe hidden
- block structure. This block structure should therefore also show up in the preconditioner in order
to derive better approximations. Additionally, in order to reduce the number of rather expensive
Least Squares problems that appear in the Frobenius norm minimization minM �AM − I�F , a
blocking of column indices related to nearly the same normal equations can save computing time.
Furthermore, blocking allows BLAS3 operations resulting in an additional speedup.
In this talk we will dicussion different blocking strategies und related algorithms in order to
derive improved sparse approximate inverse preconditioners.
S17.6: Iterative Solvers Thu, 16:00–18:00
Chair: Rozloznik S1|01–A5
Stability and Sparsity of Frames
Gitta Kutyniok (TU Berlin) Schedule
Frames in finite dimensional spaces have established themselves as a means to derive redundant,
yet stable decompositions of a signal for analysis or transmission, while also promoting sparse
expansions. The reconstruction procedure is then based on one of the associated dual frames,
which – in the case of a tight frame – can be chosen to be the frame itself.
In this talk, we focus on two structural properties of frames and their associated sets of dual
frames, namely their condition number and the sparsity of their vectors. While the first property
is related to stability, the second property ensures low-complexity computations and enables high
compressibility. We will discuss optimality results, provide algorithmic constructions, and finish
with some numerical experiments.
This is joint work with Krahmer (U. Göttingen) and Lemvig (TU Danmark).
Bounds on the range of multivariate rational functions by Bernstein expansion with
application to the enclosure of the solution set of parametric linear systems
Jürgen Garloff, Andrew P. Smith (Hochschule Konstanz) Schedule
The expansion of a given n-variate polynomial p into Bernstein polynomials can be used to tightly
bound the range of p over an n-dimensional box, see [1, 4]. The interval spanned by the minimum
and the maximum of the coefficients of this expansion encloses the range. A disadvantage of this
approach is that the number of the coefficients to be computed explicitly grows exponentially with
the number of variables n. In [3] a method was presented by which the number of coefficients
which are needed for the enclosure is only approximately linear in the number of the terms of the
polynomial.
The talk addresses the question of the way in which the tight bounds on the range of a
polynomial can be employed to construct bounds on the range of the ratio of two multivariate
polynomials. The naive method of bounding the ranges of the two polynomials independently
and dividing the two resulting intervals neglects the dependency between the variables of the
polynomials and may result in gross overestimation of the range.
In our talk, a linearisation technique is presented which leads to much tighter enclosures for
the ranges of rational functions.
In the second part of our talk, we apply these bounds to the enclosure of the solution set of a
parametric system of linear equations. This is a system of linear equations where the coefficients
of the matrix and the right hand side depend on parameters which vary within given intervals. We
employ a parametric residual iteration based on interval arithmetic [2] which requires bounding
the range of a multivariate rational function over a box. Applications to the verified solution of

Section 17: Applied and numerical linear algebra 311
some simple finite element models for truss structures are also presented.
[1] J. Garloff, Convergent bounds for the range of multivariate polynomials, in K. Nickel, ed.,
Interval Mathematics 1985, Lecture Notes in Computer Science vol. 212, 37–56. Springer,
Berlin, Heidelberg, New York (1986).
[2] J. Garloff, E. D, Popova, and A. P. Smith, Solving linear systems with polynomial parameter
dependency with application to the verified solution of problems in structural mechanics,
in A. Chinchuluun, P. M. Pardalos, R. Enkhbat, and E. N. Pistikopoulos, eds., Proceedings
of the International Conference on Optimization, Simulation and Control, Ulaanbaatar,
Mongolia (2010), Series Springer Optimization and Its Applications, Springer-Verlag (to
appear).
[3] A. P. Smith, Fast construction of constant bound functions for sparse polynomials, J. Global
Optimization 43 (2–3), 445–458 (2009).
[4] M. Zettler and J. Garloff, Robustness analysis of polynomials with polynomial parameter
dependency using Bernstein expansion, IEEE Trans. Automat. Contr. 43, 425–431 (1998).
Using block smoothers in multigrid methods
Matthias Bolten, Karsten Kahl (Universität Wuppertal) Schedule
In the context of domain decomposition methods usually block smoothers with or without overlap
are used. On parallel computers and nowadays computer architectures block smoothers possess
the advantage of a high computation/communication and/or a computation/memory access ratio,
especially when compared to traditional point smoothers. Therefore, multigrid methods should
benefit from the use of block smoothers. Nevertheless, numerical results show that block smoothers
are not as efficient as expected when standard coarsening procedures are in effect. We propose
a different coarsening scheme and a new local interpolation for the usage of block smoothers in
multigrid methods. Using this scheme, we obtain textbook multigrid efficiency with fast convergence
rate and can thus benefit from the higher amount of work that is carried out locally. In this
talk, we will present the resulting method, give an overview over the theoretical foundations and
show numerical results.
Aggregation-based Multilevel Methods for Lattice QCD
Matthias Rottmann, Karsten Kahl (Universität Wuppertal) Schedule
In this talk, we present a multigrid solver for application in Quantum Chromodynamics (QCD),
a theory that describes the strong interaction between subatomic particles. In QCD simulations
a substantial amount of work is spent in solving Dirac equations on regular grids. These large
sparse linear systems are often ill conditioned and typical Krylov subspace methods (e.g. CGN,
GCR, BiCGStab) tend to be slow. As a solution to their bad scaling behavior we present an
aggregation based multigrid method with a domain decomposition smoother and show numerical
results for systems up to the size of 450 million of unknowns.
Adaptive algebraic multigrid methods for Markov chains
Sonja Sokolovic (Universität Wuppertal) Schedule
We present an algebraic multigrid approach for computing the state vector of an irreducible Markov
chain. The presented method consists of two parts: In a multiplicative setup phase based on
the recently introduced bootstrap algebraic multigrid (BAMG) framework, a multigrid hierarchy

312 Section 17: Applied and numerical linear algebra
is developed in an adaptive fashion and a first approximation to the desired state vector is computed.
In the second part of the method, the multigrid hierarchy is used for preconditioning a
Krylov subspace iteration that further improves the approximation to the state vector. In our
approach, we propose some modifications to the basic BAMG framework, in particular to the
least squares based computation of the interpolation operator, which in some cases, especially for
large, unstructured problems, seem to be advantageous. In addition, new results concerning the
convergence of the preconditioned Krylov subspace iteration (which is not guaranteed because
the system to be solved is singular) are presented.
Adaptive smoothed aggregation multigrid
Marcel Schweitzer (Universität Wuppertal) Schedule
We investigate algebraic multigrid (AMG) methods, in particular those based on the smoothed
aggregation approach, for solving linear systems Ax = b with a general, nonsymmetric matrix A.
Recent results show that in this case it is reasonable to demand that the interpolation operator
is able to accurately approximate singular vectors corresponding to the smallest singular values
of A. Therefore, we present an extension of the bootstrap AMG setup, which is geared towards
the singular vectors of A instead of the eigenvectors as in the original approach. Numerical experiments
with systems from the discretization of convection diffusion equations show that this
new setup approach performs very well when compared to established methods. In addition, we
present results that show that our method can also be used as a very efficient preconditioner for
the generalized minimal residual (GMRES) method.

Section 18: Numerical methods of differential equations 313
Section 18: Numerical methods of differential equations
Organizers: Etienne Emmrich (Universität Bielefeld), Andreas Prohl (Universität Tübingen)
S18.1: Computational Fluid Dynamics Tue, 13:30–15:30
Chair: Bürger S1|03–221
Fully conservative time integrators for skew-symmetric compressible flow schemes
Jens Brouwer, Julius Reiss, Jörn Sesterhenn (TU Berlin) Schedule
Fully conservative finite difference schemes for the compressible Navier-Stokes equations can be
constructed by discretizing the skew-symmetric form of the analytic equations and keeping the
skew-symmetry in their respective discrete forms. For example, the momentum equation takes
the form
� �
1 ∂ρ · u
+ ρ∂u +
2 ∂t ∂t
1
� �
∂ρu · u
+ ρu∂u +
2 ∂x ∂x
∂p
∂x
= 0, (1)
where both the convective and temporal differentiation operators are skew symmetric. While conservative
semi-discrete schemes are easily constructed the unusual form of the temporal derivative
poses additional challenges which dictate the use of multistep methods. A promising ansatz is to
rewrite the time derivative as
� �
1 ∂ρ · u
+ ρ∂u
2 ∂t ∂t
= √ ρ ∂√ρu , (2)
∂t
which is based on the work of Morinishi, [1],and leads to fully conservative one-step schemes
with better stability properties and easier implementation. Implicit and explicit integrators for
both formulations are presented and discussed with respect to there applicability for practical
computations and extension to higher order schemes.
[1] Y. Morinishi, Skew-symmetric form of convective terms and fully conservative finite difference
schemes for variable density low-Mach number flows,
Journal of Computational Physics 229 (2010), 276 – 300.
Kinetic Models and the Finite Pointset Method (FPM)
Maria Kobert, Jörg Kuhnert (ITWM Kaiserslautern), Axel Klar (TU Kaiserslautern) Schedule
The overall goal is to simulate rarefied flows inside vacuum pumps. The behavior of a flow in a
vacuum pump is defined through the Knudsen number Kn, which can be very small (Kn < 0.01
continuum flow) or larger (Kn > 0.5 molecular flow).
Continuum flows are mainly simulated by using commercial CFD methods, which solve the
Navier-Stokes equations. In the case of molecular flows one uses statistical methods, such as the
Direct Simulation Monte Carlo (DSMC).
We want to develop a deterministic method for flows near continuum (Kn ≈ 0.01, ...0.1), since
the DSMC method fails in those regions due to rapid increase of particles. The deterministic
method we intend to use is the Finite-Pointset-Method (FPM) [1], which is a meshfree numerical
method developed at the ITWM Kaiserslautern and is mainly used to solve fluid dynamical problems.
The method is superior to the classical methods in the case of problems with complicated
geometries and/or moving boundaries, which is appropriate in models of vacuum pump systems.
As Boltzmann collision model we use the BGK-model [2].

314 Section 18: Numerical methods of differential equations
Two attempts of implementing the BGK-equation in FPM are presented. The first one is to
discretize the BGK-model using the IMEX-Runge Kutta scheme [3] and the second one is dealing
with the moments of the BGK-equation and the so called 13 Moment equations [4]. Numerical
examples for both methods are shown for different ranges of the Knudsen number.
[1] Tiwari, S., Kuhnert, J., Finite pointset method based on the projection method for simulations
of the incompressible Navier-Stokes equations Meshfree methods for partial differential
equations Band 1 (2004)
[2] P.L. Bhatnagar, E. P. G., Krook, M., A model for collision processes in gases. Small amplitude
processes in charged and neutral one-component systems Physical Reviews 1954 (94), 511-
525.
[3] Pieraccini, S., Puppo, G., Implicit - Explicit schemes for BGK kinetic equations
[4] Struchtrup, H., Derivation of 13 Moment equations for rarefied gas flow to second order
accuracy for arbitrary interaction potentials Multiscale Model Simul. 3 (2005) 221-243
Subspace Projection Method for Particulate Flows
Rodolphe Prignitz, Eberhard Bänsch (Universität Erlangen-Nürnberg) Schedule
A method is presented for the simulation of viscous incompressible flow with many suspended
solid particles. This method uses a finite-element discretisation in space and an operator-splitting
technique for discretisation in time and has its basis in work by Glowinski et al.. However, a
subspace projection rather than a Lagrange multiplier is used to couple the particle motion with
the fluid motion. Combined with local mesh refinement the method results in a fast and accurate
algorithm for the simulation of a huge number of particles in a flow field. Validation is achieved
using the sedimentation of one particle and comparing the resulting drag coefficient with theoretical
and experimental results.
Solving Kaup-Kupershmidt equation by using iterative methods
Shadan Sadigh Behzadi, Armin Sadigh Behzadi (Islamic Azad University Tehran) Schedule
In this paper, a nonlinear Kaup-Kupershmidt equation is solved by using the Adomian decomposition
method (ADM),modified Adomian decomposition method (MADM), variational iteration
method (VIM), modified variational iteration method (MVIM), homotopy perturnbation method
(HPM), modified homotopy perturbation method (MHPM) and homotopy analysis method
(HAM) numerically. For each method, the approximate solution of this equation is calculated
based on a recursive relation which its components are computed easily. The existence and uniqueness
of the solution and the convergence of the proposed methods are proved. Numerical
examples are studied to demonstrate the accuracy of the given algorithms.
A Stabilized Finite Element Method for Convection-Diffusion Problems using Boundary
Integral Operators
Clemens Hofreither, Ulrich Langer (Universität Linz) Schedule
We present a non-standard stabilized finite element method where stabilization is done using
element-local boundary integral operators. This approach requires the explicit knowledge of a
local fundamental solution, but permits the use of general polygonal or polyhedral meshes. Some
numerical examples confirm the stabilizing effect.

Section 18: Numerical methods of differential equations 315
A-priori error analysis for finite element approximations of Stokes problem on dynamic
meshes
Andreas Brenner, Eberhard Bänsch (Universität Erlangen-Nürnberg), Markus Bause (Universität
der Bundeswehr Hamburg) Schedule
We study finite element approximations of the time dependent Stokes system on dynamically
changing meshes. Applying the backward Euler method for time discretization we use the discrete
Helmholtz or Stokes projection to evaluate the solution at time tn−1 on the new spatial
mesh at time tn. The theoretical results consist of a priori error estimates that show a dependence
on the time step size not better than O(1/∆t). These surprisingly pessimistic upper bounds are
complemented by numerical examples giving evidence that our error estimates are sharp. These
observations imply that using adaptive meshes for flow problems is delicate and requires further
investigations.
S18.2: Applications Tue, 16:00–18:00
Chair: Banas S1|03–221
A stabilized finite volume element method for sedimentation-consolidation processes
Raimund Bürger (Universidad de Concepción, Chile), Ricardo Ruiz-Baier (EPFL Lausanne),
Héctor Torres (Universidad de La Serena, Chile) Schedule
A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by
a parabolic equation describing the evolution of the local solids concentration coupled with a
version of the Stokes system for an incompressible fluid describing the motion of the mixture.
In cylindrical coordinates, and if an axially symmetric solution is assumed, the original problem
reduces to two space dimensions. This poses the difficulty that the subspaces for the construction
of a numerical scheme involve weighted Sobolev spaces. A novel finite volume element method
is introduced for the spatial discretization, where the velocity field and the solids concentration
are discretized on two different dual meshes. The method is based on a stabilized discontinuous
Galerkin formulation for the concentration field, and a multiscale stabilized pair of P1-P1 elements
for velocity and pressure, respectively. Numerical experiments illustrate properties of the model
and the satisfactory performance of the proposed method.
On the Coupled Electromechanical Activation of the Human Heart
E. Karabelas, O. Steinbach (TU Graz) Schedule
The mathematical modeling of electro-mechanical coupled activation of the human heart results in
a system of highly non-linear time-dependent coupled partial and ordinary differential equations.
In this talk we consider the bidomain equations for modelling the electric activation of the human
heart and the quasi-stationary equations of non-linear elasticity for describing the deformation of
the heart. We will present some results on the solvability of the coupled system, and we discuss
finite element approximations for the numerical solution.
A Finite Element Approximation of Air Flow in the Area under a Platform of Bangkok
Sky Train
Nopparat Pochai (King Mongkut’s Institute of Technology Ladkrabang, Thailand) Schedule
The air pollution problems arise frequently in Bangkok, Thailand. The consideration area is the
area under Phayathai platform station of Bangkok sky train in Bangkok, Thailand. The area has
a problem of air pollution control. The Bangkok Mass Transit System Company tries to set up
the misting fans inside the area. The flow of the air is still not smooth and the air quality is still
lower than standard. The assumption of the research is the flow obstructs by platform structures.

316 Section 18: Numerical methods of differential equations
In this research, we will present the finite element method applied to problems of two-dimensional
laminar flow of incompressible viscous fluid. The governing equations of the air flow are expressed
in terms of the streamfunction and vorticity.
Basic Modelling for Large Deformation of Plates
Jens Rückert, Arnd Meyer (TU Chemnitz) Schedule
In the simulation of deformations of plates it is well known that we have to use a special treatment
of the thickness dependence. Therewith we achieve a reducing of dimension from 3D to 2D.
For linear elasticity and small deformations several techniques are well established to handle the
reduction of dimension and achieve acceptable numerical results. In the case of large deformations
of plates with non-linear material behaviour there exist different problems. So, the analytical integration
over the thickness of the plate is not possible due to the non-linearities arising from the
material law and the large deformations themselves. There are several possibilities to introduce a
hypothesis for the treatment of the plate thickness from the strong Kirchhoff assumption on one
hand up to some hierarchical approaches on the other hand. Here we consider a model of using
the Kirchhoff assumption. Mathematically it means:
x(η 1 , η 2 , η 3 ) : = x m (η 1 , η 2 ) + η 3 f(η 1 , η 2 ) (1)
⎛
= ⎝
η 1
η 2
η 3
⎞
⎠ + U + η 3 (f(U) − e3) (2)
= X(η) + U + η 3 (f(U) − e3), (3)
where X/x are the physical points of the undeformed/deformed plate,
η = (η 1 , η 2 , η 3 ) their coordinates, U the deformation vector, depending on (η 1 , η 2 ) only, and f the
normal vector of the deformed midsurface, arising from the assumption. In case of small strain
this normal direction f is approximated by a linear differential operator. We consider finite strains,
hence f has to have the true nonlinear dependence on U following the differential geometry of
the deformed midsurface. It is important that we avoid any further simplifications, which could
be crucial for large strains. This way of modelling leads to a two-dimensional strain tensor, which
depends essentially on the first two fundamental forms of the differential geometry of the deformed
midsurface. Outgoing from this new strain tensor we obtain the energy functional. The FEM
ansatz is to find the state of the plate, where the deformation energy has its minimum over a
suitable chosen finite element subspace. Therefore the first derivative of the energy functional has
to be zero. Whether the energy functional is easily calculated with the new strain tensor, there are
some difficulties in calculating the derivatives of the functional. Especially the second derivative
is ambitious to calculate and makes the Newton linearization for computing the solution very
expansive. Nethertheless, due to the fast convergence of the Newton linearization, we think that
the effort is worth the trouble. We will present the total theory and give numerical results for
comparisions.
Numerical Simulation of Plasmonic Effect at Metallic/Dielectric Interface
Shuai Yan, Christoph Pflaum (Universität Erlangen-Nürnberg) Schedule
Plasmonics concern with electromagnetic excitations at the interface between a dielectric and
a conductor, and plasmonic nanostructure is now a promising candidate as a light scattering
and trapping agent for solar cells. We solved Maxwell equation analytically and numerically in a
region with flat interface between a conductor and a dielectric, which is the most simple geometry
sustaining plasmonic effects. The simulation technique is a finite integration technique(FIT)
combined with a time harmonic inverse iteration method(THIIM). Results show the numerical

Section 18: Numerical methods of differential equations 317
solution converges to the analytical solution with order around 1.4, which implies our scheme is
well-suited for further simulation involving plasmonics. We then study the convergence behavior
of the discretization scheme theoretically, both achievements and difficulties for this analysis will
be presented.
S18.3: Computational Fluid Dynamics Wed, 13:30–15:30
Chair: Siska S1|03–221
A comparison of Rosenbrock and ESDIRK schemes for unsteady compressible flow
problems
Hester Bijl (University of Delft), Philipp Birken, Andreas Meister (Universität Kassel), Alexander
van Zuijlen (University of Delft) Schedule
We consider implicit time integration methods for unsteady flow problems. There, it has been
previously demonstrated that ESDIRK schemes are faster than BDF schemes for engineering
accuracies. Here, we compare Rosenbrock schemes to ESDIRK schemes for a model nonlinear
convection-diffusion problem and the 3D unsteady Navier-Stokes equations.
When using Newton’s method in the ESDIRK schemes, we obtain a sequence of linear systems.
This is also true of Rosenbrock time integration, but there, the system matrix is constant
during a time step. We compare different strategies of exploiting this.
The FEM and SDFEM for convection-diffusion problems with low regularity
Lars Ludwig, Hans-Görg Roos (TU Dresden) Schedule
The finite element method is applied to a convection-diffusion problem posed on the unite square
using a tensor product mesh and bilinear elements. The usual proofs that establish superconvergence
for this setting involve a rather high regularity of the exact solution - typically u ∈ H 3 (Ω),
which in many cases cannot be taken for granted. In this paper we derive superconvergence results
where the right hand side of our a priori estimate no longer depends on the H 3 norm but merely
requires finiteness of some weaker functional measuring the regularity. Moreover, we consider the
streamline diffusion stabilization method and how superconvergence is affected by the regularity
of the solution. Finally, numerical experiments for both discretizations support and illustrate the
theoretical results.
The influence of nonlinear joint characteristics on friction-induced vibrations
Sebastian Kruse (TU Hamburg, Audi AG), Pascal Reuß (Universität Stuttgart), Norbert Hoffmann
(TU Hamburg) Schedule
Friction-induced vibrations and its applications are an everlasting problem in industry and academia
that has been dealt with in many works(e.g. Kinkaid et al.,Ouyang et al.). There are two
aspects in this research field that are mainly discussed. The first aspect is the stability of systems
that tend to friction-induced vibrations. Research deals especially with questions of modelling,
sensitivity with respect to physical parameters and methods to solve the linearized equations of
motion (e.g. Sinou et al.,Wagner et al.). The second aspect is the approximation of limit cycles
due to the nonlinear terms in the equation of motions (e.g. Hoffmann et al.,Coudeyras et al.).
Well known techniques for limit cycle approximation have been discussed or extended in order to
be able to predict limit cycles and hence the criticality of friction-induced vibrations. However,
while the discussion on stability is limited to questions of linearized systems and hence fails to
determine the relevance of a predicted instability, the methods dealing with limit cycle approximation
are still limited to somewhat small models that fail to predict the reality of systems on
an engineering scale.

318 Section 18: Numerical methods of differential equations
This research tries to overcome the gap between these two fields. Therefore linear techniques
and the knowledge of dominant nonlinearities in a system are employed in order to predict the
criticality of a particular system instability.
The research starts with a few degree of freedom model that inherits a mechanism for frictioninduced
vibrations. This model includes a joint with nonlinear characteristics. We employ an
extended harmonic balance technique introduced by Coudeyras et al. in order to approximate
limit cycles for unstable regions in the parameter space of the small model. The limit cycle
shape and amplitude are analysed and compared to the results of the linear stability analysis
with the corresponding eigenvalues and eigenvectors. This analysis shows that the amplitude
or criticality of friction-induced vibrations can be predicted based on the linear stability analysis
under the assumptions that the dominant non-linearities of the system are known. These dominant
nonlinearities are usually the few joints inheriting dry friction.
Based on these results we discuss the limits of todays methods of stability analysis in frictioninduced
systems and suggest a way to extend these methods to predict critical regions in the
parameter space that may lead to large limit cycle amplitudes without loosing the possibility to
analyse systems on an engineering scale.
[1] N.M. Kinkaid, O.M. O’Reilly, P. Papadopoulos Automotive disc brake squeal, Journal of
Sound and Vibration, Volume 267, Issue 1, 9. October 2003, pages 105-166
[2] H. Ouyang, W. Nack, Y. Yuan, F. Chen, Numerical analysis of automotive disc brake squeal:
a review, International Journal of Vehicle Noise and Vibration, Volume 1, Number 3-4 /
2005 , pages 207 - 231
[3] J.-J. Sinou, L. Jezequel, Mode coupling instability in friction-induced vibrations and its dependency
on system parameters including damping, European Journal of Mechanics - A/Solids,
Volume 26, Issue 1, January-February 2007, Pages 106-122
[4] U. v. Wagner, D. Hochlenert, P. Hagedorn, Minimal models for disk brake squeal, Journal of
Sound and Vibration, Volume 302, Issue 3, 8 May 2007, Pages 527-539
[5] N. Hoffmann, S. Bieser, L. Gaul, Harmonic Balance and Averaging Techniques for Stick-Slip
Limit-Cycle Determination in Mode-Coupling Friction Self-Excited Systems, TECHNISCHE
MECHANIK, Band 24, Heft 3-4, (2004), 185 197
[6] N. Coudeyras, S. Nacivet, J.-J. Sinou, Periodic and quasi-periodic solutions for multi-instabilities
involved in brake squeal, Journal of Sound and Vibration, Volume 328, Issues 4-5, 25
December 2009, Pages 520-540
Application of the Method of Fundamental Solution for two dimensional steady viscous
fluid flow
Magdalena Mierzwiczak (Poznan University of Technology) Schedule
A meshless numerical procedure based on the method of fundamental solutions (MFS) and the
Radial Basic Functions (RBF) is proposed to solve the Navier-Stokes equations. For the best
knowledge of author, as yet, only in one paper this method was applied to solve of Navier–Stokes
equations [1]. The MFS is a meshless method since it is free from the mesh generation and numerical
integration. We will transform the NavierStokes equations into simple inhomogeneous
biharmonic equation for the stream function. The non-linear biharmonic boundary value problem

Section 18: Numerical methods of differential equations 319
we solve iteratively. At every step of the calculation we use the radial basis functions to interpolation
of the right hand side in non-homogeneous governing equation. The proposed meshless
numerical scheme is a first attempt to apply the MFS with RBF for solving the steady NavierStokes
equations in the moderate-Reynolds-number flow regimes. As computational example the flow
in stenosed arteries is considered [2]. From the computational point of view, the present numerical
procedure based on the method of fundamental solutions is efficient and simple to implement as
compared to the mesh-dependent schemes, which needs complex mesh generation procedure for
the geometrical domains.
[1] Young D.L., Lin Y.C., Fan C.M., Chiu C.L., The method of fundamental solutions for solving
incompressible NavierStokes problems, Engineering Analysis with Boundary Elements 33
(2009), 1031–1044.
[2] Zendehbudi G.R., Moayeri M.S., Comparison of physiological and simple pulsatile flows
through stenosed arteries, Journal of Biomechanics 32 (1999), 959–965.
Convergence of Iterative methods applied to Boussinesq equation
Shadan Sadigh Behzadi (Islamic Azad University Qazvin) Schedule
In this paper, a Boussinesq equation is solved by using the Adomain’s decomposition method
(ADM), variational iteration method (VIM),modified Adomian decomposition method (MADM),
modified variational iteration method (MVIM), homotopy analysis method (HAM), homotopy
perturbation method (HPM)and modified homotopy perturbation method (MHPM).The approximate
solution of this equation is calculated in the form of series which it’s components are
computed by applying a recursive relation The existence and uniqueness of the solution and the
convergence of the proposed methods are proved.A numerical example is studied to demonstrate
the accuracy of the presented methods.
S18.4: Finite Elements Wed, 13:30–15:30
Chair: Steinbach S1|03–223
Generalized Park-Sheen Finite Elements for Adaptivity
Robert Altmann (TU Berlin), Carsten Carstensen (HU Berlin) Schedule
Park and Sheen ([2003]) introduced a basis for nonconforming, piecewise linear finite elements
on triangulations into quadrilaterals of simply connected domains. Moreover, adaptive meshrefinement
has recently been proven to be optimal for the related Crouzeix-Raviart nonconforming
FEM on triangles. In order to use adaptive mesh-refinements with the Park-Sheen nonconforming
FEM on quadrilaterals, we introduce the combination of Park-Sheen with Crouzeix-Raviart nonconforming
finite elements. This requires the understanding of the Park-Sheen FEM on multiple
connected domains.
The proposed combination of the Park-Sheen and the Crouzeix-Raviart nonconforming elements
combines the minimal degrees of freedom per element domain with the flexibility of adaptive
mesh-refinement.
As main result we characterise a basis of this nonconforming finite element space with global
edge-connected exceptional basis functions and present a complete a priori error analysis with
explicit constants.
[2003] Park, C. and Sheen, D., P1-nonconforming quadrilateral finite element methods for secondorder
elliptic problems, SIAM J. Numer. Anal. (2003).

320 Section 18: Numerical methods of differential equations
FETI-DP for a class of linear elasticity problems with varying material coefficients
inside subdomains
Sabrina Gippert, Axel Klawonn, Oliver Rheinbach (Universität Duisburg-Essen) Schedule
In this talk, a domain decomposition method for a class of linear elasticity problems with varying
material coefficients is considered. In this category of problems each subdomain contains
an almost incompressible inclusion surrounded by a compressible hull. The classical FETI-DP
algorithm with primal vertices and primal edge averages is applied, i.e., the coarse space for compressible
linear elasticity is used. The condition number is found to depend only on the material
parameters of the hull and also on its thickness, but is otherwise independent of coefficient jumps
between subdomains and also between the hull and the inclusion. Thus, the condition number
does not deteriorate when the Poisson ratio of the inclusion tends to 0.5. Numerical results confirming
our theoretical findings are presented.
Comparison of different methods of choice of collocation points in boundary collocation
method for 2D harmonic problems with special purpose Trefftz function
Jan Adam Kolodziej, Magdalena Mierzwiczak (Poznan University of Technology) Schedule
Based on the special purposed Trefftz functions we present a comparison of the different methods
of choosing collocation points when boundary collocation method is used to fulfil the boundary
conditions. First, it is shown that for some geometries of a region when applying the boundary
collocation method with special purposed Trefftz function, the equidistant collocation points my
give unacceptable results. Next, for four 2-D harmonic boundary values problems: Torsion of a
triangular bar with a circular centered hole, Longitudinal laminar flow in a regular array of cylindrical
rods, Field temperature in a repeated element of regular composite, Potential flow past
a cylinder between parallel walls; four cases of different placement of the collocation points are
described and compared. Based on the results of the comparison of the test methods for the location
of collocation points it is shown that the our proposed method of location of the collocation
points which has an iterative and adaptive character is simple to implement and accurate. The
essence of this method is an adaptive determination of the consequent collocation points.
Coupling Methods for Interior Penalty Discontinuous Galerkin Finite Element Methods
and Boundary Element Methods
Günther Of (TU Graz), G.J. Rodin (The University of Texas at Austin), O. Steinbach (TU Graz),
M. Taus (The University of Texas at Austin) Schedule
This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite
element methods and boundary element methods. The new methods allow one to use discontinuous
basis functions on the interface between the subdomains represented by the finite element
and boundary element methods. This feature is particularly important when discontinuous Galerkin
finite element methods are used. Error and stability analysis is presented for some of the
methods. Numerical examples suggest that all three methods exhibit very similar convergence
properties, consistent with available theoretical results.
Combined boundary element and discrete singularity method
Reshniak Viktor, Kochubey Olexander, Yevdokymov Dmytro (Oles Gonchar Dnipropetrovsk National
University) Schedule
Permanent development and progress in science and technique leads to necessity of solving new
problems and taking into account effects, that have never been considered before. Finite element

Section 18: Numerical methods of differential equations 321
and finite difference methods are highly developed computational methods of solving PDEs problems.
But their usage has some limitation factors. For instance, they are good applicable in case
of continuously changing properties of solution area. If not, they can become incorrect because
of loosing information inside the elements. Another problem is the huge number of nodes that
are generated during the meshing procedure. The usage of specialized computational methods,
that have been rapidly developed in the last years, can help to solve some of these problems.
Among them are lagrangian methods and methods of computational potentional theory, based
on integral representations of basic PDEs. BEM and discrete singularity method are used in this
work according to this approach. These methods have certain advantages, such as precision of
BEM and simplicity of discrete singularity method. The compilation of these features can be very
effective. Besides that, using the BEM for solving elliptical PDEs of potentional theory can reduce
the dimension of the problem. The considered approach was used to solve the plain boundary
problem of vortical motion of uncompressible fluid. The boundary was approximated by boundary
elements, while the vortisity was approximated by discrete vortices. Results were visualized with
streamlines and trajectories. The analysis of estimated results shows good applicability of this
approach.
S18.5: Applications Wed, 16:00–18:00
Chair: Emmrich S1|03–221
Efficient numerical methods for initial-value solid-state laser problems
Fan Feng, Christoph Pflaum (Universität Erlangen-Nürnberg) Schedule
The difficulties of solving initial-value solid-state laser problems numerically arise from both stiffness
of the problems and near-to-zero nonnegative exact solutions.Stability and non-negativity
must be maintained simultaneously in the numerical solutions.Classical schemes unfortunately
suffer from severe time-step restriction because of the difficulties.
In this paper,we present an optimized numerical approach with which 3-dimensional laser
problems can be solved faster and much more efficiently.These techniques can not only be used
for solid-state laser system,passively Q-switched laser system, passively Q-switched intracavity
frequency-doubling laser system,but can also be applied to solve other stiff problems which have
near-to-zero nonnegative exact solutions.
To the best of our knowledge,efficient numerical approach solving initial-value passively Qswitched
intracavity frequency-doubling solid-state laser problem is introduced for the first time.
An Extrapolation Approach for Iterative Maxwell Solvers Based upon the Prony
Method
Kai Hertel (Universität Erlangen-Nürnberg), Christoph Pflaum, Raj Mittra Schedule
We present an adaptation of Prony’s extrapolation method for approximating solutions of Maxwell’s
equations for large-scale solar cell simulations. The method samples a small number of
equidistant iterates of a finite difference frequency domain (FDFD) solver and extracts the dominating
amplitude-frequency pairs in order to approximate the dominating eigenvectors of the
FDFD iteration matrix. The objective is to dampen down the initial transient sufficiently for
the resulting data to allow for a long-term prediction of the underlying sinusoidal signals. The
quality of the numerical approximation highly depends on both the sample window as well as the
assumed model order.

322 Section 18: Numerical methods of differential equations
Reduced Basis Modeling for Parametrized Systems of Maxwell’s Equations
Martin Hess, Peter Benner (MPI Magdeburg) Schedule
The Reduced Basis Method [1] generates low-order models to parametrized PDEs to allow for
efficient evaluation of parametrized models in many-query and real-time contexts. The Reduced
Basis approach is decomposed into a time-consuming offline phase, which generates a surrogate
model and an online phase, which allows fast parameter evaluations. Rigorous and sharp a posteriori
error estimators play a crucial role in this process, in that they define which snapshots are
to be taken into the reduced space and give bounds to the output quantities during the online
phase.
We apply the Reduced Basis Method to systems of Maxwell’s equations arising from electrical
circuits [2]. Using microstrip models as a microscopic view of interconnect structures, the
input-output behaviour is approximated with low order reduced basis models for a parametrized
geometry, like distance between microstrips and/or material coefficients, like permittivity and
permeability of substrates.
We show the theoretical framework in which the Reduced Basis Method is applied to Maxwell’s
equations and present first numerical results.
[1] G. Rozza, D.B.P. Huynh, A.T. Patera, Reduced Basis Approximation and a Posteriori Error
Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations, Arch.
Comput. Methods Eng. 15 (2008), 229 – 275.
[2] R. Hiptmair, Finite Elements in computational electromagnetism, Acta Numerica (2002) 237
– 339.
Consistency Results for a Contact-Stabilized Newmark Method in Time and Space
Corinna Klapproth (Zuse-Institute Berlin) Schedule
The talk is concerned with a contact-stabilized Newmark method for the numerical integration of
dynamical contact problems formulated on the basis of Signorini’s contact conditions. The focus
is on a new variant of the original contact-stabilized Newmark method, which is energy dissipative
and avoids artificial oscillations. The new scheme additionally produces velocities equal to zero at
active contact boundaries. The main topic of the talk is the investigation of the spatio-temporal
discretization error of this method in the presence of contact. For this aim, the consistency error
is measured in a physical energy norm and the solution is assumed to be of bounded total
variation. It turns out that the new contact-stabilization leads to a much better behavior of the
discretization error than previous versions of the Newmark method.
Phase lag analysis of variational integrators using interpolation techniques
O.T. Kosmas, Sigrid Leyendecker (Universität Erlangen-Nürnberg) Schedule
In the present work we investigate the construction of high order variational integrator methods
[1] combined with phase lag properties [2] for the numerical integration of systems with oscillatory
solutions. We first consider physical problems where the corresponding components of the
Lagrangian i.e. kinetic and potential energy, depend only on the generalized velocity and the generalized
position respectively (for a generalized coordinate of the configuration space). We then
express the action integral at any intermediate points along the curve segment, using a discrete
Lagrangian that depends only from the end points of the interval [3]. High order integrators can
be then obtained by defining the discrete Lagrangian in any time segment as a weighted sum on

Section 18: Numerical methods of differential equations 323
intermediate points, whose expressions for positions and velocities use cubic spline interpolation
or interpolation using trigonometric functions. The new methods depend now on a frequency,
which needs to be evaluated [4].
For that we adopt a new methodology which improves the phase lag characteristics by vanishing
both the phase lag function and its first derivatives at a specific frequency [2]. Preliminary
results show that sensitivity of the integration method is decrised on the estimated frequency
of the problem. The efficiency of the new methods should be investigated via error analysis and
numerical applications.
[1] J. E. Marsden, M. West, Discrete mechanics and variational integrators. Acta Numerica 10
(2001), 357 – 514.
[2] Z. A Anastassi, D. S. Vlachos, T. E. Simos, The Use of Phase-Lag Derivatives in the Numerical
Integration of ODEs with Oscillating Solutions. International Conference on Numerical
Analysis and Applied Mathematics 1048 (2008) 1020 – 1025.
[3] S. Leyendecker, J.E. Marsden, M. Ortiz, Variational integrators for constrained dynamical
systems. Journal of Applied Mathematics and Mechanics (ZAMM) 88 (2008) 677 – 708.
[4] O. T. Kosmas, D. S. Vlachos, Phase-fitted discrete Lagrangian integrators. Computer Physics
Communications 181 (2010) 562 – 568.
S18.6: Mesh Generation Wed, 16:00–18:00
Chair: Thalhammer S1|03–223
Adaptive anisotropic mesh refinement based on a new adaptivity paradigm
Rene Schneider (TU Dresden) Schedule
We propose a new paradigm for adaptive mesh refinement. Instead of considering local mesh
diameters and their adaption to solution features, we propose to evaluate the benefit of possible
refinements in a direct fashion, and to select the most profitable refinements. We demonstrate that
based on this approach a directional refinement of triangular elements can be achieved, allowing
arbitrarily high aspect ratios.
However, only with the help of edge swapping and/or node removal (directional un-refinement)
near optimal performance can be achieved for strongly anisotropic solution features. With these
ingredients even re-alignment of the mesh with arbitrary error directions is achieved. Numerical
experiments demonstrate the utility of the proposed anisotropic refinement strategy.
Algebraic graph theory and its applications for mesh generation
Christian Schröppel, Jens Wackerfuß (TU Darmstadt) Schedule
Discretization methods are an important aspect of finding efficient numerical algorithms for the
solution of partial differential equations. Before the advent of specialized computer programs,
mesh generation was a tedious and often time-consuming process. Computer programs can greatly
reduce the effort involved in generating meshes for a known geometry. However, it is generally not
easy to incorporate specific knowledge about the structure, such as symmetries, into the process.
This talk presents algebraic graph theory as an efficient tool for mesh generation. Algebraic
graph theory is based on the mathematical properties of graphs itself, rather than on those of
representations of graphs, such as adjacency matrices. Meshes can be generated in a systematic

324 Section 18: Numerical methods of differential equations
way, based on the algebraic operations that are available to modify and combine graphs. Specific
features of a structure, such as symmetries, can be modeled into the generation of a mesh and its
indexing system, allowing for a domain decomposition tailored to those features.
This approach is especially useful for the generation of meshes of structures of a highly symmetric
or fractal nature. Examples of such structures include the networks of covalent carbon-carbon
bonds present in carbon nanotubes.
Regularization and numerical integration of quasi-linear differential-algebraic equations
of arbitrary index
Andreas Steinbrecher (TU Berlin) Schedule
Differential-algebraic equations (DAEs) are essential tools in the modeling of dynamical processes.
For instance, the dynamical behavior of mechanical systems, electrical circuits, chemical reactions
and many other are often described by DAEs, in particular, of quasi-linear structure.
It is well known that the numerical treatment of DAEs is nontrivial in general and more complicated
than the one of ordinary differential equations (ODEs). The classification of different
types of DAEs led to the development of several (independent) index concepts. Today, the index
concept plays a key role in the numerical analysis of DAEs since the index of a DAE provides a
measure of the difficulty in the analytical as well as in the numerical solution. As a rule of thumb,
the higher the index of a DAE is, the more complicated is its numerical analysis, and the more
careful one has to be in the numerical solution of the problem. In particular, multibody systems
are modeled by DAEs of differentiation index (d-index) 3 and circuit equations have a d-index
up to 2. Arising effects in the numerical treatment of higher index DAEs are for example drift,
instabilities, convergence problems, or inconsistencies. A way out of the dilemma of a higher index
is a regularization of such classes of DAEs.
In this talk we will present two regularization methods and an approach for the numerical integration
of quasi-linear DAEs of the form
E(x(t), t) ˙x(t) = k(x(t), t), (1)
on the domain I = [t0, tf] with initial values x(t0) = x0 ∈ R n , where E ∈ C(R n × I, R n,n ) is
called the leading matrix of the quasi-linear DAE and k ∈ C(R n × I, R n ) its right-hand side.
Furthermore, x : I → R n represent the unknown variables.
We will present two iterative procedures which provide general tools for the regularization and
investigation of quasi-linear DAEs of an arbitrary index. One of this procedures is of rank inflation
type while the other one is of rank deflation type. Both procedures can be used as basis
for a regularization of the quasi-linear DAE and lead to equivalent regularized formulations of
the DAE, so called projected-strangeness-free formulations. The most important features of this
projected-strangeness-free formulations are the lowered index while all constraints, in particular,
the hidden constraints, are preserved. Therefore, projected-strangeness-free formulations can be
used as basis for numerical integration using stiff ODE solvers in an robust and efficient way.
Based on a projected-strangeness-free formulation the basic idea for a robust and efficient numerical
integration will be presented and illustrated by several examples.
Coupled FE-BE eigenvalue problems for fluid-structure interaction of submerged
bodies
G. Unger, A. Kimeswenger, O. Steinbach (TU Graz) Schedule
In this talk we present a coupled finite and boundary element eigenvalue problem formulation
for the simulation of the vibro-acoustic behavior of elastic bodies submerged in unbounded fluid
domains as submarines in the sea. Usually the fluid is assumed to be incompressible and hence

Section 18: Numerical methods of differential equations 325
modeled by the Laplace equation. In contrast, we do not neglect the compressibility of the fluid
but model it by the Helmholtz equation. The resulting coupled eigenvalue problem for the fluidstructure
interaction is then nonlinear since the frequency parameter appears nonlinearly in the
boundary integral formulation of the Helmholtz equation. We analyze this eigenvalue problem and
its discretization in the framework of eigenvalue problems for holomorphic Fredholm operator–
valued functions. For the numerical solution of the discretized eigenvalue problem we use the
contour integral method which reduces the algebraic nonlinear eigenvalue problem to a linear
one. The method is based on a contour integral representation of the resolvent operator and it is
suitable for the extraction of all eigenvalues which are enclosed by a given contour. The dimension
of the resulting linear eigenvalue problem corresponds to the number of eigenvalues inside
the contour. The main computational effort consists in the evaluation of the resolvent operator
for the contour integral which requires the solution of several linear systems involving finite and
boundary element matrices.
New boundary element algorithm for heat conduction equation
D.V. Yevdokymov (Dniepropetrovsk National University named after O. Honchar) Schedule
Boundary element method has become powerful tool of numerical analysis because of high accuracy
and unique opportunity of effective calculations in complex shape domains, al least, for
linear elliptic boundary-value problems. However, nevertheless all mentioned advantages, general
effectiveness of the boundary element method at the moment is very far from the best. Computational
difficulties of boundary element applications to inhomogeneous or non-linear problems
are so serious, that the method is practically not used in such field. Beside of that, there may
be specific computational difficulties even for linear problems, for example, effectiveness of finite
difference method for usual heat conduction equation is sufficiently higher, than boundary element
method effectiveness. As a result, the field of effective using of boundary element method
is restricted by linear elliptic problems. The aim of the present work is to develop such boundary
element algorithm, which provides effectiveness comparable with finite difference method effectiveness
at least for linear parabolic problems. Let us consider a heat conduction problem with
traditional boundary condition and enough smooth initial condition. Thus the problem can be
described by pure boundary integral equation, which provides analysis on boundary alone. Let us
assumed that the problem is solved until n-th time step. To solve the problem on (n+1)-th time
step let us introduce two sets of points: observation points, situated on the boundary, and collocation
points, situated on the perpendicular to boundary on enough small (but non-asymptotically
small) distance from correspondent observation points. Let us calculate the temperature values
at collocation points, taking into account influences only previous n time steps. After that, the
boundary thermal flux in observation point can by approximately determined by difference of
temperatures in observation and collocation points. The boundary condition and the obtained
representation for thermal flux give an opportunity to calculate desired boundary values, thus
the problem is solved on (n+1)-th time step without formulation of linear algebraic equation
system and its computer solution. The proposed algorithm is similar to explicit finite difference
and therefore it requires enough small time steps. The time step may be increased under using of
the simple iterative procedure. The proposed algorithm is illustrated by set of test calculations,
which confirm its high effectiveness comparable with finite difference method especially for small
times.
S18.7: Finite Elements Thu, 13:30–15:30
Chair: Otten S1|03–221

326 Section 18: Numerical methods of differential equations
Full discretization of the porous medium/fast diffusion equation based on its very
weak formulation
Etienne Emmrich, David Šiška (Universität Bielefeld) Schedule
The very weak formulation of the porous medium/fast diffusion equation yields an evolution problem
in a Gelfand triple with the pivot space H −1 . This allows to employ methods of the theory of
monotone operators in order to study fully discrete approximations combining a Galerkin method
(including conforming finite element methods) with the backward Euler scheme. Convergence is
shown even for rough initial data and right-hand sides. The theoretical results are illustrated,
in the one-dimensional case, for the piecewise constant finite element approximation of the porous
medium equation with the δ-distribution as initial value. As a byproduct, L p -stability of
the H −1 -orthogonal projection onto the space of piecewise constant functions is shown for the
one-dimensional case.
Finite Element Approximation of the Stochastic Landau-Lifshitz-Gilbert Equation
Lubomir Banas (Heriot-Watt University), Zdzislaw Brzeniak (University of York), Andreas Prohl
(Universität Tübingen) Schedule
The evolution of magnetization in ferromagnetic materials under the influence of thermal noise
can be described by the stochastic Landau-Lifshitz-Gilbert (SLLG) equation
�
�
�
�
dm(t, x) = −α m(t, x) × m(t, x) × Heff(t, x) − m(t, x) × Heff(t, x) dt
+ν m(t, x) × ◦dW (t, x) ∀ (t, x) ∈ (0, T ) × D ,
∂nm(t, x) = 0 ∀ (t, x) ∈ (0, T ) × ∂D ,
m(0, x) = m0(x) ∀ x ∈ D ,
where ‘◦’ denotes stochastic integration in the Stratonovich sense, α is a damping constant and
ν is a temperature dependent parameter. The magnetization field m = (m1, m2, m3) satisfies a
sphere constrain |m| = 1. The vector valued Wiener process dW = (W1, W2, W3) models the
effects of the thermal noise. The effective field Heff may include a number of terms derived from
the free energy, such as, e.g., exchange, anisotropy and magnetic field. We consider two type of
the noise: a noise uniform in space and a space-time white noise.
We denote by Ik an equi-distant partition of [0, T ] into n sub-intervals of (local) size k = T/n;
we denote ϕj+1/2 := 1
�
j+1 j ϕ + ϕ 2
� . For simplicity we set Heff = ∆m. A finite-element based
algorithm for the SLLG equation is given below.
Algorithm A. Let Mj ∈ Vh be given for some time level j ≥ 0. The solution Mj+1 ∈ Vh on
the next time level is determined from
(Mj+1 − Mj �
, Φ)h = −αk Mj+1/2 × [Mj+1/2 × � ∆hMj+1 �
], Φ − k
h
� Mj+1/2 × � ∆hMj+1 , Φ �
h
+ν � Mj+1/2 × ∆Wj+1 , Φ �
∀ Φ ∈ Vh ,
where Vh is a finite element space of piecewise linear vector fields, (·, ·)h is a discrete (mass
lumped) inner product, and � ∆h is a discrete Laplace operator.
We discuss efficient implementation strategies for Algorithm A and present a number of computational
studies including: long-time behaviour of finite ensembles of magnetic spins, finite-time
finite-energy blow-up behaviour of solutions, and thermal fluctuations in magnetic nanoparticles.
[1] Baňas L., and Brzeźniak Z., and Prohl A.: Convergent Finite Element Based Discretization
of the Stochastic Landau-Lifshitz-Gilbert Equations. Submitted.
h

Section 18: Numerical methods of differential equations 327
Stable coupling of finite and boundary element methods
Olaf Steinbach (TU Graz) Schedule
We analyze the one-equation coupling of finite and boundary element methods which is very
popular in applications since it requires only single and double layer integral operators, and which
also allows the use of simple collocation schemes. We provide necessary and sufficient conditions
to ensure ellipticity of the underlying bilinear form. Numerical examples confirm the sharpness
of the theoretical estimates.
On the visualization of solution of fractional differential equations
Djurdjica Takači (University of Novi Sad) Schedule
We consider a class of fractional differential equations (ordinary and partial) and construct its
exact and approximate solution, The visualizations of fractional integral, fractional derivative and
the approximate solution of fractional differential equations are presented by using the dynamic
properties of package GeoGebra.
On the error estimate for calculating some singular integrals
Alexander V. Vasilyev (Belgorod State University, Russia), Vladimir B. Vasilyev (Lipetsk State
Technical University, Russia) Schedule
We consider multi-dimensional singular integral of convolution type
�
K(x − y)u(y)dy (1)
R m
with Calderon-Zygmund kernel K [1], and suggest to replace it by series’ sum over lattice points
from Z m h (the lattice in Rm with step h). Assuming the kernel K has a certain smoothness
property, the function u(y) satisfies the Hölder condition of order α, 0 < α < 1, and certain
condition on decay at infinity, we show that the error between (1) and series’ sum is equivalent
h α .
[1] S. G. Mikhlin, S. Prössdorf, Singular Integral Operators, Berlin, Akademie-Verlag, 1986.
S18.8: Theoretical Numerical Analysis Thu, 16:00–18:00
Chair: Prohl S1|03–221
A finite element method for a noncoercive elliptic problem with Neumann boundary
conditions
Klim Kavaliou, Lutz Tobiska (Universität Magdeburg) Schedule
We study a noncoercive convection-diffusion problem with Neumann type boundary conditions
appearing in modelling of magnetic fluid seals [1,2]. In [3] the existence and uniqueness of the
continuous problem has been analyzed. The associated operator has a non-trivial one-dimensional
kernel spanned by a positive function. A finite volume discretization was proposed in [4] which
shows the same properties on the discrete level.
We apply a maximum principle preserving low order finite-element approach developed in
[5,6] for coercive convection-diffusion equations. The properties of the discrete problem and its
relationship to the finite volume method in [4] are discussed. Under additional assumptions on
the data both the continuous and discrete problem are coercive. Numerical tests confirm the
theoretical predictions.

328 Section 18: Numerical methods of differential equations
[1] S. Beresnev, V. Polevikov, and L. Tobiska, Numerical study of the influence of diffusion
of magnetic particles on equilibrium shapes of a free magnetic fluid surface, Commun.
Nonlinear Sci. Numer. Simulat. 14 (2009), 1403–1409
[2] V. Polevikov and L. Tobiska, Influence of diffusion of magnetic particles on stability of a
static magnetic fluid seal under the action of external pressure drop, Commun. Nonlinear
Sci. Numer. Simulat. 16 (2011), 4021–4027
[3] J. Droniu and J.-L. Vázquez, Noncoercive convection-diffusion elliptic problems with Neumann
boundary conditions, Calc. Var. 34 (2009), 413–434
[4] C. Chainais-Hillairet and J. Droniou, Finite-volume schemes for noncoercive elliptic problems
with Neumann boundary conditions, IMA J. Numer. Anal. 31 (2011), 61–85
[5] H.-G. Roos, M. Stynes, and L. Tobiska, Robust numerical methods for singularly perturbed
differential equations. Convection-diffusion-reaction and flow problems, volume 24 of
Springer Series in Computational Mathematics, Springer-Verlag, Berlin (2008)
[6] T. Ikeda, Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena,
North-Holland (1983)
Adaptive exponential operator splitting methods for nonlinear evolution equations
Mechthild Thalhammer (Universität der Bundeswehr München, Universität Innsbruck) Schedule
In this talk, I shall primarily address the issue of efficient numerical methods for the space and
time discretisation of nonlinear Schrödinger equations such as systems of coupled time-dependent
Gross–Pitaevskii equations arising in quantum physics for the description of multi-component
Bose–Einstein condensates. For the considered class of problems, a variety of contributions confirms
the favourable behaviour of pseudo-spectral and exponential operator splitting methods
regarding efficiency and accuracy. However, due to the fact that in the absence of an adaptive
local error control in space and time, the reliability of the numerical solution and the performance
of the space and time discretisation strongly depends on the experienced scientist selecting the
space and time grid in advance, I will exemplify different approaches for the reliable time integration
of Gross–Pitaevskii systems on the basis of a local error control for splitting methods. The
approach also extends to other problem classes such as parabolic problems.
An adaptive DG space-time method
Martin Neumüller, Olaf Steinbach (TU Graz) Schedule
For evolution equations we present a flexible space-time method based on Discontinuous Galerkin
finite elements. Space-time methods have advantages when we have to deal with moving domains
and if we want to do local refinement in the space-time domain. For this we use a residual based
error estimator. This method will be applied to the heat equation and to the Navier Stokes equations.
Numerical examples and some applications will be given.
Exponential decay of two-dimensional rotating waves
Denny Otten (Universität Bielefeld) Schedule
In this talk we show exponential decay in space and time for solution kernels of complex-valued
parabolic systems in several dimensions with negative absolute term. The convection terms of
these systems have unbounded coefficients and they are of rotational type.

Section 18: Numerical methods of differential equations 329
A model equation in R 2 is given by
Ut = A△U + cDφU + B(x)U, x ∈ R 2
where U(x, t) ∈ C N , 0 �= c ∈ R, A ∈ C N,N is positive definite and B(x) ∈ C N,N converges to some
negative definite matrix as |x| → ∞. By Dφ we denote the angular derivative which in Cartesian
coordinates reads Dφ := −x2D1 + x1D2.
For the constant coefficient operator obtained for |x| → ∞ we derive a representation for the
solution kernel from the Feynman-Kac formula. This is used to show exponential decay in time
and space for solutions of the variable coefficient inhomogeneous equation. Moreover, this also
leads to exponential decay for the stationary equation.
This study is motivated by the stability problem for rotating waves in several variables.
Adaptive stochastic collocation on sparse grids
Bettina Schieche, Jens Lang (TU Darmstadt) Schedule
Keywords: PDEs with random parameters, stochastic collocation, error estimation, adaptivity.
Numerical simulations become more reliable if random effects are taken into account. To this end,
the describing parameters can be expressed by random variables or random fields, which leads to
partial differential equations (PDEs) with random parameters.
Common numerical methods to solve such problems are spectral methods of Galerkin type
[1] and stochastic collocation on sparse grids [2,3]. We focus on stochastic collocation, because it
decouples the random PDE into a set of deterministic equations that can be solved in parallel.
In order to keep the computational costs at a moderate level, it is inevitable to place the collocation
points adaptively. Therefore, error estimates are required. For spectral methods, adjoint
a posteriori error analysis has been proposed in [4].
We want to combine stochastic collocation with an adjoint approach in order to estimate the
error of some stochastic quantity, such as the mean or variance of a solution functional. Thereby,
our goal is to develop appropriate error estimates that require less computational effort then the
solution itself.
[1] B. Schieche, Stochastische finite Elemente, diploma thesis, 2009
[2] B. Schieche, Stochastic Analysis of Nusselt Numbers for Natural Convection with Uncertain
Boundary Conditions, Preprint, 2010
[3] F. Nobile, R. Tempone, C.G. Webster, An anisotropic sparse grid stochastic collocation method
for partial differential equations with random input data, SIAM J. Numer. Anal., 46, pp
2411–2442, 2008.
[4] L. Mathelin, O.P. Le Maître, Uncertainty quantification in a chemical system using error
estimate-based mesh adaptation, TCFD, (in press)

330 Section 19: Optimization of differential equations
Section 19: Optimization of differential equations
Organizers: Roland Herzog (TU Chemnitz), Barbara Kaltenbacher (Alpen-Adria Universität
Klagenfurt)
S19.1: Algorithmic Approaches I Tue, 13:30–15:30
Chair: Roland Herzog S1|03–121
Unified numerical treatment for optimal transport of geometric objects
Andreas Günther (Zuse-Institut Berlin) Schedule
An important task in medical imaging is segmentation of anatomical objects. Identifying corresponding
points on different shapes is therefore a fundamental prerequisite for quantitative shape
analysis.
Currents provide a unified mathematical description of geometrical objects of dimension 0
(points), 1 (curves), 2 (surfaces) or 3 (volumes) which are embedded in R 3 . The Large Deformation
Diffeomorphic Metric Mapping framework [Joshi and Miller, IEEE Transactions on Image
Processing, 2000] solves the correspondence problem between them by evolving a displacement
field along a velocity field.
In this talk we develop two innovative aspects for this ode / pde optimization problem: First,
we spatially discretize the velocity field with conforming adaptive finite elements and discuss
advantages of this new approach. Second, we directly compute the temporal evolution of discrete
m-current attributes. Numerical tests confirm the practicability of our findings.
Semismooth Newton for time-optimal control of parabolic equations
Konstantin Pieper, Boris Vexler (TU München) Schedule
We consider a time-optimal control problem where the state u is subject to the nonlinear parabolic
equation
∂tu(t) + Au(t) + ϕ(u(t)) = q(t) in Ω for t ∈ (0, T ),
u(0) = u0.
The control q has to be admissible with respect to the pointwise constraints qa ≤ q(t) ≤ qb for all
t ∈ (0, T ). The objective is now to find a control which minimizes the transfer time
min T
such that u is driven sufficiently close to some target condition ud, i.e.,
�u(T ) − ud� L 2 (Ω) ≤ δ.
To derive an efficient numerical algorithm for the time-optimal problem, we consider a Tichonovregularized
version and analyze the influence of the regularization parameter on the optimal solutions.
Finally we describe a semismooth Newton method for the regularized problem where
the time T and the control q are updated simultaneously in each iteration. When incorporating
the pointwise control constraints into the Newton method, we also have to be careful to retain
symmetry of the linear system which is solved in each step.
An Approach to Shape Optimization with State Constraints
Christian Leithäuser (Fraunhofer ITWM, TU Kaiserslautern), Robert Feßler (Fraunhofer ITWM)
Schedule

Section 19: Optimization of differential equations 331
We study an approach into shape optimization with state constraints by considering flow problems
controlled by the shape of the domain with certain constraints on the flow velocity. Especially
this enables us to deal with supremum norm cost functions, but also other state constraints are
possible.
For simplicity we model the domain dependency through conformal metrics, which leads to a
flow problem on a fixed reference domain where the shape dependency is contained in the differential
operators. In order to solve the optimization problem the state equations and constraints
are discretized leading to a nonlinear programming problem which can be solved on the discrete
level.
A Robust Solver for Distributed Optimal Control for Stokes Flow
Markus Kollmann, Walter Zulehner (Universität Linz) Schedule
In this talk we consider the following optimal control problem:
subject to
Minimize J(u, f) = 1
2
||u − ud|| L
2 2 α
(Ω) +
2 ||f||2L
2 (Ω)
−∆u + ∇p = f in Ω
div u = 0 in Ω
u = 0 on Γ
+ inequality constraints.
Here Ω is an open and bounded domain in R d (d ∈ {1, 2, 3}), Γ denotes the boundary and α > 0
is a cost parameter. We consider two types of inequality constraints:
• inequality constraints on the control f,
• inequality constraints on the state u.
In both cases, the first order system of necessary and sufficient optimality conditions of (1) is
nonlinear. A semi-smooth Newton iteration is applied in order to linearize the system. In every
Newton step a linear saddle point system has to be solved (after discretization). For these linear
systems solvers are discussed. Numerical examples are given which illustrate the theoretical results.
Lossy Compression of State Trajectories
Sebastian Götschel, Martin Weiser (Zuse Institute Berlin) Schedule
In large-scale, time-dependent optimal control problems, adjoint methods for gradient computations
are often employed. As the state enters into the adjoint equation, the state trajectory has
to be stored, which can result in high demand of storage capacity and bandwidth. In this talk
we address lossy compression of state trajectories as a means to reduce these demands, without
a significant loss of accuracy or increase of computational complexity. We present a-priori error
estimates as well as heuristic schemes for adaptively selecting the quantization level. The different
trade-offs compared to checkpointing or model reduction are discussed. Quantitative aspects are
illustrated on numerical examples.
S19.2: Algorithmic Approaches II Tue, 16:00–18:00
Chair: Anton Schiela S1|03–121
(1)

332 Section 19: Optimization of differential equations
Adaptive Multilevel SQP-Methods with Reduced Order Models for PDE-constrained
Problems
Jan Carsten Ziems, Stefan Ulbrich (TU Darmstadt) Schedule
We present an adaptive multilevel generalized SQP-method for optimal control problems governed
by nonlinear time-dependent PDEs with control constraints. For such problems, standard
discretization techniques require in general many degrees of freedom for the optimization process
and a good resolution of the optimal solution which is very time consuming. To overcome this
difficulty the algorithm generates a hierarchy of adaptively refined discretizations. The discretized
problems are then each approximated by an adaptively generated sequence of reduced order
models. The adaptive refinement strategies are based on a posteriori error estimators for the
original and the discretized PDE, the adjoint PDE and a criticality measure. In our numerical
examples we construct the reduced order models by the proper orthogonal decomposition (POD)
method from snapshots of the state and adjoint state. The effort for the nonlinearities of the
resulting POD Galerkin discretization is additionally reduced by the discrete empirical interpolation
method (DEIM) recently proposed by Chaturantabut and Sorensen. Numerical results for
test problems and a 3D glass cooling application are presented.
The Quadratic Penalty Method for solving Control-Constrained Optimal Control
Problems
Max Winkler (Universität der Bundeswehr München), Christian Grossmann (TU Dresden) Schedule
We consider a method for solving elliptic optimal control problems with control constraints. The
constraints are penalized by the quadratic penalty function. The resulting parameter-dependent
unconstrained problems are investigated for existence and uniqueness of solutions, optimality
conditions and convergence of its solutions.
It can be proven [1] that the auxiliary solutions converge linearly towards the optimal control.
The optimality condition of the auxiliary problems possess a resolution for the control depending
only on the adjoint state. Thus, one can eliminate the control out of the optimality system. This
leads to a nonlinear homotopy mapping whose roots characterize a central path towards the solution
of the original optimal control problem. Since Fréchet differentiability is not given for this
mapping we have to apply semi-smooth Newton methods for the solution of this operator equation.
These methods converge Q-superlinearly and even Q-quadratically under some additional
assumptions.
[1] Ch. Grossmann, M. Winkler, Mesh-Independent Convergence of Penalty Methods Applied
to Optimal Control with Partial Differential Equations, submitted (2011)
Optimization of PDEs with state constraints via Infinite Penalization methods
Richard C Barnard, Martin Frank, Michael Herty (RWTH Aachen) Schedule
We consider optimization problems constrained by partial differential equations (PDEs) with additional
constraints placed on the solution of the PDEs. We develop a general framework using
infinite-valued penalization functions and Clarke subgradients and apply this to problems with
box constraints as well as constraints arising in applications, such as constraints on the average
value of the state in subdomains. We present numerical results of this algorithm for the elliptic
case and compare with other state-constrained algorithms.
Space Mapping Optimization and Model Hierarchies
Rene Pinnau (TU Kaiserslautern) Schedule

Section 19: Optimization of differential equations 333
Industrial optimization problems often require information on the adjoint variables for very complex
model equations. Typically, there is a whole hierarchy of models available which allows to
balance the computational costs and the exactness of the model. We use these hierarchies in combination
with space mapping techniques to speed up the convergence of optimization algorithms.
In this talk we present three applications where this approach proved to be very successful. We
will cover questions from semiconductor design, the control of particles in fluids and shape optimization
for filters.
An Adaptive Semismooth Newton-CG Method for Constrained Parameter Identification
in Seismic Tomography
Christian Böhm, Michael Ulbrich (TU München) Schedule
Earthquakes excite seismic waves that propagate through the Earth and can be recorded as seismograms
at remote receiver locations. Seismic tomography means to infer the Earth’s material
structure based on these observations. This can be stated as a PDE-constrained optimization
problem that seeks to minimize the misfit between observed and synthetically generated seismograms.
We present a semismooth Newton-CG method for full-waveform seismic inversion with boxconstraints
on the material parameters. The implementation features the adjoint-based computation
of the gradient and Hessian-vector products of the reduced problem, a Krylov subspace
method to solve the Newton system in matrix-free fashion and globalization by a trust-region
method.
The governing equations are given by a coupled system of the acoustic and elastic wave
equation for the numerical simulation in solid and fluid media. The wave equation is spatially
discretized by high-order Lagrange polynomials and solved with an explicit time-stepping scheme.
The parallel implementation utilizing MPI communication enables us to tackle large-scale seismic
inverse problems.
The ill-posedness of the problem is addressed by inverting sequentially for increasing frequencies.
Thereby, the parameter grid is adaptively refined using goal-oriented a-posteriori error
estimates. This enables us to choose the resolution of the reconstruction based on the information
that is provided by the observed data.
We show numerical results for the application of our method to a dataset of marine geophysical
exploration in the North Sea.
We gratefully acknowledge the support of this work by the Munich Centre of Advanced Computing
and by the DFG.
S19.3: Numerics and Error Estimation I Wed, 13:30–15:30
Chair: Carsten Ziems S1|03–121
Finite element error estimates for parabolic optimal control problems with semilinear
state equation
Ira Neitzel, Boris Vexler (TU München) Schedule
In this talk, we present a priori error estimates for the space-time finite element discretization
of control constrained optimal control problems governed by semilinear parabolic PDEs. We discuss
a dG(0)cG(1) discretization of the state equation, i.e. we discretize it piecewise constant in
time and cellwise (bi)linear in space. We extend error estimates shown by Meidner and Vexler
for a linear-quadratic setting. Throughout, we focus on the specific difficulties introduced by the
nonlinear state equation, such as associated boundedness resultson the semidiscrete and discrete
level independent of the discretization parameters, as well as second-order sufficient optimality

334 Section 19: Optimization of differential equations
conditions with quadratic growth conditions in L 2 -neighborhoods. We foucs in detail on piecewise
constant control discretization and briefly discuss different types of control discretization and the
extension to certain different problem classes such as problems with Lavrentiev-regularized state
constraints, cf. the results by Hinze and Meyer for elliptic problems. We end the talk by showing
some numerical experiments.
Shape sensitivity analysis in the extended finite element method
Franz-Joseph Barthold, Daniel Materna (TU Dortmund) Schedule
The stiffness matrix K = ∂R/∂U , the pseudo load matrix P = ∂R/∂X and the sensitivity
matrix S = −K −1 P can be derived from the residual vector R (weak form) by the analytical derivative
(variation) with respect to the nodal displacements (displacement field) U and the nodal
coordinates (geometry field) X, respectively. Thus, any design variation ∆X generates a variation
of the displacement ∆U = S ∆X. These derivatives must be derived, implemented and computed
in a consistent fashion to the underlying structural analysis. The term consistent linearisation is
well-known in nonlinear continuum mechanics and nonlinear finite element methods and regularly
applied to compute the consistent stiffness matrix K.
This technique is applied to sensitivity analysis as well to derive the above mentioned pseudo
load matrix P in a consistent way both with the physical (displacement field) as well as material
(geometry field) model, see [?]. Nevertheless, it is practically important to set up a reliable
technique to check all derived sensitivities in comparison with the numerical sensitivities.
We outline our strategy to instantaneously check the analytical sensitivities with finite difference
values for different classes of design variables. This is especially important for the extended
finite element method (XFEM) and the above explained difficult situation of general shapes of
the background mesh and the great influence of the chosen integration scheme. We outline what
kind of differences between both variants can be expected and tolerated.
The combined shape optimisation of the overall domain as well as of the internal boundaries
violates some of the assumptions of standard XFEM approaches. Thus, special attention has to
be devoted to a consistent approach both in structural and sensitivity analysis. Here, the choice
of Ansatz functions modelling the desired discontinuities along the interfaces in the element
must be considered and revised. These modifications should be designed such that the described
complexities are unlikely to occur in case of general design modifications. Furthermore, existing
elements from sensitivity analysis of traditional finite elements should adequately be applied to
XFEM. Thus, XFEM could be a model problem where the complexity of sensitivity analysis
dominates the choice of the underlying structural analysis model.
In this talk, we like to outline a modified XFEM formulation which is proved to generate
correct sensitivity information for shape modifications of the background mesh as well as of the
level set based boundaries of multi-material designs. Numerical examples illustrate the advocated
theoretical concept.
Time discretization with almost third order convergence for parabolic optimal control
problems with control constraints
Andreas Springer, Boris Vexler (TU München) Schedule
We consider a linear quadratic parabolic optimal control problem with time-dependent control
and box constraints on the control. For such problems it is straightforward to show that a timediscrete
solution with second order convergence can be obtained either by the variational discretization
approach or by a post-processing strategy. Here, by combining those two approaches we
demonstrate that almost third order convergence with respect to the size of the time steps can
be achieved.

Section 19: Optimization of differential equations 335
To this end we discretize the state variable in time with the piecewise linear discontinuous Galerkin
(dG(1)) method. The control is not discretized but instead computed from the semidiscrete
adjoint state through the first order optimality condition. Exploiting superconvergence properties
of the dG(1) method at the nodes of the Radau quadrature, we reconstruct an improved adjoint
state from the optimal adjoint of the semidiscrete equation by piecewise quadratic interpolation.
It is shown that this reconstructed adjoint converges with almost third order as the fineness of
the time discretization approaches zero. An improved control solution is obtained by point-wise
projection of this reconstructed adjoint, again employing the first order optimality condition. This
post-processed solution also converges with almost order three with respect to the size of the time
step.
A-posteriori verification of optimality conditions for control problems with finitedimensional
control space
Saheed Akindeinde, Daniel Wachsmuth (Johann Radon Institute for Computational and Applied
Mathematics) Schedule
In this paper we investigate non-convex optimal control problems. We are concerned with aposteriori
verification of sufficient optimality conditions. If the proposed verification method confirms
the fulfillment of the sufficient condition then a-posteriori error estimates can be computed.
A special ingredient of our method is an error analysis for the Hessian of the underlying optimization
problem. We derive conditions under which positive definiteness of the Hessian of the
discrete problem implies positive definiteness of the Hessian of the continuous problem. The article
is complemented with numerical experiments.
Optimality conditions based on a numerical approximation
Martin Naß, Arnd Rösch (Universität Duisburg-Essen) Schedule
We consider an abstract nonlinear optimization problem. We derive sufficient optimality conditions
for a local solution ū based on a coercivity condition for a known numerical approximation
ūh. Further we derive error estimates for ū in terms of the discretization parameter h, assumed
the sufficient optimality conditions are fulfilled. The results are specified on an example of an
optimal control problem with pointwise state constraints.
S19.4: Numerics and Error Estimation II Wed, 16:00–18:00
Chair: Ira Neitzel S1|03–121
A Multiharmonic Finite Element Solver for Time-Periodic Parabolic Optimal Control
Problems
Ulrich Langer (Universität Linz) Schedule
This paper presents the numerical analysis of distributed parabolic optimal control problems
in a time-periodic setting. In particular, the desired state and the control are assumed to be
time-periodic. After eliminating the control from the optimality system, we arrive at the reduced
optimality system for the state and the co-state that is nothing but a coupled system of a
forward and a backward parabolic partial differential equation (PDE). Due to the linearity, the
state and the co-state are time-periodic as well. This coupled system of PDEs is discretized by
the multiharmonic finite element method. Finally, we arrive at a large system of algebraic equations,
which fortunately decouples into smaller systems each of them defining the cosine and sine
Fourier coefficients for the state and co-state with respect to a single frequency. For these smaller
systems, we construct preconditioners resulting in a fast converging minimal residual solver with
a parameter-independent convergence rate. All these systems can be solved totally in parallel

336 Section 19: Optimization of differential equations
with optimal or, at least, almost optimal complexity.
This talk is based on a joint work with M. Kollmann, M. Kolmbauer, M. Wolfmayr and W.
Zulehner. We gratefully acknowledge the financial support by the Austrian Science Fund (FWF)
under the grants DK W1214 (projects DK4 and DK12) and P19255. We also thank the Austria
Center of Competence in Mechatronics (ACCM), which is a part of the COMET K2 program of the
Austrian Government, for supporting our work on optimization problems with PDE constraints
in electromagnetics.
Identification of an unknown parameter in the main part of an elliptic PDE
Ute Aßmann, Arnd Rösch (Universität Duisburg-Essen) Schedule
We are interested in identifying an unknown material parameter a(x) in the main part of an
elliptic partial differential equation
−div (a(x) grad y(x)) = g(x) in Ω
with corresponding boundary conditions. We discuss a Tichonov regularization
min
a J(y, a) = �y − yd� 2
L 2 (Ω) + α�a�2 H s (Ω)
with s > 0. Moreover, we require the following constraints for the unknown parameter
0 < amin ≤ a(x) ≤ amax.
The talk starts with results on existence of solutions and necessary and sufficient optimality conditions.
The second part of the talk will be devoted to numerical aspects and recent results of the
problem.
Transient simultaneous multi-layered shape and material optimization for elastic vocal
fold models
Bastian Schmidt, Michael Stingl (Universität Erlangen-Nürnberg) Schedule
Multi-layered bodies, characterized by at least two inner parts with different materials, are frequently
used in various industrial or medical applications. The numerical optimization of the outer
shape of these bodies as well as the material properties within the layers with respect to a given
cost criterion are standard questions addressed in shape and material optimization, respectively.
We consider a combination of both these techniques, however, we are interested in optimizing
the inner partition of the body into its layers and material parameters in each of the layers
while keeping the outer shape fixed. This is done by allowing shape parameters to modify a given
reference configuration. Moreover, we use a tracking type objective functional in order to minimize
the distance between a given reference displacement field and the response of the elastic body
with respect to one or several dynamic loading scenarios.
We present a rigorous mathematical formulation of the optimization problem and state equation
together with results for existence of solutions and analysis of convergence of suitable discretizations
involving a transient finite-element approach with either isotropic or transversal-isotropic
material. Furthermore we apply the adjoint method in order to derive an adjoint problem allowing
the efficient calculation of shape and material gradients and thus the use of gradient based
optimization algorithms.
We demonstrate the feasibility of the approach by a numerical study in the framework of
which the behavior of a numerical model of the human vocal folds is optimally adapted to a set
of measured displacement fields obtained from physical experiments.

Section 19: Optimization of differential equations 337
Adjoint Based Optimal Control of Multiphase Multicomponent Flow in Porous Media
with Applications to CO2 Sequestration in Underground Reservoirs
Moritz Simon, Michael Ulbrich (TU München) Schedule
With the target of optimizing CO2 sequestration in underground reservoirs, we investigate constrained
optimal control problems with multiphase multicomponent flow in porous media. Currently,
we consider a two-phase (wetting and non-wetting), two-component (saline water and CO2)
model, and the objective is to maximize the amount of trapped CO2 in an underground reservoir
after a fixed period of CO2 injection. The time-dependent injection rates in multiple wells are
used as control parameters. Extensions to more general models and to other optimization variables
or objectives are readily possible. We describe the governing multiphase multicomponent Darcy
flow PDE system, formulate the optimal control problem and derive the corresponding adjoint
equations.
For the discretization we use a variant of the BOX method, a control volume FE method with
linear Lagrange elements on the primal mesh and piecewise constant test functions on the dual
mesh. The timestep-wise Lagrange function of the control problem is implemented as a variational
form in Sundance, a toolbox for rapid development of parallel finite element simulations, which
is part of the HPC software Trilinos. The symbolic capabilities of Sundance allow to derive the
discrete state equation, adjoint equation and reduced gradient automatically from this variational
form. In order to prepare Sundance for the BOX method, several new concepts, like control volume
boundary integrals and upwinding, were added to its core structure.
Via a C++ interface, the Sundance state and adjoint solvers are linked to the interior point
optimization code IPOPT. Since we currently do not provide second derivative information, the
interface is configured to use limited memory BFGS updates for approximating the Hessian matrix
of the Lagrange function. The (non-)linear systems in the forward and adjoint simulations are
solved in parallel, using interfaces to packages such as NOX, Amesos and AztecOO within Trilinos.
In this talk we present several optimization results for partially miscible two-phase flow in both
homogeneous and inhomogeneous reservoirs.
The presented work is conducted in project K1 of the Munich Centre of Advanced Computing
(MAC) within the KAUST–TUM Special Partnership. The funding by the King Abdullah
University of Science and Technology (KAUST, Saudi Arabia) is gratefully acknowledged.
Implementation and validation of an adjoint high-Reynolds number model for thermally
driven flows
Anne Lincke, Arthur Stück, Thomas Rung (TU Hamburg) Schedule
This paper presents a high-Reynolds number (high-Re) approach to the adjoint Navier-Stokes-
Fourier equations based upon a modified high-Re sensitivity equation for buoyancy-driven flows.
For reasons of efficiency, the computational framework adheres to the continuous adjoint method
using a frozen-turbulence assumption. In former approaches the primal equations were either solved
with a wall function or a low-Re approach at the boundary, whereas the adjoint equations
were usually solved without any wall function features. The consequence is an inconsistent treatment
of the primal and adjoint equations which leads to sensitivity-errors. Opposed to the state
of the art, the present model uses a high-Re model for the primal equations and a high-Re model
for the adjoint equations. The adjoint high-Re model can easily be implemented and be used
for flow problems where wall functions are needed. The impact of this approach is an improved
consistency of primal and adjoint equations which leads to stable and realistic shape optimization
results for industrial flows.
In the first part of the paper a high-Re model for solving the adjoint Navier-Stokes-Fourier

338 Section 19: Optimization of differential equations
equations is introduced. The idea is to transfer the information of the law of the wall directly into
the adjoint system. This also leads to a modified sensitivity equation which adheres to the wall
function.
In the second part of the paper the model is validated by incompressible, steady-state test
cases. Examples included are restricted to ducted flows. Results are compared to simulations
where no wall functions are used for the primal and the dual solution. It can be seen that the
sensitivities provided by the new application are smoother and therefore the design cycle becomes
less sensitive to the step size.
Keywords: adjoint Navier-Stokes-Fourier equations, buoyancy-driven flow, frozen-turbulence
model, design optimization, shape sensitivities, wall functions.
Optimal Control of the Wave Equation with Trigonometric Operators
Stefan Reiterer (Universität Graz) Schedule
In our work we consider minimization of a quadratic functional of the form
subject to the wave equation
1
α
�y − z�2 L2(0,T ;V ) +
2 2 �u�2 L2(0,T ;H) ,
∂2 y + Ay = βu,
∂t2 y(0) = y0,
yt(0) = y1,
where V ⊂ H are Hilbert spaces, A : V → H is an linear elliptic operator, and the initial data
y0 ∈ V , y1 ∈ H, as the constant α > 0, and the weight function β are given.
To minimize the functional we use an inexact Conjugate Gradient Method on the operator
S ∗ S+αI, where S : L2(0, T ; H) → H 1 (0, T ; V ) denotes the solution operator of the wave equation.
The evaluation of the operators is realized with help of the Gautschi timestepping method proposed
by Hochbbruck and Lubich in [1], where we evaluate the occurring trigonometric operators
with help of rational Krylov methods proposed by Hochbbruck and Grimm in [2].
We will prove convergence, and structural properties of the occurring optimization scheme in
this abstract setting. Additionally we provide numerical results whith spectral element methods
for space discretization. We will also outline benefits and drawbacks of this approach and discuss
fast implementation and preconditioning of the algorithms.
[1] M. Hochbruck, C. Lubich, A Gautschi-type method for oscillatory second-order differential
equations Numerische Mathematik Vol. 83, Nr. 3 (1999) 403–426
[2] V. Grimm and M. Hochbruck, Rational approximation to trigonometric operators, BIT Numerical
Mathematics Vol. 48, Nr. 2 (2008), 215–229, Springer
S19.5: Applications I Thu, 13:30–15:30
Chair: Andreas Günther S1|03–121
PDE-constrained optimization in electromagnetic problems
Irwin Yousept (TU Berlin) Schedule

Section 19: Optimization of differential equations 339
Electromagnetism plays an essential role in many modern advanced technologies and applications.
Optimal control and parameter estimation of electromagnetic problems are delicate issues and
call for a careful study. In this talk, we discuss application problems arising from electromagnetic
induction heating, electrorheological (ER) fluids, and parameter estimation of electromagnetic
materials. Recent theoretical and numerical results of these topics are presented.
Multilevel Optimization for PDAE-Constrained Optimal Control Problems - Application
to Radiative Heat Transfer in 3d
Debora Clever (TU Darmstadt) Schedule
During the last decade it has been becoming of growing interest to not only simulate the behavior
of engineering, medical or financial applications but to also optimize their performance. Modeling
the considered process by a system of space-time dependent partial differential algebraic equations
(PDAEs), the task can be formulated as a PDAE-constrained optimal control problem, most likely
with additional constraints on control and state. For real world applications, the bottleneck of
solving such problems is the high complexity of the involved PDAEs, which have to be solved
several times within each optimization iteration. Therefore, an efficient optimization environment
has to combine highly efficient optimization techniques with fully adaptive PDAE solvers of high
order. To even gain more efficiency without loss of accuracy for the optimal control, multilevel
techniques are an attractive means.
We present an approach, where we reduce the considered problem to the control component
and apply a generalized multilevel SQP-method [1,2]. Control constraints are handled by an appropriate
projection. Reduced gradients and actings of the reduced Hessian are computed with
the continuous adjoint approach. We follow Rothe’s method with adaptive Rosenbrock methods
in time and adaptive multilevel finite elements in space. To be able to choose the discretization
scheme in accordance to the structure of the considered PDAE, we explicitly allow for an independent
discretization of state and adjoint systems. The resulting inexactness is controlled by
refining grids adaptively in space and time as the optimization proceeds.
We present numerical experiments for the cooling of hot glass down to room temperature,
modeled by radiative heat transfer and semi-transparent boundary conditions. We consider the
so called gray scale model, which is a space-time-dependent PDAE, including the highly nonlinear
and nonlocal exchange of energy between glass temperature and mean radiative intensities
[3]. Due to the high efficiency of the developed optimization environment it is possible to solve
such complex space-time-dependent optimal control problems even on non-trivial computational
domains in three spatial dimensions.
[1] D. Clever, J. Lang, S. Ulbrich, and J. C. Ziems. Combination of an adaptive multilevel SQP
method and a space-time adaptive PDAE solver for optimal control problems. Procedia
Computer Science, 1:1429–1437, 2010.
[2] D. Clever, J. Lang, S. Ulbrich, and J. C. Ziems. Generalized multilevel SQP-methods for
PDAE-constrained optimization based on space-time adaptive PDAE solvers. In G. Leugering,
et al., Constrained Optimization and Optimal Control for Partial Differential Equations,
pages 37–60. International Series of Numerical Mathematics, Vol. 160, Basel, 2012.
[3] E. W. Larsen, G. Thömmes, A. Klar, M. Seaïd, and T. Götz. Simplified PN approximations to
the equations of radiative heat transfer and applications. Journal of Computational Physics,
183:652–675, 2002.

340 Section 19: Optimization of differential equations
An optimization problem in the human knee
Anton Schiela (TU Berlin), Oliver Sander (FU Berlin) Schedule
Among the various difficulties in the modelling and simulation of the human knee the coupling
between ligaments and bone poses particularly interesting problems. While bones can be modelled
as elastic bodies, it is appropriate to model the ligaments as geometrically exact elastic
rods, so called cosserat rods. The task is to derive coupling conditions that allow for a rigorous
mathematical treatment and a well founded physical interpretation.
Our approach is to consider the coupled problem as an energy minimization problem, in which
the stored energy of both the rod and the elastic body is minimizer, subject to the equality constraints
that both bodies coincide at the coupling interface. We show existence of energy minimizers
for two variants of coupling conditions, and derive, under suitable assumptions, first order optimality
conditions. These optimality conditions can be interpreted as force and momentum balances
at the interface, and the involved Lagrangian multipliers are identified as constraint forces.
Optimal Control of Transient Drift diffusion Models
Prof.Dr. Martin Burger, Marcisse Fouego (Universität Münster) Schedule
In this paper We investigate the optimal control of transient drift-diffusion models for semiconductors.
Our main focus is the control of the current by optimizing the applied voltage and/or
the doping profile, which are the natural control variables.
The control problem is analyzed incluing existence, first-oder optimality and existence of adjoint
variables.
For the numerical simulation a simple but efficient Gummel iteration is derived . Furthermore we
investigage the augmented Lagrangian method for the contraints on the control. Numerical resuls
are presented for the n-p diode, in particular for the application of time-optimal switching
Quantitative hybrid electrical impedance imaging
Wolf Naetar (Universität Wien) Schedule
In recent years, several new hybrid imaging methods which combine Electrical Impedance Tomography
(which on its own is ill-posed) with other physical modalities have been proposed.
We apply the Levenberg-Marquardt algorithm to a hybrid conductivity imaging problem originating
from the coupling of Electrical Impedance Tomography with acoustic modalities. To be
precise, we aim for estimating the spatially varying conductivity σ inside the object of interest Ω
from measurements of the power density E(σ) = σ|∇u(σ)| 2 in Ω.
Under the assumption of Lipschitz-stability of the linearized inverse problem, we are able to
verify conditions for local convergence of the iteration method for Galerkin approximations of the
problem. Moreover, we implemented the algorithm and two fast modifications, which we tested
on simulated data.
S19.6: Applications II Thu, 16:00–18:00
Chair: Barbara Kaltenbacher S1|03–121
Optimal control of multiphase induction hardening
Dietmar Hömberg, Thomas Petzold (WIAS Berlin), Elisabetta Rocca (Universita’ degli studi di
Milano) Schedule
In my talk I investigate a new hardening process called multi-frequency induction hardening. In
contrast to standard induction heating approaches it allows for a true contour hardened pattern
of gears. The mathematical model consists of a vector potential equation of Maxwells equations
coupled with an energy balance and rate law to describe the growth of the high temperature

Section 19: Optimization of differential equations 341
phase in steel.
The equations are coupled via phase dependent material parameters. In the talk I will briefly
explain the model, comment on existence and uniqueness results, derive optimality conditions
and conclude with some numerical simulations.
Specific challenge for the numerical treatment is the resolution of the different spatial and
temporal scales. To this end we employ an hp-adaptive edge element discretization of Maxwells
equations and use different time scales to resolve magnetic and temperature effects, respectively.
Parameter identification in the crystallization of polymers
Shuai Lu (Fudan University), Yikan Liu (University of Tokyo), Xiang Xu (Michigan State University),
Masahiro Yamamoto (University of Tokyo) Schedule
Nucleation and growth mechanisms are the most important kinetics of the phase transformation
model which arises in the crystallization of the polymer materials. In each stage, the nucleation
rate and the growth rate have been the crucial coefficients describing the kinetics of the process as
well as the properties of the specimens. In this talk, we will firstly revisit the time cone approach
by Cahn where a hyperbolic governing equation is derived for the heterogenous nucleation rate
and spatially homogeneous growth rate. As for the inverse problem, by utilizing the eigenfunction
expansion method, we investigate the identification of the growth rate for an isothermal one
dimension specimen. Such a problem can be seem as an inverse coefficient problem for a hyperbolic
equation which is highly nonlinear with respect to the observation data. A two-step Tikhonov
type regularization method is proposed to reconstruct the growth rate provided with the final
noisy observation data. Numerical prototype examples are presented to illustrate the validity and
effectiveness of the proposed scheme.
An optimal control problem in polyconvex elasticity
Lars Lubkoll, Anton Schiela, Martin Weiser, Stefan Zachow (Zuse Institut Berlin) Schedule
Congenital malformations or trauma-related defects of facial bones are often corrected by patientspecific
implants to substitute or complement bone structures. As the implant’s shape and position
affect the soft tissue and hence the visual appearance of the patient, the prediction of implant
formation and placement are of utmost importance for the final outcome of rehabilitative facial
surgery. Currently the shape of an implant is customized individually during the operation, which
is a tedious and time consuming process. A preoperative design of implants using CAD methods
has the potential to shorten operation time and to open new perspectives regarding education of
surgeons, surgical planning and the verification procedure.
From a mathematical point of view the task of finding an optimal implant shape, such that a
desired result is achieved, can be formulated as an optimal control problem of the form
min J(u, g) s.t. u ∈ Ig(v)
v∈Uad
where u is the resulting displacement of the material and the sequentially weakly lower semicontinuous
cost functional J measures the deviation from the desired result. Ig is an elastic
energy functional associated with the boundary force g and a compressible, polyconvex stored
energy function in the sense of [1]. For this inverse problem, we give an existence result using the
direct method of the calculus of variations, discuss the occuring lack of regularity and difficulties
in the derivation of necessary optimality conditions as well as implications on the numerical
solution process. Finally we give some numerical examples for the case that Ig is associated with
a compressible Mooney-Rivlin material.

342 Section 19: Optimization of differential equations
[1] J.M. Ball, Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Rat.
Mesh. Anal. 63 (1977), 337–403
Shape Optimization for an Interface Problem in (linear) Elasticity for distortion
compensation
Kevin Sturm, Dietmar Hömberg (WIAS Berlin), Michael Hintermüller (Humboldt Universität)
Schedule
In this talk I will introduce a sharp interface model describing a workpiece made of steel. In
the heat treatment of steel different phases e.g. martensite and pearlite can be produced in the
workpiece. The goal of my work is to obtain a desired workpiece shape by controlling the final
phase distribution. Therefore our control variables are sets and thus we have to consider a shape
optimization problem. I will show how one can derive the shape derivative for this problem,
which then can be used to solve the shape optimization problem. Moreover, numerical results for
different workpiece shapes in two dimensions will be presented.
Dynamic PET Reconstruction based on aReaction-Diffusion Model
Louise Reips, Ralf Engbers, Martin Burger (Universität Münster) Schedule
PET is an imaging technique applied in nuclear medicine able to produce images of physiological
processes in 2D or 3D. The use of 18F-FDG PET is now a widely established method to quantify
tumour metabolism, but other investigations based on different tracers are still far from clinical
use, although they offer great opportunities such as radioactive water as a marker of cardiac
perfusion. A major obstacle is the need for dynamic image reconstruction from low quality data,
which applies in particular for tracers with fast decay like H 15
2 O.
Here we present a model-based approach to overcome those difficulties. We derive a set of
differential equations able to represent the kinetic behavior of H 15
2 O PET tracers during cardiac
perfusion. In this model one takes into account the exchange of materials between artery, tissue
and vein which predicts the tracer activity if the reaction rates, velocities, and diffusion coefficients
are known. One then interpretes, the computation of these distributed parameters as a nonlinear
inverse problem, which we solve using variational regularization approaches. For the minimization
we use the gradient-based methods and Forward-Backward Splitting.
The main advantage is the reduction of the degrees of freedom, which makes the problem
overdetermined and thus allows to proceed to low quality data. Instead of reconstructing the
4D tracer activity distribution (in space and time) we identify a set of 3D parameters (spatially
dependent only).
[1] M. Benning, T. Kösters, F. Wübbeling, K. P. Schäfers, and M. Burger. A nonlinear variational
method for improved quantification of myocardial blood flow using dynamic H15 2 O PET,
IEEE Nuclear Science Symposium Conference Record, (2008), 4472–4477.
[2] M. E. Kamasak, C. A. Bouman, E. D. Morris, and K. Sauer, Direct Reconstruction of Kinetic
Parameter Images from Dynamic PET Data, IEEE Transactions on Medical Imaging,
24(2005), 636-650.
[3] M. N. Wernick and J. N. Aarsvold. Emission Tomography: The Fundamentals of PET and
SPECT. Elsevier Academic Press, 2004.

Section 20: Dynamics and control 343
Section 20: Dynamics and control
Organizers: Knut Graichen (Universität Ulm), Stephan Trenn (Universität Kaiserslautern)
S20.1: Differential algebraic equations and applications Tue, 13:30–15:30
Chair: Stephan Trenn, Knut Graichen S1|01–A4
Positivity preserving simulation of Differential-Algebraic Equations
Ann-Kristin Baum (TU Berlin) Schedule
Positive dynamical systems arise in every application in which the considered variables represent
a material quantity that does not take negative values, like e.g. the concentration of chemical and
biological species or the amount of goods and individuals in economic and social sciences. Beside
positivity, the dynamics are often subject to constraints resulting from limitation of resources,
conservation or balance laws, which extend the differential system by additional algebraic equations.
In order to obtain a physically meaningful simulation of such processes, both properties, the
positivity and the constraints, should be reflected in the numerical solution. In this talk, we discuss
these issues for linear time-varying systems, as they arise for example in the linearization of
non-linear systems in chemical reaction kinetics or process engineering. We first consider index-1
problems, in which the differential and algebraic equations are explicitly given and explain under
which conditions we can expect a positive numerical approximation that meets the algebraic
constraints. We extend these results to higher index problems, i.e., problems in which some of the
algebraic equations are hidden in the system, by a positivity preserving index reduction. This is a
remodeling procedure which filters out these hidden constraints without destroying the positivity
property and thus admits to trace back these systems to the index-1 case.
Normal forms for DAEs and tracking control
Achim Ilchmann, Thomas Berger (TU Ilmenau), Timo Reis (Universität Hamburg) Schedule
As a counterpart to the Byrnes-Isidori form for linear time-invariant ODEs, we derive a normal
form (“almost a canonical form”) for linear time-invariant DAEs whose transfer function
C(sE − A) −1 B has either positive strict relative degree or has proper inverse. These forms are
exploited to investigate the zero dynamics of the system and to show that funnel control of a
rather large class of tracking signals is feasible.
Regularization of descriptor systems in behaviour form
S. L. Campbell (North Carolina State University), P. Kunkel (Universität Leipzig), V. Mehrmann
(TU Berlin) Schedule
Differential-algebraic equations (DAEs) present today the state-of-the-art in dynamical systems
arising from automated modularized modeling in almost all areas of science and engineering.
While the modeling becomes more and more convenient, the resulting models are typically not
easy to treat with current numerical simulation, control and optimization methods. In many cases
a reformulation of the models or even a regularization is necessary to avoid failure of the
computational methods. We will discuss general DAE control problems and how they can be
systematically reformulated and regularized so that the resulting system can be used in control
and optimization procedures without much further difficulties.
Self-Adjoint Differential-Algebraic Equations arising in Linear-Quadratic Optimal
Control Problems
Lena Scholz (TU Berlin) Schedule

344 Section 20: Dynamics and control
Motivated from the linear-quadratic optimal control problem for differential-algebraic equations
(DAEs) given in the form
minimize
1
2 x(t)T Mex(t) + 1
2
� t
subject to E ˙x = Ax + Bu + f, x(t) = x ∈ R n ,
t
� x T W x + x T Su + u T S T x + u T Ru � dt
we study the functional analytic properties of the operator associated with the necessary optimality
boundary value problem and show that it is associated with a self-conjugate operator and
a self-adjoint pair of matrix functions. If we denote the differential-algebraic equation associated
with the necessary optimality boundary value problem by
E ˙z = Az + ˜ f,
then the pair (E, A) has the property that E T = −E and A T = A + ˙
E.
We analyze the structure of the resulting self-adjoint pair of matrix functions and of the associated
boundary value problem via condensed forms under orthogonal congruence transformations
that preserve the self-adjoint structure. Based on these condensed forms we can characterize the
consistency of boundary values, as well as the consistency and smoothness requirements for the
inhomogeneities, and thus derive altogether the conditions for unique solvability of the system.
Further, we show that the underlying ordinary differential equation of a differential-algebraic system
associated with a self-adjoint pair of matrix functions is a Hamiltonian system and generates
a symplectic flow. For self-adjoint DAEs with symplectic flow a global condensed form is derived
and, furthermore, we discuss the structure preserving construction of the symplectic flow from
derivative arrays.
This is a joint work with Volker Mehrmann (TU Berlin) and Peter Kunkel (Universität Leipzig).
A projection method for the solution of large-scale Lur’e equations
Federico Poloni (TU Berlin), Timo Reis (Universität Hamburg) Schedule
The Lur’e equations
A ∗ X + XA + Q =K ∗ K,
XB + C =K ∗ L,
R =L ∗ L,
to be solved for a Hermitian n × n X, and K, L with as few columns as possible, arise in optimal
control and in model reduction. Typically, the system is reduced to an algebraic Riccati equation
by inverting R, but this is not a viable approach when R is singular, which is often a structural
property.
In this work, we present a numerical method for their solution which works when R is singular
and is suitable to provide approximate low-rank factored solution in the large and sparse case.
We compute the even invariant subspace of the associate even matrix pencil (as per the theory
of [Reis, Lur’e equations and even matrix pencils, LAA 2011]) relative to the singular and infinite
Kronecker blocks, and use it to deflate the Lur’e equations to a smaller version with nonsingular
R. The whole procedure has to be carried out implicitly in order to be able to exploit the sparsity
properties of A, and thus we have to deal with implicit representations of these coefficients in
terms of invariant subspace projectors. We show that the Newton-ADI method [Benner, Li, Penzl,

Section 20: Dynamics and control 345
Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal
control problems, NLAA 2008] [LYAPACK library, http://bit.ly/vnHgUh] can be applied
to this projected Riccati equation in implicit form, and that an extended matrix approach can be
used to provide an efficient solver for the linear systems that appear in the ADI iteration.
Reduced Order State Space Modeling of Piezo-Mechanical Systems
Jens Saak, Peter Benner , Mohammed Monir Uddin (MPI Magdeburg), Burkhard Kranz (Fraunhofer
IWU Dresden) Schedule
We are investigating the fine positioning of a spindle head structure in machine tool control [1].
The tool center point (tcp) is steered by a redundant axis model allowing to distribute large scale
head movements to the structure mounting and small scale positioning of the tcp to a set of piezo
actuators. The special focus in this contribution lies on the structural model of the spindle head
with the piezo actuators included. The large scale movements are realized by mounting the device
to the surrounding machine tool. They are thus not contained in our model. The finite element
(FEM) discretization of the structural CAD model leads to a very large second order model of
the form
M ¨x(t) + E ˙x(t) + Kx(t) = Bu(t), y(t) = Cx(t) + Du(t). (1)
Due to the modeling of the piezo actuation the M and E matrices are singular, but the part in K
corresponding to the joint null-space of M and E is invertible and thus the differential algebraic
equation is of index 1.
The FEM model is much to large to be feasible for fast simulation and controller design. We
seek to replace it by a reduced order surrogate model. We concentrate on the derivation of the
first order standard state space model required in the following steps of the controller design.
We tackle this equation by an S-LRCF-ADI [2] based balanced truncation approach. To this
end we reformulate (1) in first order form, exploiting that in our case we additionally have that
C = B T and M, E and K are symmetric. This allows us to reduce the amount of necessary
computations in the balancing even further, since the two system Gramians coincide.
[1] Neugebauer, R., Drossel, W.G., Bucht, A., Kranz, B., Pagel, K.: Control design and experimental
validation of an adaptive spindle support for enhanced cutting processes. CIRP
Annals - Manufacturing Technology 59(1), 373–376 (2010). http://www.sciencedirect.
com/science/article/pii/S0007850610000302
[2] Freitas, F., Rommes, J., Martins, N.: Gramian-based reduction method applied to large sparse
power system descriptor models. IEEE Transactions on Power Systems 23(3), 1258–1270
(2008)
S20.2: Mechatronics Tue, 16:00–18:00
Chair: Knut Graichen, Stephan Trenn S1|01–A4
On Measuring Vibration of Cutting-Off Machines with Endless Bandsaw Based on
Zigbee Technique
Józef Wojnarowski, Wladysław Kaliński (Silesian University of Technology Gliwice), Bohdan Borowik
(University of Bielsko-Biala) Schedule
As has been found, the dominants in the spectra of the acceleration of vibrations are most affected
by the tooth pitch of the saw, its rate of travel and the value of the force of pressure exerted on
the cut object, which value is adjusted by hand (1). If the feed is to large, the frequencies of the

346 Section 20: Dynamics and control
dominants decrease due to the reaction of the asynchronous motor: in many cases there occur
vibrations characterized by beats. While analyzing the presented spectra it has been found that
they include components with a characteristic frequency for the determined scale on teeth and
the speed of their shift along the object or pack of objects which is be cut. These values depend
on the pressure of the saw on the object, i.e. on the feed. Knowing the admissible feed of the saw
in relation to one tooth, this fact may be utilized in the development of the system of automatic
control of the feed of saws operating under differing conditions. For measuring and monitoring
vibration we proposed wireless network based on ZigBee technique such, that sensor with end
device node is attached to moving element of the machine and sensor reading are sent over the air
to remote coordinator node. ZigBee module with inherent firmware provides a wireless personal
area networking PAN of data from the sensor to microcontroller dsPIC33FJ256. The base of
Zigbee hybrid module is IC ZDMAI128-B0. It provides point-to-point communication. As our
investigation show, PIC24 microcontroller appears suitable in monitoring vibration of dynamic
mechanical object.
[1] Wojnarowski J. et al., The restriction of vibrations of cutting-off machines with endless
bandsaws. Monograph. SP Department of Applied Mechanics, Silesian Technical University,
Gliwice 2007, pp. 392. (In Polish).
jozef.wojnarowski@polsl.pl
LQR Control for Vibration Suppression of Piezoelectric Integrated Smart Structures
Shun-Qi Zhang, Rüdiger Schmidt (RWTH Aachen) Schedule
In the present paper, a motion equation of piezoelectric integrated beams has been derived by
using Hamiltons principle and the finite element method based on the First-Order Shear Deformation
(FOSD) theory. Then, for control design a state space model is constructed from the motion
equation. Linear Quadratic Regulator (LQR) control has been implemented on the mathematical
model of a piezoelectric bonded beam for vibration suppression. Finally, a numerical application
has been performed to testify the applicability and effectiveness of present method.
Force Control of a 6DoF parallel Platform driven by Fluidic Muscles
C.Michael, A. Kecskemethy (Universität Duisburg-Essen) Schedule
Described in this paper is a force control scheme for a six-legged parallel platform driven by hybrid
actuators. Each leg of type RRPS is equipped with a fluidic muscle and a coaxial linear spring
providing push and pull forces. Fluidic muscles require that the gas model as well as the nonlinear
pressure stroke force relation is included in the control scheme. In addition, the dynamics of the
proportional control valve needs to be taken into account.
The presented model based force control scheme computes the target pressure for the desired
force by evaluating a polynomial in the actual position and pressure. Computation of the control
input u requires the generation of set-points for the pressure change ˙p. Two different approaches
are presented. First a backward difference method with prescribed time to target pressure is illustrated.
The second approach evaluates the compliance of the close loop of the actuator with
the environment.
End-Effector Trajectory Tracking of Serial Flexible Manipulators
Robert Seifried, Mark Wörner, Thomas Gorius (Universität Stuttgart) Schedule
Modern light weight manipulator designs result in low energy consumption and allow often high
working speeds. However, due to the light weight design the bodies have a significant flexibility
which yields undesired vibrations. In the control design these flexibilities must be taken into

Section 20: Dynamics and control 347
account, yielding a flexible multibody system. In order to obtain a good performance in endeffector
trajectory tracking of flexible manipulators an accurate and efficient feedforward control
is very helpful. This is then supplemented by additional feedback control to account for small
disturbances and uncertainties.
In this contribution feedforward control design based on model inversion is presented and
applied to a serial manipulator with two flexible arms. Thereby, for a given system output the
inverse model provides the control input for exact output reproduction. In addition the inverse
model provides the trajectories for all generalized coordinates, which can be used in additional
feedback control. The derived inverse model consists of a chain of differentiators, driven internal
dynamics and an algebraic part. For flexible manipulators in end-effector trajectory tracking
the internal dynamics is in most cases unbounded. This requires stable inversion by solution of
a boundary value problem. The accuracy of the feedforward control depends on the number of
modes used in flexible multibody system model, and is investigated in detail by simulation. As
feedback strategy a combination of PID control for the joint coordinates and curvature feedback
is used as first approach. Further, the obtained results from the model inversion can be used in a
passivity based robust control schema.
Fault detection, diagnosis, and reconfiguration of planetary rovers
Alexandre Carvalho Leite, Bernd Schäfer (DLR), Marcelo Lopes de Oliveira e Souza (National
Institute for Space Research - Brazil) Schedule
This work describes the theoretic development of new FDDR (Fault Detection, Diagnosis, and
Reconfiguration) methods and a path following control simulation which illustrates the application
of these methods in an ExoMars-type rover. Planetary exploration rovers are wheeled vehicles
devoted to provide mobility in hostile extraterrestrial environment. An imperative characteristic
of such vehicles is fault tolerance, because maintenance in case of severe failures is not yet a practicable
option. To employ fault tolerance we propose new FDDR methods coping with robustness in
fault detection and safe decision to reconfigure the control system based on inconclusive diagnosis
statements. The new methods are twofold: 1) a variable threshold based on adaptive filtering is
applied; 2) a multi-objective decision maker is used acting between multiple diagnosis statement
and reconfiguration switching, called Dilemma Diagnoser. A fault tolerant control system has been
designed and applied to the European Space Agencys ExoMars rover B2X2 simulation model: it
is motorized by six independently steerable wheels mounted on a passive suspension for all-terrain
locomotion. A multi-body simulation model describes the rigid mechanical structure and interacts
with the environment (stones, bedrocks, and sandy terrain) through a detailed contact model.
Realistic and important terrain features like multi-pass effects in deformable terrain and multiple
contacts with complexly shaped stones are taken into account for modeling and simulation of
the overall dynamics behaviour. The simulation cases are to be tested in our planetary testbed
with the breadboard model of the B2X2 ExoMars rover. Some experiments were carried out to
correlate our contact model against experimental data; additional tests are planned to further
model tuning and experimentation of the simulated FDDR scheme.
S20.3: Controller design and MPC Wed, 13:30–15:30
Chair: Knut Graichen, Stephan Trenn S1|01–A4
Model predictive control for optimal invariance problems
Lars Grüne (Universität Bayreuth) Schedule
We consider the problem of keeping the state of a nonlinear discrete time control system within
a prespecified admissible set with minimal control effort. We use a model predictive control ap-

348 Section 20: Dynamics and control
proach without terminal constraints in order to obtain a feedback law for this task. We prove
that under appropriate controllability conditions this approach yields near optimal performance
with the gap to optimality tending to zero for increasing prediction horizon. Several numerical
simulations illustrate our theoretical result.
Computationally efficient receding horizon tracking control applied to a tubular reactor
example
Tilman Utz, Knut Graichen (Universität Ulm) Schedule
Receding horizon control (or model predictive control) relies on the repeated solution of an optimal
control problem over a prediction horizon and is widely considered as a powerful design
method for feedback control, in particular if constrained nonlinear dynamical systems are concerned.
Besides the classical stabilization task, the control of transient processes such as setpoint
transitions, is often carried out using a suitable (model-based) feedforward controller. If the system
under consideration is unstable or in order to account for model uncertainties and disturbances,
the feedforward control has to be amended by a trajectory tracking controller that stabilizes the
tracking error.
This contribution focuses on the combination of feedforward control with a receding horizon
tracking controller in the context of the well-known two-degrees-of-freedom control scheme. The
receding horizon controller is based on the tracking error dynamics in order to stabilize the system
along the nominal trajectory of the feedforward part. However, the error dynamics are in general
nonlinear and time-varying. A linear (but still time-varying) error dynamics can be obtained by
linearizing the system along the nominal trajectories, which leads to a linear-quadratic optimal
control problem for the receding horizon controller.
The two tracking control schemes based on the nonlinear and linearized time-varying error
dynamics are evaluated for transitions between unstable setpoints of a tubular reactor example.
An early lumping approach is used to reduce the parabolic partial differential equation to a
nonlinear finite-dimensional system. This system constitutes a suitable test case, since on the one
hand high-dimensional discretizations have to be chosen in order to capture the relevant dynamics
of the system, whereas on the other hand the optimization has to be completed in a short period
of time in order to stabilize the system.
Multi-Agent Motion Control of Autonomous Vehicles in Three-Dimensional Fluid
Flow Fields
Axel Hackbarth, Edwin Kreuzer (TU Hamburg) Schedule
Motion control of multiple autonomous vehicles is necessary to assure safe interaction of agents
operating in the same environment. Under the influence of fluid flow the control strategy for the
agents has to adapt to the forces acting upon the vehicles.
A potential-field based algorithm for multi-agent control has been extended to account for
correct guidance under the influence of flow. Path following and collision avoidance are the main
objectives for the control algorithm which is developed for an underwater sensor network. An
approximation of the flow is used for the path planning with model predictive control, whereas
path following is assured through sliding mode control.
The controller has yet been tested in simulations only, but experiments are planned with a
swarm of five to ten micro submarines in a water tank with natural and forced convection. The
fluid field in the simulation originates from a CFD analysis of the water tank under steady flow
conditions where the impact of the vehicles has been neglected.

Section 20: Dynamics and control 349
Optimal Control on Stable Manifolds for a Double Pendulum
Kathrin Flaßkamp, Julia Timmermann (Universität Paderborn), Sina Ober-Blöbaum (TU München/Universität
Paderborn), Michael Dellnitz and Ansgar Trächtler (Universität Paderborn)
Schedule
Optimal control problems for mechanical systems often arise in technical applications, e.g. in the
computation of energy efficient or time optimal steering maneuvers between operation points. To
find solutions with minimal control effort, the system’s natural, i.e. uncontrolled dynamics should
be used whenever appropriate. Promising candidates to consider for energy efficient trajectories
are the highly dynamic, but uncontrolled motions on (un)stable manifolds of equilibria.
In this contribution, we propose a control strategy for mechanical systems that includes uncontrolled
trajectories on (un)stable manifolds in a sequence together with short control maneuvers
to design a feedforward control. In particular, we present optimal swing-up solutions for a double
pendulum that are based on trajectories on the stable manifold of the pendulum’s upper
equilibrium. Approximations of the manifolds are computed by the software tool GAIO (Global
Analysis of Invariant Objects). For the numerical solution of the optimal control problems we use
the method DMOC (Discrete Mechanics and Optimal Control). To demonstrate the advantages
of our approach compared to a black box optimization, we perform a post optimization with the
optimal control sequence as an initial guess. The numerical results are evaluated in a simulation
environment for the double pendulum.
The Bang-Bang Funnel Controller: An experimental verification
Christoph Hackl (TU München), Stephan Trenn (TU Kaiserslautern) Schedule
We adjust the newly developed bang-bang funnel controller [1] such that it is more applicable
for real world scenarios. The main idea is to introduce a third “neutral” input value to account
for the situation when the error is already small enough and no control action is necessary. We
present simulation and experimental results which show the advantage to the bang-bang funnel
controller with only two input values. Finally, we compare the experimental results with the one
obtained by the application of the continuous funnel controller as reported in [2].
[1] Daniel Liberzon and Stephan Trenn. The bang-bang funnel controller. In Proc. 49th IEEE
Conf. Decis. Control, Atlanta, USA, pages 690695, 2010.
[2] Christoph M. Hackl, Norman Hopfe, Achim Ilchmann, Markus Mueller, and Stephan Trenn.
Funnel control for systems with relative degree two. Submitted for publication, preprint
available from the websites of the authors, 2010.
Approximately linear tracking control of nonlinear systems
Klaus Röbenack, Fabian Paschke (TU Dresden) Schedule
An elegant approach to control nonlinear state-space systems is the exact input-to-state linearization,
where a nonlinear change of coordinates combined with a nonlinear feedback law yields
a linear controllable system [1]. In this contribution, we treat the single-input case, where inputto-state
linearizability is equivalent to flatness. Sufficient and necessary existence conditions are
well-known, but quite restrictive.
Although the flat output can be guessed in many practical applications, the formal computation
is complicated due to the required symbolic solution of a system of partial differential
equations resulting from Frobenius’ theorem. We propose the design of a tracking controller for
flat single-input systems, where the explicit knowledge of the flat output is not required. Our

350 Section 20: Dynamics and control
approach is based on a series expansion of the tracking error along a given reference trajectory.
For point-to-point control, the desired reference trajectory can be obtained numerically solving
a boundary value problem [2]. For a first order approximation, our method coincides with the
linear time-varying controller suggested by Föllinger [3], where the linearization of the nonlinear
system is carried out along the reference trajectory. In this case, the controller is in some sense
dual to the extended Luenberger observer developed by Zeitz [4]. Nevertheless, our approach can
also be modified for zeroth as well as high order approximations.
[1] A. Isidori. Nonlinear Control Systems: An Introduction. Springer-Verlag, London, 3rd edition,
1995.
[2] K. Graichen, V. Hagenmeyer, and M. Zeitz. A new approach to inversion-based feedforward
control design for nonlinear systems. Automatica, 41(12):2033–2041, 2005.
[3] O. Föllinger. Entwurf zeitvarianter Systeme durch Polvorgabe. Regelungstechnik, 26(6):189–
196, 1978.
[4] M. Zeitz. The extended Luenberger observer for nonlinear systems. Systems & Control
Letters, 9:149–156, 1987.
S20.4: Control theory Wed, 16:00–18:00
Chair: Stephan Trenn, Knut Graichen S1|01–A4
Some remarks concerning differential flatness and tangent systems.
Matthias Franke (Fraunhofer IIS, Design Automation Division), Klaus Röbenack (TU Dresden)
Schedule
We consider control systems governed by ˙x = f(x) + �m i=1 gi(x)ui . A possible way of calculating
a flat output yi , i = 1, .., m of such a system is as follows, see [1]. Assuming the tangent system
�
∂f
d ˙x =
∂x +
m� ∂gi
∂x ui
�
m�
dx + gidu i .
i=1
is controllable, we can directly determine a flat output ω = (ωi )i=1,..,m of this linear time-varying
system. If ω satisfies an integrability condition, the flat output y of the nonlinear system can be
calculated by integration of dyi = �m j=1 µijω j (possibly with an integrating factor µ i j). In contrast
to [1], where a generalized version of the moving frame structure equations is used for checking
integrability, an adapted version of the Frobenius theorem is employed here. We investigate two
special cases.
For systems with one input, the integrability condition reads as dω1 ∧ ω1 = 0, where ω1 can
be taken as the last row of the inverse of the local controllability matrix. This condition is a dual
version of the well known involutivity condition (see for example [3]). For systems with m + 1
states and m inputs, there are ω depending on the state x only, i.e.
ω i =
m+1 �
j=1
ω i j(x)dx j ,
provided that the tangent linear system is controllable. In this case, the integrability conditions
dω i ∧ ω 1 ∧ · · · ∧ ω m = 0, i = 1, . . . , m are always fulfilled. This result can be found (derived
differently) in [3], cf. also [4].
i=1

Section 20: Dynamics and control 351
[1] J. Lévine, Analysis and Control of Nonlinear Systems: A Flatness-based Approach (Springer,
Berlin, 2009).
[2] P. Martin, A geometric sufficient condition for flatness of systems with m inputs and m + 1
states, Proc. 32nd CDC (1993), 3431 – 3436.
[3] R. Su, On the linear equivalents of nonlinear systems, Systems & Control Letters 2 (1982),
48–52.
[4] K. Schlacher and M. Schöberl, Construction of flat outputs by reduction and elimination,
Proc. 7th NOLCOS (2007).
Orbital stabilization of a class of underactuated mechanical systems
Carsten Knoll, Klaus Röbenack (TU Dresden) Schedule
Typically, the aim of a controller applied to a mechanical system with an unstable equilibrium
is to alter the system dynamics such that the equilibrium becomes stable. Another possibility,
however, would be to design the controller such that the closed loop system has a stable limit
cycle with the considered equilibrium as center. Even if the controller is designed to stabilize the
equilibrium, limit cycles may occur in mechanical control systems due to discontinuous effects
such as backlash or dry friction. Explicitly imposing a stable limit cycle by a suited controller,
in contrast, would at least allow to influence directly properties such as frequency and amplitude
of the resulting oscillation. Moreover, other applications of orbital stabilization are possible, e.g.
in the field of parameter identification and adaptive controllers where conditions for persistent
excitation have to be fulfilled.
In this contribution we consider underactuated mechanical systems whose linearization about
the equilibrium is stabilizable and has at least a controllable subspace of dimension two. We design
the feedback in two steps: A linear feedback ensures that the linearization of the resulting
system has exactly one pair of eigenvalues on the imaginary axis, while the rest is located in the
left half-plane. Then, an additional nonlinear feedback basing on a suited bilinear form renders
one closed orbit asymptotically stable. As an illustrative example we consider the well known ball
and beam benchmark system.
Passivity based stabilization of mechanical systems with dissipation in unactuated
degrees of freedom
Paul Kotyczka, Sergio Delgado L. (TU München) Schedule
Passivity based techniques allow a systematic nonlinear controller design using physically inspired
energetic arguments. The method Interconnection and Damping Assignment Passivity Based Control
(IDA-PBC) is one approach to solve the stabilization problem for underactuated mechanical
systems [1]. IDA-PBC aims at finding a state feedback control law such that the closed loop dynamics
is represented as a Port-Hamiltonian (PH) system with the desired properties positive definiteness
of the virtual energy function (around an equilibrium (q ∗ , 0)) and a positive semi-definite
damping structure such that the closed loop energy is non-increasing along the system trajectories.
PH systems generalize the Hamiltonian formulation of dynamical systems, known from mechanics.
In its common version for (underactuated) mechanical systems IDA-PBC requires the closed loop
system to have simple mechanical structure, i. e. the closed loop energy to be a sum of potential
plus kinetic energy. It is known that the presence of physical damping in unactuated degrees
of freedom can impede the closed loop energy and the dissipation matrix to be positive (semi-)
definite at the same time [2].

352 Section 20: Dynamics and control
The present contribution proposes a possibility to overcome this dissipation obstacle in the
application of IDA-PBC by adding a cross term between coordinates and momenta to the closed
loop energy. A solution is derived for the 2 DOF Acrobot system with physical damping. Stability
of the equilibrium with a well-defined estimate of the domain of attraction can be proven
analytically by the closed loop energy as a Lyapunov function. Even though (locally) predefined
closed loop dynamics is realized by Local Linear Dynamics Assignment [3] the reasonable
parametrization of the remaining design quantities is an open issue.
[1] R. Ortega, M. W. Spong, F. Gómez-Estern, G. Blankenstein, Stabilization of a Class of
Underactuated Mechanical Systems Via Interconnection and Damping Assignment, IEEE
TAC 47 (2002), 1218 – 1233.
[2] F. Gómez-Estern, A. J. van der Schaft, Physical Damping in IDA-PBC Controlled Underactuated
Mechanical Systems, EJC 10 (2004), 451 – 468.
[3] P. Kotyczka, Local Linear Dynamics Assignment in IDA-PBC for Underactuated Mechanical
Systems, In: Proc. 50th CDC/ECC, Orlando (2011).
On the number of zero crossings in the step response of linear time-delay systems
Luc N. Muhirwa, Tobias Damm (Universität Bayreuth) Schedule
The similarities between the linear time-delay systems and the standard linear time-invariant
systems are widely studied and discussed in the literature. In this paper we are going to study
the effects of the zeros of the transfer function of the time-delay system on the the step response,
this can be regarded as a genaralization of the familiar results on linear time-invariant system.
It will be demonstrated that the phenomena like zerocrossings, undershoot and overshoot in the
step response of a time-delay system -which present difficulities in control design- appear as a
result of the existence of non-minimum phase zeros.
Convergent systems and Incremental Stability
Björn S. Rüffer (Universität Paderborn), Nathan van de Wouw (Eindhoven University of Technology),
Markus Mueller (University of Exeter) Schedule
We consider two similar stability notions that are of interest in output-regulation, synchronization,
as well as observer design (see [2] for an overview).
One is the long established notion of convergent systems, which is mainly known from the
Russian literature: A system
˙x = f(t, x) (1)
is (globally) uniformly convergent [2] if
1. all solutions x(t, t 0 , x 0 ) exist for all t ≥ t 0 for all initial conditions (t 0 , x 0 ) ∈ R × R n ;
2. there exists a unique solution x(t) in R n defined and bounded for all t ∈ R;
3. the solution x(t) is (globally) uniformly asymptotically stable, i.e., there exists a function
β ∈ KL such that for all (t 0 , x 0 ) ∈ R × R n and t ≥ t 0 ,
�x(t, t 0 , x 0 ) − x(t)� ≤ β � �x 0 − x(t 0 )�, t − t 0� .

Section 20: Dynamics and control 353
The other one is the younger notion of incremental stability: System (1) is (globally) incrementally
asymptotically stable [1] if there exists a function β ∈ KL such that for any ξ1, ξ2 ∈ R n and t ≥ t 0 ,
�x(t, t 0 , ξ1) − x(t, t 0 , ξ2)� ≤ β(�ξ1 − ξ2�, t − t 0 ) .
Both notions require that any two solutions of a system converge to each other. Yet these
stability concepts are different, in the sense that none implies the other, as we will show using
several examples.
Next, we will illustrate under what additional assumptions one property indeed implies the
other. To that end we characterize both properties in terms of Lyapunov functions. We will find
that incremental stability implies uniform convergence if the vector field f(t, x) satisfies a specific
bound or if there exists a compact invariant set for system (1). Uniform convergence implies
incremental stability if the Lyapunov function for convergence satisfies a growth condition. And
lastly, the properties are equivalent when the dynamics of system (1) is constrained to a compact
set.
[1] David Angeli, A Lyapunov approach to the incremental stability properties, IEEE Trans.
Autom. Control 47 (2002), no. 3, 410–421.
[2] Alexey Pavlov, Nathan van de Wouw, and Henk Nijmeijer, Uniform output regulation of
nonlinear systems. A convergent dynamics approach, Birkhäuser, Boston, 2006.
Optimal value functions for weakly coupled systems: a posteriori estimates
Péter Koltai, Oliver Junge (TU München) Schedule
We consider weakly coupled LQ optimal control problems and derive estimates on the sensitivity
of the optimal value function in dependence of the coupling strength. Our main result is that if
a weak coupling suffices to destabilize the closed loop system with the optimal feedback of the
uncoupled system (i.e. when additional efforts has to be made in order to stabilize the coupled
system), then the value function might change drastically with the coupling. As a consequence,
it is not reasonable to expect that a weakly coupled system possesses a ”weakly coupled” optimal
value function. This lack of regularity suggests that the approximation of the optimal value function
in high dimensions is even for weakly coupled systems a rather difficult task.
S20.5: Partial differential equations Thu, 13:30–15:30
Chair: Stephan Trenn, Knut Graichen S1|01–A4
An approach for parameter identification in distributed parameter systems
T. Knüppel, F. Woittennek (TU Dresden) Schedule
Recently, an approach for the parameter identification in linear finite-dimensional systems introduced
in [1] has been generalized to linear distributed parameter systems [3]. The approach is
based on algebraic computations over certain convolution rings of generalized functions. The fact
that only boundary measurements are necessary makes the approach very attractive for applications.
The present contribution is concerned with a modified approach to the same problem. As
before only boundary measurements are necessary. The starting point is a linear boundary value
problem involving partial differential equations of hyperbolic or parabolic type. It is assumed that
the equations depend linearly on several initially unknown parameters.
As in the flatness based approach to the control of infinite dimensional systems the first
step is the reformulation of the boundary value problem under consideration as a system of

354 Section 20: Dynamics and control
convolution equations for the boundary trajectories [2]. These equations which constitute the basis
for the parameter identification may involve derivatives of the boundary trajectories. Therefore,
the identification is preceded by a regularization procedure. Then the parameters are computed
by minimizing appropriate error functionals.
The approach is demonstrated with the help of simple examples comprising the heat equation
and the wave equation.
[1] M. Fliess and H. Sira-Ramírez, An algebraic framework for linear identification, ESAIM:
COCV (Control, Optimisation and Calculus of Variations) 9, 151–168 (2003).
[2] H. Mounier, J. Rudolph, and F. Woittennek, Boundary value problems and convolutional systems
over rings of ultradistributions, in: Lecture Notes In Control and Information Sciences
Vol. 407 (Springer-Verlag, 2010).
[3] J. Rudolph and F. Woittennek, An algebraic approach to parameter identification in linear
infinite dimensional systems, in: Proc. 16th Mediterranean Conference on Control and
Automation, (2008), pp. 332–337.
Algebraic parameter identification for a heavy rope with internal damping
Nicole Gehring (Universität des Saarlandes), Torsten Knüppel (TU Dresden), Joachim Rudolph
(Universität des Saarlandes), Frank Woittennek (TU Dresden) Schedule
Extending work of M. Fliess and H. Sira-Ramírez [1], two of the authors proposed an algebraic
approach to the parameter identification for systems described by linear partial differential equations
with constant coefficients [2,3]. The approach uses operational calculus to generate equations
that involve only convolution products of known (boundary) measurements and the system parameters.
Here, by considering a heavy rope model the approach is extended to a partial differential
equation with spatially dependent coefficients. As in the case of constant coefficients, the time
derivatives are replaced by the operator s and the system variables and their derivatives are
represented by Mikusiński operators and operational functions. As well known, the resulting
ordinary differential equation is a Bessel equation. Hence, the solution of the boundary value
problem can be expressed as a linear combination of Bessel functions of the first and second kind.
Note that these Bessel functions satisfy a known differential relation with respect to s. Assuming
homogeneous initial conditions this knowledge can be exploited to eliminate the Bessel functions.
The resulting equation involves convolution products of the system variables and is polynomial
with respect to the system parameters. Based on these equations the parameters can be calculated
either by solving nonlinear equations or by considering them as mutually independent and using
overparameterization.
The rope is modeled with an internal damping and a horizontally moving suspension point.
A mass may be attached to the free end. It will be shown that the knowledge of the trajectories
of the boundary values at the suspension is sufficient to identify all physical parameters of the
rope. Simulation results are given to illustrate the approach.
[1] M. Fliess, H. Sira-Ramírez, An algebraic framework for linear identification, ESAIM: COCV
9 (2003), 151–168.
[2] J. Rudolph, F. Woittennek, Ein algebraischer Zugang zur Parameteridentifikation in linearen
unendlichendimensionalen Systemen, at – Automatisierungstechnik 55 (2007), 457–467.

Section 20: Dynamics and control 355
[3] J. Rudolph, F. Woittennek, Identification de paramètres d’un modèle d’échangeurs de chaleur,
in: Actes Conf. Int. Francophone d’Automatique, Nancy (France), 2–4 juin 2010.
Identification of transmission line parameters using algebraic methods
Nicole Gehring, Joachim Rudolph (Universität des Saarlandes), Christian Stauch (ZeMA gGmbH,
Saarbrücken) Schedule
An algebraic approach to parameter identification for transmission lines is proposed. The class of
systems under consideration can be modelled by means of a pair of coupled first order linear partial
differential equations in one spatial dimension. That includes examples from different technical
domains such as the telegrapher’s equations or models for fluid transmission lines. Under the
assumption of homogeneous initial conditions, replacing the system variables for effort and flow
by operational functions ê and ˆ f leads to
d
dz ê(s, z) + ˆ Γ(s) ˆ Z(s) ˆ f(s, z) = 0 (1a)
d
� �
ˆZ(s) f(s, ˆ z) +
dz
ˆ Γ(s)ê(s, z) = 0, (1b)
where z denotes the spatial variable and ˆ Γ(s) and ˆ Z(s) are the propagation operator and the
impedance operator. The use of operational calculus has been shown to be suitable for parameter
identification in systems of both finite and infinite dimension (see e.g., [1,2]). The main idea of
this approach is to generate a set of equations involving only measured signals and parameters,
in such a way that it can be easily interpreted in the time domain. To this end, operators are
eliminated using the differential equations they satisfy. Finally, time domain equations are used
for pointwise calculation of the unknown parameters.
The proposed identification method is illustrated considering a fluid transmission line model
with laminar flow and frequency dependent viscous friction [3]. Using simulation data, the
kinematic viscosity and the bulk modulus of the fluid are identified.
[1] M. Fliess, H. Sira-Ramírez: An algebraic framework for linear identification, ESAIM: COCV,
9, 151–168 (2003).
[2] J. Rudolph, F. Woittennek: Ein algebraischer Zugang zur Parameteridentifikation in linearen
unendlichdimensionalen Systemen, at – Automatisierungstechnik, 55, 457–467 (2007).
[3] A.F. D’Souza, R. Oldenburger: Dynamic response of fluid lines, Journal of basic engineering,
86, 589–598 (1964).
POD and CVT Galerkin reduced-order modeling of the flow around a cylinder
Sebastian Ullmann, Jens Lang (TU Darmstadt) Schedule
In this talk the application of Galerkin reduced-order models to the laminar incompressible vortexshedding
flow around a circular cylinder is presented. The methods rely on approximate bases of
the solution space computed from a set of velocity snapshots {�un} N n=1. While the proper orthogonal
decomposition (POD) delivers basis functions {�ϕr} R r=1 that minimize the kinetic energy of the
projection error,
min
{�ϕr}
N� � R� �
�
�
��un − (�ϕr, �un)�ϕr � 2
,
n=1
r=1

356 Section 20: Dynamics and control
the centroidal Voronoi tessellation (CVT) delivers basis functions that are themselves approximations
of snapshots. This is achieved by arranging the snapshots in clusters {Vr} R r=1 and using
the cluster centroids as basis functions, which leads to the minimization problem
min min
{�ϕr} {Vr}
R� � � �
� �
��un − �ϕr � 2
.
r=1 �un∈Vr
The errors in the reduced velocities are dependent on the number of modes and the accuracy of
the underlying finite element simulation. An appropriate choice of the outflow boundary condition
eliminates the need for pressure modeling or calibration. Still, to obtain drag and lift forces, a
reduced-order pressure model can be solved, additionally. A comparison of the CVT and POD
methods with respect to their efficiency and accuracy will be presented.
Flatness-based Feedforward Control Design of a System of Parabolic PDEs Basedon
Finite Difference Semi-Discretization
Tilman Utz (Universität Ulm), Andreas Kugi (TU Wien) Schedule
Tubular catalytic fixed-bed reactors constitute a form of chemical reactors which can be found in a
wide range of applications from automotive catalytic converters to large polymerization reactors.
An important control objective for chemical reactors is the realization of setpoint transitions for
example for ignition or extinction as well as for grade transitions. A main difficulty thereby can
be identified by the usually very significant nonlinearities caused by the chemical reaction.
In order to mathematically model fixed-bed reactors, in particular to sufficiently describe
the chemical reaction, it is necessary to consider the distribution of the temperature and of
the reacting species concentration over the length of the reactor. Taking into account nonlinear
reaction expressions, for example in terms of the Arrhenius equation, this leads to a system of
semilinear parabolic partial differential equations in a one-dimensional spatial domain. Control
thereby usually is applied via one of the boundaries, namely the inlet of the reactor, e. g., [1].
For the feedforward control design, an approach is applied, which is based on the semidiscretization
of the governing partial differential equations and of the boundary conditions using
finite differences with respect to the spatial coordinate. It is shown that the temperature and
the concentration at the reactor outlet represent a so-called flat output of the semi-discretized
system. This allows for the parametrization of the states and the boundary inputs of the semidiscretized
system in terms of the flat output and its time derivatives and therefore constitutes a
systematic approach to the design of feedforward control for the considered transition problems
[2]. Furthermore, it is shown that with the use of non-equidistant grids for the semi-discretization
it is possible to partly resolve the antagonistic demands to carry out the parametrization on a
very fine grid in order to properly reflect the nonlinearities and to use a coarse grid in view of the
computational efficiency.
[1] van Doesburg, H.; de Jong, W. A.: Chem. Eng. Sci. 31 (1976), 45–51.
[2] Utz, T.; Meurer, T.; Kugi, A.: Int. J. Control., 83 (2010), 1093–1106.
Modelling and control of a smart beam
Nader Ghareeb, Rüdiger Schmidt (RWTH Aachen) Schedule
In modern engineering, weight optimization has always the highest priority during the design of
structures. It has the advantage of minimizing the amount of raw material used and this will

Section 20: Dynamics and control 357
reduce the manufacturing and operational costs. On the other hand, it results in lower stiffness
and thus more sensitivity to vibrations.
In this work, a simple and active controller is presented. It is used to attentuate the vibrations
of a smart beam. A modified FE-Model of that beam is used and the adequate damping coefficients
are calculated and added to it. After that, a super element is created and then represented in the
form of state-space equations prior to the design of the controller.
Finally, the model is excited by its natural frequency and it is left to vibrate freely. Through
the design of a suitable controller, these vibrations are minimized, and results are shown.
S20.6: Model reduction and simulation Thu, 16:00–18:00
Chair: Knut Graichen, Stephan Trenn S1|01–A4
Model reduction for optimal control problems in field-flow fractionation
Carina Willbold, Tatjana Stykel (Universität Augsburg) Schedule
We discuss the application of model order reduction to optimal control problems governed by
coupled systems of the Stokes-Brinkmann and advection diffusion equations. Such problems arise
in field-flow fractionation processes for the efficient and fast separation of particles of different
size in microfluidic flows. Our approach is based on a combination of balanced truncation and
tangential interpolation for model reduction of the semidiscretized optimality system. Numerical
results demonstrate the properties of this approach.
Balanced Truncation of positive linear systems
Christian Grußler (TU Kaiserslautern), Prof. Tobias Damm (Universität Bayreuth) Schedule
We consider methods of model order reduction for positive linear time-invariant systems
preserving the positivity. This issue has been addressed earlier e.g. in [1] − [3]. The methods
presented there, however, often do not give a good approximation in the H ∞ -norm and neglect
the advantage of a projection approach such as standard balanced truncation.
In our talk we first show that standard balanced truncation to first order always leads to
a positive system, which outperforms earlier methods in many examples, especially in case of
SISO systems. This idea is then extended to obtain higher order positive approximations. To
this end we derive a symmetry property of the balanced realization of any linear SISO system.
Again we provide numerical examples to illustrate the properties of this approach.
[1] T. Reis and E. Virnik, Positivity preserving balanced truncation for descriptor systems, SIAM
J. Control Optim., vol. 48, no.4, pp. 2600 - 2619, 2009
[2] J. Feng, J. Lam, Z. Shu and Q. Wand, Internal positivity preserved model reduction, Int. J.
Control, vol. 83, no. 3, pp. 575 - 584, 2010
[3] P. Li, J. Lam and Z. Wang, Positivity-preserving H∞ model reduction for positive systems,
Automatica, vol. 47, pp. 1504 - 1511, 2011
Model order reduction methods and their possible application in compliant mechanisms
Malte Rösner, Rolf Lammering (Universität der Bundeswehr Hamburg) Schedule
A new approach to develop a feed unit of small machine tools for small workpieces is based
on the application of compliant mechanisms. Currently, non-intuitive design and optimization

358 Section 20: Dynamics and control
techniques are in progress as well as controlling, measuring and calibration strategies. To describe
the mechanical behavior of a feed unit in an accurate way, very large and sparse finite element
models arise. This leads to numerical simulations which require an unacceptable amount of time
and memory space and motivates the introduction and application of model order reduction
(MOR) techniques.
Model order reduction appears to be beneficial for the synthesis and simulation of compliant
mechanisms due to computational costs. It is an established method in many technical fields for
the approximation of large-scale linear time-invariant and nonlinear dynamical systems described
by differential equations. Based on system theory, underlying representations of the dynamical
system are introduced from which the general reduced order model is derived by projection.
During the last years, numerous new procedures were published and investigated appropriate to
simulation, optimization and control. Methods based on condensation [1], Krylov subspacess [2],
singular value decomposition [3] and proper orthogonal decomposition [4] are reviewed and their
advantages and disadvantages are outlined. The convenience of applying model order reduction
in compliant mechanisms is quoted.
[1] Gasch, R. and Knothe, K.: Strukturdynamik, Bd. 2, Springer, New York, NY, USA, 1989.
[2] Eid, R.: Time Domain Model Reduction by Moment Matching, Ph.D. thesis, TU München,
2009.
[3] A. Antoulas. Approximation of large-scale dynamical systems. Society for Industrial Mathematics,
2005.
[4] Liang, Y.; Lee, H.; Lim, S.; Lin, W.; Lee, K. Wu, C. Proper orthogonal decomposition and its
applications - Part I: Theory. Journal of Sound and Vibration, Elsevier, 2002, 252, 527-544
.
Simulating steady flows with Gappy POD
Alexander Vendl (TU Braunschweig) Schedule
We will use a reduced order method called Gappy POD to simulate steady aerodynamic flows for
varying angles of attack. Gappy POD is - as the name suggests - based on Proper Orthogonal
Decomposition (POD). Given a set of snapshots, which are solutions characteristic of the dynamics,
POD stores these snapshots in a matrix and computes a Singular Value Decomposition of
it. This yields an optimal basis to represent the flow solutions.
The basic idea of Gappy POD is to find coefficients for the POD basis vectors such that the
thus given POD representation best fits some given data. This is achieved by a least-squares linear
regression approach.
In our work we try to match the boundary conditions of the farfield, which are strongly
dependent on the varying parameter, that is, the angle of attack. Since the boundary conditions
are known a priori, it is in fact justified to speak of simulating the solution.
The simulation model of a laboratory truck crane
Dawid Cekus, Pawel Warys (Częstochowa University of Technology) Schedule
The exhaustive construction of prototypes of all classes of cranes or other labour-machines of
interest to experimental research is economically and practically infeasible. Therefore, simulation
modelling is very useful and has fundamental influence on the design of new structures as well as

Section 20: Dynamics and control 359
the modification of existing structures. For these reasons, this paper presents a simulation model
of a laboratory truck crane [1].
The simulation model has been worked out using the SolidWorks and Matlab-Simulink programs.
In the SolidWorks program, a parametric geometrical model (CAD model) has been worked
out. Next, thanks to the existence of an interface between the above-mentioned programs, the
CAD model has been converted into an XML physical model and implemented in the Matlab-
Simulink environment. In the Matlab-Simulink package, the model has been verified and supplemented
by signal sources, executive and measuring elements.
This simulation model allows the creation of advanced kinematic simulations (e.g. motion
trajectories, components of velocity and acceleration of the end of boom) for any configuration
of the analysed system based on control functions, which are responsible for the realization of
movements of two telescopic boom members, rotation and slope of the telescopic boom.
[1] L. Tomski, W. Chwalba:, System for testing the vibration of a truck-crane model, Proceedings
of Conference RResearch Methods of Labour-Machines“, Papers of Construction Equipment
Research Institute 1-3 91 (1989), 206 – 214 (in Polish).
The dynamics study of load carried by the two-member grab system
Pawel Warys, Dawid Cekus (Częstochowa University of Technology) Schedule
This paper presents the formulation of the theoretical and calculation model which enables the
simulation of the motion of a load carried by a forest crane [2]. The lifted load and carrying
system have been modeled as a 3D rigid body. The application of such a load model results in
the simplification and improvement of the calculation algorithm. The equations of the coupled
motion of the system load-machine elements have been derived.
During lift different dynamics effects occur. Consequently, the position of a carried load is
sometimes difficult to control [1]. The kinematic model presented enables the analysis of the basic
motion of the load as a response of the system to operational control of the forest crane. In order
to determine the motion parameters, it is assumed that all system elements are rigid. The lifted
load is also treated as a rigid body that moves as the result of the movement of the suspension
point of load and the dynamic interactions generated during the motion of the system.
The primary focus of the dynamic model is to describe the movement of load as a body in threedimensional
space. This model allows calculation of the movement of a load under the influence
of kinematic effects and further the free motion of the load as a result of the previous forced
motion. In the next step, the dynamic model is modified to permit the mathematical description
of additional displacements resulting from the finite stiffness of various machine elements.
The sample numerical calculations have been derived using the Matlab system. The initial
problem has been solved by the Runge-Kutta method. The numerical program has been developed
based on the presented model which allows analysis of the motion of load arising from crane
operating mechanisms.
[1] B. Posiadala: Influence of crane support system on motion of the lifted load, Mechanism and
Machine Theory, 32 (1997), 9-20.
[2] P. Warys: Modeling and investigation of dynamics of the forest crane, PhD Thesis, Czestochowa
University of Technology, 2011, 97-128.

360 Section 21: Mathematical image processing
Section 21: Mathematical image processing
Organizers: Tobias Preusser (Jacobs University Bremen), Gabriele Steidl (Universität Kaiserslautern)
S21.1: Mathematical Image Processing I Tue, 13:30–15:30
Chair: Gabriele Steidl S1|03–110
Convex Relaxation Techniques in Image Analysis
Daniel Cremers (TU München) Schedule
Numerous image analysis problems correspond to non-convex energies, giving rise to suboptimal
solutions and often strong dependency on appropriate initialization. In my presentation, I will
show how problems like image segmentation, multiview stereo reconstruction and optic flow
estimation can be formulated as variational problems. Subsequently, I will introduce methods of
convexification which allow to compute globally optimal or near-optimal solutions. The resulting
algorithms provide robust solutions, independent of initialization. Parallel GPU implementations
allow for acceptable runtimes.
A Convex Shape Prior and Shape Matching Based on the Gromov-Wasserstein Distance
Bernhard Schmitzer, Christoph Schnoerr (Universität Heidelberg) Schedule
We present a novel convex shape prior functional with potential for application in variational
image segmentation. Based on the Gromov-Wasserstein distance an approximation is derived that
takes the form of an optimal transport problem with relaxed constraints. The approach inherits
the ability to incorporate vast classes of geometric invariances beyond rigid isometries and is
apt for processing additional (non-geometric) feature information within the same framework.
The resulting functional can be minimized by standard linear programming methods and yields
a unique assignment of a given shape template to a given image. Numerical experiments are
reported that illustrate key aspects of the approach, and open problems are outlined.
Nonconvex TV q -Models in Image Restoration: Analysis and a Trust-Region Regularization
Based Superlinearly Convergent Solver
Tao Wu (Universität Graz), Michael Hintermüller (HU Berlin) Schedule
A nonconvex variational model is introduced which contains the ℓ q -“norm”, q ∈ (0, 1), of the
gradient of the image to be reconstructed as the regularization term together with a least-squares
type data fidelity term which may depend on a possibly spatially dependent weighting parameter.
Hence, the regularization term in this functional is a nonconvex compromise between the
minimization of the support of the reconstruction and the classical convex total variation model.
In the discrete setting, existence of a minimizer is proven, a Newton-type solution algorithm is
introduced and its global as well as locally superlinear convergence is established. The potential
indefiniteness (or negative definiteness) of the Hessian of the objective during the iteration is
handled by a trust-region based regularization scheme. The performance of the new algorithm
is studied by means of a series of numerical tests. For the associated infinite dimensional model
an existence result based on the weakly lower semicontinuous envelope is established and its
relation to the original problem is discussed.
An Estimation Theoretical View on Ambrosio-Tortorelli Image Segmentation
Kai Krajsek, Ines Dedovic, Hanno Scharr (Forschungszentrum Jülich) Schedule

Section 21: Mathematical image processing 361
In this contribution, we consider the Ambrosio-Tortorelli (AT) functional for image segmentation
from an estimation theoretical point of view. The Mumford-Shah (MS) functional is maybe
the most well-known constraint used for image segmentation. A major difficulty in using it is
the handling of inner image borders as lines, being circumvented by Ambrosio and Tortorellis
approximation. They introduce a smooth edge indicator function instead of the original line-like
edge indicator. The AT approach contains the Mumford-Shah functional as the limit of a certain
parameter. Unlike many other approaches, e.g. using level-sets, open boundaries can be handled
easily. Using such a functional, image segmentation is understood to be joint image regularization
and edge-map reconstruction.
Previous approaches consider AT segmentation as a deterministic optimization problem by minimizing
the energy functional, resulting in a single point estimate, i.e. the maximum-a-posteriori
(MAP) estimate. We adopt a wider estimation theoretical view-point. Instead of minimizing an
energy functional in the original formulation, we interpret the AT functional as the energy of a
posterior probability density function and derive an effective block-Gibbs-sampler for approximating
the minimum mean square and the minimum medium estimator. The merit of our approach
is multi-fold: First, sampling from the posterior PDF allows to apply different types of estimators
and not only the MAP estimator. Second, sampling allows to estimate higher order statistical
moments like the variance as a confidence measure. Third, our approach is not prone to get
trapped into local minima as other AT image reconstruction approaches, but our approach is
asymptotically statistical optimal.
Nonlinear eigenproblems for high-dimensional data analysis
Simon Setzer, Matthias Hein (Universität des Saarlandes) Schedule
In many fields such as machine learning, computer vision and exploratory data analysis, a major
goal is the development of solutions for the automatic and efficient extraction of knowledge from
data. A great number of important methods for data analysis are based on eigenproblems. While
linear eigenproblems are standard tools in many applications, e.g., in the form of the principal
component analysis or spectral clustering, they are limited in their modeling capabilities. In this
talk, we will discuss nonlinear eigenproblems since they significantly extend the modeling freedom.
In particular, the important principles of sparsity and robustness can be incorporated. After
an introduction of the framework, we will present recent results on an important application of
nonlinear eigenproblems, namely tight relaxations of balanced graph cuts. Moreover, an efficient
algorithm - a generalization of the inverse power method - is introduced for the resulting nonconvex
and nonsmooth optimization problems.
S21.2: Mathematical Image Processing II Tue, 16:00–18:00
Chair: Tobias Preusser S1|03–110
Analysis of Space-Discrete Image Filters Involving Inverse Diffusion
Martin Welk (UMIT Hall) Schedule
Discontinuity-enhancing image filters based on nonlinear diffusion PDEs are well established in
image processing. Promising candidates for such filters, however, involve negative diffusivities that
pose challenges for their analysis and numerical treatment. Spatial discretisations of these PDEs
can be analysed using ODE systems. In some cases, they give rise to interesting nonstandard
numerical methods for the image filters in question. In the talk, recent results in this area will be
presented.
Robust Nonlinear PDEs for Multiscale Morphological Image Analysis
El Hadji S. Diop, Jesus Angulo (Mines ParisTech) Schedule

362 Section 21: Mathematical image processing
In many image processing and computer vision tasks (e.g. data compression, feature detection, motion
analysis/detection, multiband frequency analysis, . . . ), it is important to perform a multiscale analysis
i.e. analyze the image at multiple spatial scales. Owing to that fact, mathematical morphology [1] appeared
as a powerful tool in multiscale analysis [2], mainly due to its nonlinearity aspects, shape and
geometry description properties. Let E = Z 2 or a subset of Z 2 . Morphological operators can be defined
by combination and/or duality of the elementary dilation operation defined for any function f : E → ¯ R,
by: (f ⊕b)(x) = ∨y∈E[f(y)+b(x−y)] (1), where ∨ represents the supremum, and b : R 2 → ¯ R is a concave
structuring function (ST) that could be flat i.e. b = 0 in a convex bounded set B and −∞ outside, or
non flat i.e. a general concave function. For t ≥ 0, one can define then a multiscale dilation (or erosion)
by replacing b by the family of multiscale ST (bt)t≥0 defined for t > 0 by bt(x) = tb(x/t), and for t = 0
by 0 for x = 0 and −∞ otherwise. In the case of flat ST, this is equivalent to consider sets Bt = tB.
Alternatives to perform multiscale continuous flat dilation (erosion) by using PDEs were proposed [3-4]:
∂ut = ±�∇u�, u(x, 0) = f(x) (2), with (+) (resp. (−)) for the multiscale dilation (resp. erosion). Despite
various and successful applications, it is clear that neither the discrete (1) nor the continuous (2)
formulations are robust in a noisy environment. Indeed, in that case, taking the supremum as in (1) will
definitely lead to wrong values, while hyperbolic PDE (2) will blow up. The main reason is that all image
pixels are treated in a same global way. To avoid that, adapted morphological filters based on image
edges were proposed by means of spatially-variant shape kernels [5] or bilateral ST [6]. Using a PDE approach,
an adaptive method was presented in [7] by multiplying the image gradient with a space-variant
matrix, in order to enhance coherence of flow-like structures. Herein, we overcome these drawbacks by
providing more robust and more adaptive PDEs, as well as corresponding operators. We first proposed
Gaussian regularized versions of (2): ∂ut = ±�∇uσ�, u(x, 0) = f(x) (3). Second proposed PDEs are
locally adaptive, and account intrinsic image features: ∂ut = ±g(�∇uσ�)�∇u�, u(x, 0) = f(x) (4), where
g is either increasing or decreasing. PDEs (3) and (4) are implemented using different numerical schemes
and a proposed one.
[1] J. Serra, Image Analysis and Mathematical Morphology (AP, 1982).
[2] P. Soille, Morphological Image Analysis (Springer-Verlag, England, 1999).
[3] L. Alvarez, F. Guichard, P. -L. Lions, and J. -M. Morel, Arch. Rational Mech. Anal. 123, 199-257
(1993).
[4] G. Sapiro, R. Kimmel, D. Shaked, B. B. Kimia, and A. M. Bruckstein, Pattern Recognition 26 (1993),
1363-1372.
[5] R. Lerallut, E. Decencière, and F. Meyer, IVC 25 (2007), 395-404.
[6] J. Angulo, in: ISMM, LNCS 6671 (Italy, July 2011), pp. 212–223.
[7] M. Breuβ, B. Benedi, and J. Weickert, in: LNCS 4487 (Ger., 2007), pp. 515-522
Volumetric Nonlinear Anisotropic Diffusion on GPUs
Arjan Kuijper (Fraunhofer IGD/TU Darmstadt), Andreas Schwarzkopf, Thomas Kalbe, Michael
Goesele (TU Darmstadt) Schedule
We present an efficient implementation of volumetric nonlinear anisotropic image diffusion on
modern programmable graphics processing units (GPUs). We avoid the computational bottleneck
of a time consuming eigenvalue decomposition in R 3 . Instead, we use a projection of the Hessian
matrix along the surface normal onto the tangent plane of the local isodensity surface and solve for
the remaining two tangent space eigenvectors. We derive closed formulas to achieve this resulting
in efficient GPU code. We show that our most complex volumetric nonlinear anisotropic diffusion

Section 21: Mathematical image processing 363
gains a speed up of more than 600 compared to a CPU solution.
Image analysis of four-dimensional data from fluorescence microscopy
Hendrik Dirks (Universität Münster) Schedule
The image analysis of four-dimensional data from fluorescence microscopy is a challenging task,
in particular in living probes. We discuss advanced image processing techniques to tackle this
issue, from denoising of Poisson distributed data using a total variation model to optical flow and
particle models for the analysis of intracellular flow.
Our focus lies on the movement of proteins in developmental neurobiology such as the polarization
of the axon from previously unspecific neurites. The transport properties obtained by
imaging can be used to identify certain proteins and their role in development.
Quantitative X-ray tomography with X-ray tubes
Stefan Günther, Stefan Odenbach (TU Dresden) Schedule
X-ray tomography is used to generate three-dimensional models of opaque objects from projections
at various angles. This non-destructive method is increasingly applied in non-medical diagnostic,
where a spatial resolution of some micrometers is possible. Laboratory tomography setups with
a high availability are equipped with X-ray tubes as radiation source, which emit polychromatic
radiation. The non-linear attenuation of polychromatic radiation causes beam hardening artifacts
and is a significant problem for a quantification. Using precise fabricated wedges, it is possible to
determine a corrective function to compensate the non-linearity for single material systems. For
multi material systems a system of equations has to be solved to decompose the projection data.
The result of this decomposition is a linear information about each material independent from
the photon energy. It will be shown, how this calibration method was applied for a cone beam
geomety to get tomograms without beam hardening artifacts.
Hyperelasticity in Correspondence Problems
Jan Modersitzki (University of Lübeck Institute of Mathematics and Image Computing Maria-
Goeppert-Str. 1a, 23562 Lübeck), Lars Ruthotto (University of Lübeck Institute of Mathematics
and Image Computing Maria-Goeppert-Str. 1a, 23562 Lübeck) Schedule
Image registration is one of the challenging problems in image processing. Given are two images
that are taken for example at different times, from different devices or perspectives. The goal is
to determine a reasonable transformation, such that a transformed version of one of the images is
similar to the second one. The problem is typically phrased in a variational setting for the wanted
transformation and regularization is a key issue.
In this talk, we present an introduction to hyperelastic image registration which is motivated
by an applications from cardiac PET imaging. More specifically, we present a hyperelastic
regularizer and we show that this regularizer enables the recovery of large and highly non-linear
transformations. We also show that this regularization results in diffeomorphic mappings. The
price to be paid is a non-convex but polyconvex objective function.
We also present a stable and efficient numerical implementation. This implementation is based
on the discretize then optimize paradigm and uses a sophisticated computation of the discrete
analogues of the three invariants of the transformation tensor: lengths, areas and volumes. We
show several numerical examples that illustrate the potential of the hyperelastic regularizer. We
also show the mass-preserving registration of cardiac PET images, where hyperelastic regularization
is mandatory.

364 Section 21: Mathematical image processing
S21.3: Mathematical Image Processing III Wed, 13:30–15:30
Chair: Brigitte Forster-Heinlein S1|03–110
Higher Order Multiphase Image Segmentation and Registration
Stephen Keeling (Universität Graz) Schedule
Based upon successes with higher order regularization for image restoration using the Graz developed
Total Generalized Variation (TGV), we seek to develop counterparts for image segmentation
and registration. For segmentation, an image approximation is conceived in terms of a sum of
multiple phase functions which are supported on disjoint sets. The boundaries of these supports
define the image edges, and each phase function is smoothed independently on connected components
of its support with higher order regularization. By contrast, familiar piecewise constant
segmentations correspond to a very strong first order regularization applied simultaneously to all
connected components of the support of each phase function. Advantages of the proposed segmentation
approach will be elucidated with computational examples. After defining the edge set
in terms of the phase function decomposition, images are registered in a contrast invariant fashion
by registering their edge sets. Registration of edge sets is performed by transforming each edge set
to a diffuse surface using blurring, and then by registering the diffuse surfaces with progressively
less blurring. Results will be shown for an epicardial matching problem in which Purkinje Fibers
of one epicardium are to be mapped to the other. Convergence and discretization issues will also
be addressed.
Inverse source problems and the windowed Fourier transform
Roland Griesmaier, Martin Hanke, Thorsten Raasch (Universität Mainz) Schedule
The reconstruction of time-harmonic acoustic or electromagnetic sources from measurements of
the corresponding radiated wave is an ill-posed inverse problem with fascinating applications in
science and technology. We present a new approach to this problem, observing that the windowed
Fourier transform of the far field of the radiated wave is related to an exponential Radon
transform with purely imaginary exponent of a smoothed approximation of the source. Based
on this observation we present a filtered backprojection algorithm to recover information on the
unknown source. We discuss this algorithm, consider numerical results, and comment on possible
extensions of the reconstruction method to inverse scattering problems.
Adaption of Prony’s method for non-standard bases
Thomas Peter, Gerlind Plonka-Hoch (Universität Göttingen) Schedule
classification: 41A30, 94A12
Within the last years, there has been an increasing interest in exploiting sparsity of solutions in
suitable bases or frames. If a signal f can be represented with M basis functions in a certain basis
B, one could ask, if a number N(M, B) of functional values F (f, k), k = 1, . . . , N of f is sufficient
to represent the complete signal f. Thereby N(M, B) is only dependent on the order of sparsity
M of f and the used basis B.
For trigonometric functions this problem can be solved by the Prony-method. In this talk we want
to discuss how this approach can be adapted to other bases. Further we discuss the question of
what kind of functional F will be sufficient to ensure an exact representation of f.
Adaptive Total Variation Regularization
Frank Lenzen, Florian Becker, Stefania Petra, Christoph Schnörr (Universität Heidelberg) Schedule
For several variational denoising methods, locally adaptive extensions have been proposed in li-

Section 21: Mathematical image processing 365
terature. Most approaches determine adaptivity either by examining the noisy input data in a
preprocessing step or by estimating additional variables along with the denoised image during the
optimization process.
In our work, we model the adaptivity to directly depend on the unknown solution of the
optimization problem. We refer to this approach as ’solution-dependent adaptivity’. Our extension
has a significant impact on the theoretical and numerical aspects of the optimization process. In
particular, instead of a convex optimization problem, which would be obtained with standard
adaptivity, we end up with a quasi-variational inequality to be solved.
In our talk, we will address these theoretical and numerical aspects in detail and provide several
applications of solution-dependent adaptivity.
Discrepancies and Halftoning
Manuel Gräf, Daniel Potts (TU Chemnitz), Gabriele Steidl (TU Kaiserslautern) Schedule
The notion of discrepancy was originally introduced for measuring the uniformity of point distributions.
In this talk we recapitulate some well-known facts in the theory of discrepancies, cf. the
book of Drmota and Tichy [1], and the relation to the process of halftoning an image [2]. In its
generality discrepancy may considered as a notion of similarity between two different measures.
In the setting of image processing we think of an image as a certain measure which we aim to
approximate by a discrete measure. The support of the latter measure is given by the stippling
points, which create the halftoning of the image. The approximation is achieved by minimizing a
certain discrepancy between these two measures. For a large number of points the minimization
of the discrepancy is a serious challenge and requires fast algorithms. For that reason we present
an algorithm which is based on the nonlinear conjugate gradient method. The efficiency of the
algorithm and the quality of the resulting halftoning is demonstrated by several examples.
[1] M. Drmota and R. F. Tichy. Sequences, Discrepancies and Applications. Springer, Berlin,
1997.
[2] M. Gräf, D. Potts, and G. Steidl. Quadrature Errors, Discrepancies and their Relations to
Halftoning on the Torus and the Sphere. Preprint 2011-5, Fakultät für Mathematik, TU
Chemnitz, 2011.
S21.4: Mathematical Image Processing IV Wed, 16:00–18:00
Chair: Martin Welk S1|03–110
Parameterization of all (1, 2, 3)-generalized inverses with an application to scattered
data approximation
Dominik Stahl (Fraunhofer ITWM), Tobias Damm (Universität Bayreuth) Schedule
In our talk we present a method to approximate scattered data based on the lifting scheme.
A central task in the algorithm is the solution of a rank-deficient linear least squares problem
minx∈R n �Ax − b�2. The minimal-norm solution, obtainable by the Moore-Penrose-inverse, turns
out to be not a good choice here, since it produces artifacts at the boundary of the given domain.
Using extra information on the matrix A, we suggest the construction of a different generalized
inverse A ♯ which is much more appropriate to our problem and yields better solutions. Moreover,
our construction leads to a parameterization of all (1, 2, 3)-generalized inverses of an arbitrary
matrix A. We compare these with respect to their approximation properties in the scattered data
approximation problem.

366 Section 21: Mathematical image processing
Geodesics in shell space
Behrend Heeren (Universität Bonn), Martin Rumpf Schedule
The representation and deformation of thin shells has been a topic of recent research in analysis
as well as in applications ranging from computer graphics to material sciences. Shells are thin,
flexible structures with a high ratio of width to thickness which are mathematically represented
by surfaces. Elastic energies resulting from the deformation of shells can be described by classical
strain energies or by bending energies if the deformation is solely isometric. We use these
results to introduce a notion of time-discrete shortest paths in the space of shells, i.e. our timediscrete
geodesic is defined via a variational approach based on elastic matching deformations.
The corresponding deformation energy captures tangential strain as well as general bending.
In order to compute time-discrete geodesics the shells are discretized by parameterized triangular
meshes. We introduce discrete counterparts of geometric objects, e.g. the second fundamental
form, by using concepts from Discrete Differential Geometry. The minimization of the objective
functional is performed by means of hierarchical meshes. Our computational results emphasize in
particular the impact of the bending energy on the regularization of the geodesic path.
Data de-noising via adaptive wavelet transforms on paths
Dennis Heinen, Gerlind Plonka-Hoch (Universität Göttingen) Schedule
De-noising is an important problem in image processing as well as in the situation of higher dimensional
data. Consider, we are given a set of D-dimensional points (possibly on a non-uniform
grid). Furthermore, suppose there are function values, perturbated by an additive Gaussian noise,
defined on these points.
Our de-noising method works as follows: We successively construct certain path vectors
through the point set. We start from a random point and the choice of every following point
depends on the proximity to the previous point on the path and the corresponding function values.
Subsequently, we apply a one-dimensional wavelet shrinkage procedure along the constructed
path vectors.
The method is closely related to the easy path wavelet transform (EPWT) in image approximation
by Plonka (2009) and to the generalized tree-based wavelet transform by Ram et al
(2011). Moreover there is a relation to the diffusion maps framework in dimensionality reduction
(see e.g. Coifman and Lafon (2006)), where random walks on a weighted graph of a given data
set are employed.
This talk will explain the proposed data de-noising method with its modifications and also
feature some numerical results.
Tight wavelet frames of splines of fractional order
Brigitte Forster (TU München), Ole Christensen (Technical University of Denmark), Peter Massopust
(Helmholtz Zentrum München) Schedule
Schoenberg’s piecewise polynomial B-splines are traditionally used for multiresolution analyses in
signal and image processing. In recent years, generalizations of these function families to fractional
and complex order have been developed, which allow for a better adaptation of the analyzing
basis to the image and signal analysis model at hand. Up to now, mainly wavelet bases or the
undecimated wavelet transform have been used. We contribute to the theory in providing a novel
family of tight multi-wavelet frames generated by splines of fractional order. Our approach is
based on the unitary extension principle and yields closed form high-pass and low-pass filters—
ideal for a fast and simple implementation in Fourier domain.
Image Inpainting and Sparse Approximation
Emily King (Universität Bonn), Gitta Kutyniok, Xiaosheng Zhuang (TU Berlin) Schedule

Section 21: Mathematical image processing 367
One main problem in data processing is the reconstruction of missing data. In the situation of
image data, this task is typically termed image inpainting. Recently, inspiring algorithms using
sparse approximations and ℓ1 minimization have been developed and have, for instance, been
applied to seismic images. The main idea is to carefully select a representation system which
sparsely approximates the governing features of the original image – curvilinear structures in case
of seismic data. The algorithm then computes an image, which coincides with the known part of
the corrupted image, by minimizing the ℓ1 norm of the representation coefficients.
In this talk, we will develop a mathematical framework to analyze why these algorithms
succeed and how accurate inpainting can be achieved. We will first present a general theoretical
approach. Then we will focus on the situation of images governed by curvilinear structures, in
which case we analyze both wavelets as well as shearlets as the chosen representation system. Using
the previously developed general theory and methods from microlocal analysis, under certain
conditions on the size of the missing parts we will prove that such images can be arbitrarily well
reconstructed.

368 Section 22: Scientific computing
Section 22: Scientific computing
Organizers: Peter Bastian (Universität Heidelberg), Axel Voigt (TU Dresden)
S22.1: Particle Methods Tue, 13:30–15:30
Chair: Axel Voigt S1|03–104
Construction and analysis of variational multirate integrators
Sina Ober-Blöbaum (TU München/Universität Paderborn), Sigrid Leyendecker (Universität
Erlangen-Nürnberg) Schedule
Variational integrators [2] are based on a discrete variational formulation of the underlying
system. The resulting integrators are symplectic and momentum preserving and have an excellent
long-time energy behavior. For the integration of systems on different time scales, multirate
methods have been developed [1], where the slow part of the system is integrated with a relatively
large step size while the fast part is integrated with a small time step to save function evaluations
and decrease integration time.
In this talk, the construction and an analysis of a variational multirate integrator [3] are
presented. Based on a derivation in closed form via a discrete variational principle on a time
grid consisting of macro and micro time nodes the resulting integrator is symplectic and momentum
preserving. Its performance and approximation order depending on different discretization
schemes are demonstrated by numerical examples.
[1] C. W. Gear and R. R. Wells, Multirate linear multistep methods. BIT 24 (1984) 484–502.
[2] J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numerica
10 (2001), 357–514.
[3] S. Leyendecker and S. Ober-Blöbaum, A variational approach to multirate integration for
constrained systems, In Proceedings of Multibody Dynamics, ECCOMAS Thematic Conference,
Brussels, Belgium, 4-7 July 2011
Molecular dynamics simulation of liquid-liquid equilibria using molecular models
adjusted to vapor-liquid equilibrium data
Stefan Eckelsbach, Zhongning Wei, Thorsten Windmann, Jadran Vrabec (Universität Paderborn)
Schedule
For the design and optimization of chemical process engineering applications, knowledge on vaporliquid
(VLE) and liquid-liquid equilibria (LLE) is crucial. Typically, these thermodynamic properties
are determined by experiment and described by empirical correlations that are subsequently
employed to model distillation or extraction columns. Because of the effort that is associated with
the respective experiments, there is significant interest in predictive approaches to VLE and LLE
data. There are numerous fluid mixtures for which both types of data are required simultaneously.
However, empirical correlations are not capable to cover VLE and LLE consistently such that
different models and/or different parameters have to be used for a given mixture [1].
Molecular modeling and simulation is a modern approach for the prediction of thermodynamic
properties. Being based on mathematical representations of the intermolecular interactions, it has
strong predictive capabilities as it adequately covers structure, energetics and dynamics on the
microscopic scale that govern the fluid behavior on the macroscopic scale. In preceding work,

Section 22: Scientific computing 369
molecular models (force fields) were developed to accurately describe pure substance VLE data
and successfully assessed with respect to VLE data of multicomponent mixtures [2]. In the present
work, the capability of those models to predict the LLE data is studied for the binary mixture
nitrogen + ethane. Systems containing 20000 particles, starting from a random distribution of
the species, are simulated by molecular dynamics (MD) and phase separation is observed with
a direct method. The calculations are made with the massively parallel MD code ls1 mardyn [3]
that is developed in our group. The program scales linearly with the particle number and has a
very good parallel effciency up to thousands of computing cores. It is shown that LLE data can
be determined in this way and that molecular models are capable to consistently cover VLE and
LLE data in good agreement with experiments.
[1] E. Hendriks, et al., Ind. Eng. Chem. Res. 49 (2010), 11131.
[2] J. Stoll, et al., AIChE J. 49 (2003), 2187.
[3] M. Buchholz, et al., J. Comput. Sci. 2 (2011), 124.
Adapting Molecular Dynamics for the Simulation of a Lightweight Material
Tobias Steinle, Andrea Walther, Jadran Vrabec (Universität Paderborn) Schedule
Increasing awareness of climate change and limited fossil fuel supply have the emphasized need for
highly efficient cars and machines. Lightweight materials play an important role in this endeavor.
A problem with these materials is that vibration, for example, caused by an engine, is more likely
to occur than with a traditional solid material of the same dimensions.
The Fraunhofer Institute for Manufacturing Technologies and Advanced Materials in Dresden
has developed a new kind of material that uses embedded hollow spheres filled with particles to
quickly suppress such vibrations. By converting kinetic energy to heat through friction, arising
from the collisions of the particles with each other and the hull of the sphere, a high dampening
factor is achieved. Thus, wear, tear and noise are reduced.
To numerically simulate the behavior of the particles, we use an adapted molecular dynamics
method. These methods are able to simulate large numbers of particles, but use a series of assumptions
that require changes, such as reflective boundary conditions. The static simulation
volume of molecular simulations is adapted to allow for a deformation of the hull of the sphere.
Additionally, friction and gravity are introduced.
Some results of these dynamic simulations are presented.
Hybrid GPU Accelerated Mesoscopic Particle Simulation
Katrin Fischer, Georg-Peter Ostermeyer (TU Braunschweig) Schedule
During the past few years, the performance enhancement of existing algorithm implementations
through massive parallelization on modern graphics processing units (GPU) based on NVIDIA’s
Compute Unified Device Architecture (CUDA) has become very popular in a large variety of applications.
Particle methods e.g. are dedicated for parallelization because of their basic algorithmic
structure. The neighbourhood search, the computation of interaction forces and the final state
update via time integration can be parallelized directly among the particles.
In order to evaluate the potential of such a GPU implementation compared to the single CPU
execution, a parallel and hybrid implementation with OpenMP and CUDA has been developed
for a special particle method, the so-called mesoscopic particle method. This method takes into
account mechanical as well as thermodynamical degrees of freedom. On the basis of the hybrid

370 Section 22: Scientific computing
implementation, the performance of different types of execution architectures (sequential on single
CPU core, parallel on multi-core CPU, parallel on GPU) can be determined and compared.
This talk gives an introduction to the developed parallel and hybrid mesoscopic particle implementation
as well as some performance results for different CPUs and different generations of
NVIDIA GPUs.
Counting Droplets: A solver for the droplet population balance equation
Timo Wächtler (TU Kaiserslautern), Jörg Kuhnert (Fraunhofer Institut für Techno- und Wirtschaftsmathematik),
Menwer Attarakih (CAPE The University of Jordan), Axel Klar (TU Kaiserslautern)
Schedule
Liquid-Liquid-Extractions is one of the basic operations in chemical engineering and the simulation
of those processes provides several numerical difficulties. From the point of CFD, a dispersive
flow has to be resolved numerically. Assuming, that the droplets of the dispersed phase of this
flow are distributed statistically, one can formulate an equation for the distribution function
f = f(t, x, v) for the droplets depending on time, space and the droplet volume
∂tf + ∇x · (vdf − D∇xf) = + 1/2 ·
�
vmax
0
− f(t, x, v)
ω(v − v ′ , v ′ )f(t, x, v − v ′ )f(t, x, v ′ )dv ′
�
vmax
− Γ(v) · f(t, x, v) +
v
ω(v, v ′ )f(t, x, v ′ )dv ′
�
vmax
v
Γ(v ′ ) · β(v|v ′ )f(t, x, v ′ )dv ′ .
The droplet information is transported due to the droplet velocity vd and diffusion D. The right
hand side represents the births and deaths of droplets due to aggregation and breakage events. This
contribution will present a moment based numerical method to deal with the kind of equations
above and is going to involve this method in a two-phase flow simulation using the Finite Pointset
Method. The presentation will be closed with an exposition of 2D test problems for special cases
of (1).
[1] T. Wächtler, J. Kuhnert, M.M. Attarakih et. al
The Normalized Qudrature Method of Moments coupled with Finite Pointset Method
Proc. of the International Conference on Particle-based method Fundamentals and Applications
Barcelona, Spain, 26-28 October 2011
[2] C.Drumm, S.Tiwari, J.Kuhnert, H.-J. Bart, Finite pointset method for simulation of the
liquid-liquid flow field in an extractor, Computers & Chemical Engineering 32 (2008), 2946-
2957
S22.2: PDE Applications and Fast Solvers Tue, 16:00–18:00
Chair: Jörg Wensch S1|03–104
Parallel simulation of soft biological tissue
Oliver Rheinbach, (TU Chemnitz), Sarah Brinkhues, Axel Klawonn, Jörg Schröder (Universität
Duisburg-Essen) Schedule
(1)

Section 22: Scientific computing 371
Numerical simulation of soft biological tissue based on patient specific data is demanding with
respect to the modeling, the discretization, as well as the solution of the arising nonlinear elasticity
problems. In this talk, we present our approach to a software environment composed of a nonlinear
finite element code (FEAP) and a parallel domain decomposition solver (FETI-DP method). We
also present parallel results obtained on a Cray XT6m.
Comparison of variational and non-variational multigrid methods based on nonnested
meshes
Thomas Dickopf, Rolf Krause (University of Lugano) Schedule
This talk is about two classes of multigrid methods based on non-nested meshes for the fast
solution of partial differential equations on complicated domains. For finite element discretizations
with unstructured meshes in 3D, these methods combine the flexibility of algebraic multigrid
methods with the efficiency of geometric multigrid methods by a flexible choice of the coarse
meshes. We present a detailed performance analysis comparing the variational setting, where the
coarse spaces are built by recursively considering the ranges of suitable prolongation operators in
the next finer space, and the non-variational (“auxiliary space”) setting. In particular, numerical
studies of specially designed mesh hierarchies, which are structured but non-nested, provide new
insight into the dependence of the convergence on the mesh size ratios.
A Three-Dimensional Panel Method for the Simulation of Sheet Cavitation in Marine
Propeller Flows
M. Bauer, M. Abdel-Maksoud (TU Hamburg) Schedule
This paper presents the development and application of a three-dimensional panel method based
on potential theory for the modeling and simulation of sheet cavitation on marine propellers.
In potential theory the governing equations are derived from the assumption that the flow is
irrotational, incompressible and inviscid combined with adequate boundary conditions on the
body and cavity surface. The resulting boundary value problem is solved numerically by means
of a panel method where the body surface is discretized into flat quadrilateral elements. The
advantage of the developed panel method is its short computation time which allows for a wide
rage of parameter variations in the design procedure.
The present work is motivated by the difficulties which occur in the propeller flow under cavitating
conditions. Cavitation is a physical effect where the pressure falls below the vapour pressure such
that a vapour region occurs in the flow. Cavitation influences the flow characteristics on propeller
blades significantly and can lead to a decrease of propeller thrust or in sever cases cause material
damages on propeller blades. The most relevant features of the cavitation model are described in
the first part of the paper. The model is implemented in the in-house boundary element code -
panMARE - which is based on a first-order panel method and is able to simulate potential flows
in marine applications [1].
In the second part of the paper the model is validated by representative two- and three-dimensional
examples. Validation studies refer to the results obtained by other authors, e.g. published in [2].
To demonstrate the abilities of the developed method a marine propeller is simulated under
cavitating conditions and the influence of cavitation on propeller’s performance is outlined.
[1] J. Hundemer, M. Abdel-Maksoud, Prediction of tip vortex cavitation inception on marine
propellers at an early design stage, 7th International Symposium on Cavitation, Ann Arbor,
(2009).
[2] A. K. Singhal, M. M. Athavale, H. Li, Y. Jiang, Mathematical Basis and Validation of the
Full Cavitation Model, Journal of Fluids Engineering, Vol. 124, (2002), p. 617-624.

372 Section 22: Scientific computing
Simulation of Non-Newtonian Fluid Flow
A. Naumann, J. Wensch (TU Dresden) Schedule
The simulation of non-Newtonian fluids is a challenging task in computational rheology. The
dynamics of the fluid are described by the Navier-Stokes equations. Whereas Newtonian fluids
have constant viscosity, in non-Newtonian fluids a variety of models for the viscous terms are
available. Viscosity may depend on the shear rate or even on the deformation history. The latter
leads to models for the stress-strain rate relation analogous to viscous solids. The corresponding
evolution equations often constitute a stiff problem.
The proposed numerical scheme is based on finite elements with a semi-Lagrangian discretization
of the advection operator The combination of a transport process and stiff reaction terms
requires special care to avoid restrictive stepsize limitations.
Stability analysis of solid-state lasers regarding thermal lensing effect
Thomas Graupeter, Christoph Pflaum (Universität Erlangen) Schedule
The thermal lensing effect in the crystal influences the stability of solid-state lasers. The deformation
of the end faces of the crystal and the temperature dependence of the refraction index
causes this effect. The photoelastic effect produced by thermal induced stress in the crystal has
also an influence. For high power lasers and for lasers with a radially polarized laser beam the
analysis of the photoelastic effect is important. We use FE model to calculate the deformation,
heat and stress distribution in the laser crystal with high accuracy in this work. Using the calculated
stress distribution we also simulated the refraction index anisotropy with respect to the
crystal orientation. We can study stability of laser resonators for both radially and azimuthally
polarized laser beam, as a result of our simulation.
S22.3: Efficient Numerical Schemes for Nonlinear Mechanics Thu, 13:30–15:30
Chair: Peter Bastian S1|03–104
On the superlinear convergence in computational elasto-plasticity
Christian Wieners (KIT) Schedule
We consider the convergence properties of return algorithms for a large class of rate-independent
plasticity models. Based on recent results for semismooth functions, we can analyze these algorithms
in the context of semismooth Newton methods guaranteeing local superlinear convergence.
This recovers results for classical models but also extends to general hardening laws, multi-yield
plasticity, and to several non-associated models. The superlinear convergence is also numerically
shown for a large-scale parallel simulation of Drucker-Prager elasto-plasticity and an example for
the modified Cam-clay model.
Dual weighted residual error control for frictional contact problems
Andreas Rademacher (TU Dortmund), Andreas Schröder (HU Berlin) Schedule
Frictional contact problems play an important role in the modeling of mechanical engineering processes,
for instance in forming processes. Variational formulations of contact problems are given,
e.g., via the introduction of Lagrange multipliers capturing the geometrical and frictional contact
conditions. A low-order finite element dicsretization of such mixed approaches is described in [1],
where the displacement field is discretized by the usual low-order conforming ansatz and the Lagrange
multipliers via piecewise constant functions on coarsened boundary meshes ensuring the
stability of the mixed method.

Section 22: Scientific computing 373
In the simulation of engineering processes, adaptive methods based on a posteriori error estimates
become more and more indispensable, because they automatically solve the given problem
as accurate as needed while minimizing the overall numerical effort. One of the most popular
techniques from the last decades to derive error estimates for user-defined, probably non-linear
error measures (quantities of interest) is known as the dual weighted residual method (DWR). It
relies on representing the error in terms of the solution of a dual problem. This note focusses on
the application of the DWR method for quasi static contact problems. In extension of the results
presented in [2,3], the error is measured with respect to quantities of interest in the displacement
field as well as in the Lagrange multipliers to control the error of the contact forces directly.
Using a mixed dual problem, one obtains the general residuals of the DWR method and a term
for the error in the contact conditions, which are numerically evaluated by suitable interpolation
techniques. Numerical results substantiate the applicability of the presented techniques.
[1] A. Schröder, H. Blum, H. Kleemann, A. Rademacher, Mixed FEM of higher-order for contact
problems with friction, J. Num. Anal. & Model. 8 (2011) 302-323.
[2] A. Rademacher, Adaptive finite element methods for nonlinear hyperbolic problems of second
order, Dissertation, Technische Universität Dortmund, 2009.
[3] A. Schröder, A. Rademacher, Goal-oriented error control in adaptive mixed FEM for Signorini’s
problem, Comput. Methods Appl. Mech. Engng. 200 (2011) 345-355.
A posteriori control of modeling and discretization errors in finite elastoplasticity
André Große-Wöhrmann, Heribert Blum (TU Dortmund) Schedule
The concept of adaptive error control for finite element Galerkin discretizations has more recently
been extended from the pure treatment of the discretization errors [1], [3] also to the
control of modeling errors [5]. These techniques can be employed for a rigorous justification of
the local choice of the model out of a given hierarchy with increasing complexity. In the present
paper the concept is exemplified by a hierarchy of elastoplasticity models [2] including kinematic
(Armstrong-Frederick-) hardening, scalar- and tensor-valued damage [6] and a Taylor model of
polycrystals. Significant reduction of the computational complexity shall be achieved by a proper
choice of the model in different subdomains, automatically chosen by the error estimators. The
method is applied to finite element simulations [4] of metal forming.
This project is supported by the Deutsche Forschungsgemeinschaft (DFG) under grant SFB-TR
73 ”Sheet-Bulk Metal Forming”(https://www.tr-73.de)
[1] M. Ainsworth, J. T. Oden: A Posteriori Error Estimation in Finite Element Analysis, Wiley
2000.
[2] F. Armero, C. Zambrana-Rojas: Volume-preserving energy-momentum schemes for isochoric
multiplicative plasticity, Comput. Methods Appl. Mech. Engrg. 196 (2007) 4130-4159.
[3] R. Becker, R. Rannacher: An optimal control approach to a posteriori error estimation in finite
element methods, Acta Numerica, Vol. 10, pp. 1-102, edited by A. Iserles, Ed., Cambridge
Univ. Press, 2002.
[4] W. Bangerth, R. Hartmann and G. Kanschat: deal.II Differential Equations Analysis Library,
Technical Reference: http:// www.dealii.org.

374 Section 22: Scientific computing
[5] M. Braack, A. Ern: A posteriori control of modeling errors and discretization errors, Multiscale
Model. Simul. Vol. 1, No. 2, pp 221-238, 2003.
[6] A. Menzel, P. Steinmann, A theoretical and computational framework for anisotropic continuum
damage mechanics at large strains, Int. J, Solids Structures 38 (2001) 9505-9523.
On the dynamic behaviour of fluid-saturated soil within the framework of elastoplasticity
Maik Schenke, Bernd Markert, Wolfgang Ehlers (Universität Stuttgart) Schedule
Phenomena related to porous media dynamics, such as wave propagation and liquefaction, are encountered
in many engineering applications, especially, in geomechanics and earthquake engineering.
Drawing our attention to fluid-saturated granular materials with heterogeneous microstructures,
the modelling is carried out within a continuum-mechanical framework by exploiting the
well-established macroscopic Theory of Porous Media (TPM) together with thermodynamically
consistent constitutive equations. In this regard, the solid skeleton is described within the
framework of elasto-plasticity [1, 2].
The underlying equations are discretised and implemented into the coupled porous-media finiteelement
solver PANDAS. A general interface to the well-established Abaqus finite-element package
allows for a straight-forward usage of PANDAS material models within Abaqus, thereby exploiting
the advantages of Abaqus, such as the graphical user interface, the contact algorithms and the
possibility to deal with large problems through parallelisation. Moreover, the coupling introduces
a convenient environment to define new material models through PANDAS. In conclusion, the
interface allows to define complex intial-boundary-value problems through Abaqus, but involves
state-of-the-art material models of PANDAS.
The underlying interface will be used to analyse the wave propagation, through fluid-saturated
soils, which is caused by transient loading conditions as they occur, for instance, during
earthquakes or geotechnical installation processes.
[1] Y. Heider, B. Markert, W. Ehlers, Dynamic wave propagation in infinite saturated porous
media half spaces. Comput. Mech., DOI 10.1007/s00466-011-0647-9
[2] W. Ehlers, O. Avci, Stress-dependent hardening and failure surfaces of dry sand. Int. J.
Numer. Anal. Meth. Geomech., in press 2011.
Cosserat rod and string models for viscous jets in rotational spinning processes
Walter Arne (Universität Kassel), Nicole Marheineke (Universität Erlangen-Nürnberg), Raimund
Wegener (Fraunhofer Institut für Techno- und Wirtschaftsmathematik) Schedule
We present asymptotic Cosserat rod and string models for the simulation of slender viscous jets.
In the set-up of rotational spinning processes we examine the models analytically and numerically
with respect to their applicability/validity and efficiency. The string models are asymptotic limits
of the rod in terms of a vanishing slenderness parameter (slender-body theory). They consist of
smaller systems of equations, but as a result of a singular asymptotic perturbation their applicability
is restricted to certain parameter regimes – in contrast to the complexer and hence superior
Cosserat rod. We investigate the existence regimes of two string models that differ in the closure
conditions, determine their transition hyperplane numerically and present analytical results for

Section 22: Scientific computing 375
low and high Reynolds number limits.
S22.4: Scientific Computing Thu, 16:00–18:00
Chair: Peter Bastian S1|03–104
Computing roots for the analytic modeling of guided waves in acoustic waveguides
Andrea Walther, Fabian Bause, Bernd Henning (Universität Paderborn) Schedule
Computer aided simulation of guided acoustic waves in single- or multilayered waveguides is an
essential tool for several applications of acoustics and ultrasonics (i.e. pipe inspection, noise reduction).
To simulate wave propagation in geometrically simple waveguides (plates or rods), one
may employ the analytical global matrix method [1]. This requires the computation of all roots of
the determinate of a certain submatrix. The evaluation of all real or even complex roots is actually
the methods most concerning restriction. Previous approaches based on so called mode-tracers
which use the physical phenomenon that solutions (roots) appear in a certain pattern (waveguide
modes) and thus use known solutions to limit the root finding algorithms searchspace with respect
to consecutive solutions. As the limitation of the searchspace might be unstable in some cases,
we propose to replace the mode-tracer with a suitable version of an interval Newton method
based on Intlab [2]. To apply this interval based method, we extended the interval and derivative
computation provided by Intlab such that corresponding information is also available for Bessel
functions used in the circular model (rods) of acoustic waveguides. We present numerical results
of a simple acoustic waveguide and discuss extensions required for more realistic scenarios.
[1] Pavlakovic, B., Lowe, M. J. S.: Disperse: A System for Generating Dispersion Curves. Users
Manual. Non-Destructive Testing Laboratory, Imperial College London, 2003
[2] INTLAB - INTerval LABoratory, http://www.ti3.tu-harburg.de/rump/intlab/
Discrete Willmore Flow on surfaces using Subdivision
Sara Grundel (MPI Magdeburg), Thomas Yu, Jingmin Chen (Drexel University) Schedule
Gradient flows on surfaces play a role in a wide range of applications, for example in biological
modeling, computer graphics and shape optimization. We present a new approach to compute
a discrete gradient flow by using a newly developed C 2 smooth subdivision algorithm. We will
briefly present the subdivision algorithm and how we can use it to compute any gradient flow. We
will study the discrete Willmore flow and its application in detail. One of the advantages of this
subdivision approach is that it can be refined adaptively very easily. In this approach the surface
is given explicitly as a triangular mesh.
Flow Modeling in Rock Fracture for Long Time Simulation of Geothermal Reservoirs
Georg-Peter Ostermeyer, Tarin Srisupattarawanit (Institute of Dynamics and Vibrations) Schedule
The exploitation of geothermal power is an energy source with great potential for the future.
But the exploration and development of deep geothermal energy is connected with high cost and
risk, these require a reliable numerical prediction. The analysis of geothermal reservoir is usually
interested in long time physical properties (e.g. 50-100 years). Typical CFD simulation tool could
be used somehow, but the computational effort may be limited due to incompatibility of small
scale heterogeneities.
Here we developed flow modeling in rock fracture, which describe the different characteristic
flow in different dimension. The fluid flow in tube is described by one dimensional flow (1D flow),

376 Section 22: Scientific computing
while flow in rock fracture is modeled as two dimensional flow (2D flow) on fracture plane. The
1D flow in tube and 2D flows in fracture are coupled to represent three dimensional flows in
reservoirs. The solution of coupling system (1D and 2D flow) is obtained by iterative procedure,
while the flow inside 2D fracture is calculated by cellular automaton. This algorithm is relatively
fast for calculating flow inside geothermal reservoir, especially for long time physical flow.
Kombinierte Identifikation von Material- und Geometrieparametern bei strukturierten
Probekörpern
Hans Wulf (TU Chemnitz), Dirk Schellenberg (Deutsches Institut für Kautschuktechnologie), Jörn
Ihlemann (TU Chemnitz ) Schedule
Aus experimentell ermittelten inhomogenen Feldgrößen können Materialparameter mit Hilfe eines
Optimierungsverfahrens gewonnen werden, das FEM-Berechnungen als Unterroutine verwendet.
In der Regel werden dabei die Materialparameter innerhalb des Probekörpers als konstant vorrausgesetzt.
Diese Annahme ist nicht immer gerechtfertigt. Ortsabhängige Materialparameter
treten beispielsweise in Bauteilen nach Massivumformung aufgrund lokal unterschiedlicher Kornfeinung
oder in mehrphasigen biologischen Geweben auf. In diesem Fall muss statt eines einzelnen
Parametersatzes eine Verteilung von Parametern über dem Ort ermittelt werden.
Ein einfaches Beispiel stellt ein aus zwei Arten biologischer Gewebe bestehender Probekörper
dar. Es wird dabei angenommen, dass das betrachtete Gebiet sich in zwei zusammenhängende
Bereiche mit konstantem Materialverhalten unterteilen lässt. Allerdings ist die Form der Gebiete,
speziell die Grenzfläche zwischen den Gebieten, unbekannt. Als Stoffgesetz wird ein einfaches
Gesetz für poröse Materialien verwendet. Das Ziel der Identifikation besteht darin, die Materialparametersätze
in beiden Gebieten sowie die Form der Gebiete zu bestimmen. Die Form der
Grenzfläche zwischen den Gebieten wird mit einem Non-Rational Uniform B-Spline (NURBS)
parametrisiert. Außerdem wird ein Verfahren für die Generierung von entsprechend angepassten
FEM-Netzen vorgestellt. Insgesamt sollen 6 Materialparameter und 5 Geometrieparameter bestimmt
werden. Es wird ein Algorithmus gezeigt, welcher beide Parameterarten gleichzeitig in
einer kombinierten Optimierung identifiziert.
Um das Verfahren zu testen, wurden zwei Indentationsversuche simuliert und die Reaktionskraft
am Indenter sowie die Verformung der Außenkontur berechnet. Die Resultate wurden
mit einem additiven Gaußschen Rauschen von 5% belegt und werden als synthetische Messwerte
verwendet. Auf Basis dieser Daten werden alle 11 Parameter mit einer einzelnen gekoppelten
Optimierung identifiziert.
The synthesis of adequate mathematical description as special inverse problem
Yu.Menshikov (Dnepropetrovsk University, Ukraine) Schedule
The main problem of mathematical modeling is the construction (synthesis) of mathematical
model (MM) of motion of real dynamic system which in aggregate with model of external load
(MEL) gives the adequate to experimental observations the results of mathematical modeling.
Such pair (MM+MEL) was named as adequate mathematical description. In paper one way of
solution of such problem was considered which based on identification method of external loads.
These problems are inverse problems and they have typical properties of incorrect problems.
The regularization methods are being used for obtaining the stable solutions. But there are some
features. For example, the size of error of approximate solution of inverse problem has not essential
importance for future use. The error of MM has not to be taken into account under calculations in
these problems. It is necessary the use of special filtration of initial data for decrease of influence
of uncontrollable inaccuracy into initial data.
For expansion of area of use of approximate solution the method of choice of special operator

Section 22: Scientific computing 377
was suggested. The different variants of choice of MEL which are depending from final goals of
mathematical modeling (modeling of given motion of system, different estimation of responses
of dynamic system, modeling of best forecast of system motion, the most stable model to small
change of initial data, unitary model) are considered.
In paper some real calculations of adequate mathematical descriptions of real dynamic systems
were executed using of which give adequate results of mathematical modeling.
Failproof GRID-enabled framework for large-scale computations in mechanics
Andrei V. Zinchenko (Institute of Transport Systems and Technologies, NAS of Ukraine), Sergei
N. Kodak (Dnepropetrovsk National University) Schedule
Last time the Grid computing is gaining a lot of attention within the scientific community. Unlike
to chemistry, molecular biology and nuclear physics applications, Grid technologies just have
been finding their way in fields of mechanical engineering, material modeling, computational fluid
dynamics. Due to intensive enough data exchange between nodes the Grid implementation of
PDE based mechanical problems in some cases is really difficult especially in scavenging Grid
infrastructure.
Based of ideas of BOINC open source projects authors have developed VALERIA Grid middleware
capable for implementation in scavenging or computational Grid environment. The distinctive
features of developed middleware are the dynamic topology scan, failover procedure and
automatic reconfiguration of computational resources based on keep-alive tests. The failover procedure
is specially designed to be time-effective and suitable for use inside iteration of distributed
PDE solvers with message passing interface.
VALERIA middleware consists of control router hosted configuration, topology and cryptographic
engines and the control interface. Router maintains communication with hierarchy of
computational clusters or nodes as well as the database server provides initial data and results
storage. For redundancy VALERIA Grid infrastructure could be configured with several backup
routers. The primary router also hosts job control and dispatch service. Computational nodes
must have loader software installed capable of executing piece of distributed code. Loaders are
now available for Win32 and Linux environments.
First attempts to implement the finite volume PDE solver showed essential limitations of scavenging
Grid for the fluid mechanics problems. Distributed CFD code requires huge memory allocations
on computational nodes. This fact induced lots of node reconfigurations and significantly
slowed down the calculation speed in our experiments. Finally we have moved from scavenging
to computational Grid infrastructure.
Overall performance was tested on a cluster consists of four SONY PlayStation3 computational
nodes with Linux installed. The prime calculation tests gave 470 times speed up in comparison
with Athlon X2 2,5GHz. The next step will be computational experiments with distributed PDE
solvers.

378 Section 23: Applied operator theory
Section 23: Applied operator theory
Organizers: Jussi Behrndt (TU Graz), Carsten Trunk (TU Ilmenau)
S23.1: Spectral Theory in Hilbert and Krein Spaces Tue, 13:30–15:30
Chair: Carsten Trunk S1|03–107
Dirac-Krein operators on star graphs
Vadim Adamyan (Odessa National I.I. Mechnikov University) Schedule
The talk focuses on the description of the spectrum of a self-adjoint Dirac-Krein differential
operator
�
0
H = −
1
�
−1 d
0 dx +
�
p(x)
q(x)
�
q(x)
,
−p(x)
on an n-pointed compact star graph Γ, where p(x), q(x) are continuous real-valued functions on
the edges of Γ. The operator H is considered as a perturbation of the orthogonal sum H(12) of the
self-adjoint Dirac-Krein operators on the disjoint edges of Γ, defined on two-component vector
functions with zero first component at one end point and zero second component at the other
end point of each edge of Γ; the domain of H is assumed to consist of all vector functions the
first components of which coincide at the unique vertex of the star graph where all edges touch,
while the boundary conditions at the pendent ends of all edges are the same as for H(12). As a
main tool we use Krein’s resolvent formula for the resolvent kernels (Green’s functions) of H(12)
and H. We prove that the set of common eigenvalues of H and H(12) coincides with the set of
multiple eigenvalues of H(12), but their multiplicities as eigenvalues of H decreases by one. We
also prove that the sets of simple eigenvalues of H and the set of all eigenvalues of H(12) interlace.
The asymptotic behaviour of the number of eigenvalues of H, multiplicities taken into account,
on spectral intervals (−Λ, 0) and (0, Λ) as Λ → ∞ is derived.
The talk is based on a joint work with Heinz Langer and Christiane Tretter.
Spectral functions of products of selfadjoint operators
Tomas Ya. Azizov, Mikhail Denisov (Voronezh State University), Friedrich Philipp (TU Berlin)
Schedule
Given two possibly unbounded selfadjoint operators A and G such that the resolvent sets of AG
and GA are non-empty, it is shown that the operator AG has a spectral function on R with
singularities if there exists a polynomial p �= 0 such that the symmetric operator Gp(AG) is
non-negative. We apply this result to weighted Sturm-Liouville problems.
Variation of discrete spectra of non-negative operators in Krein spaces
Jussi Behrndt (TU Graz), Leslie Leben (TU Ilmenau), Friedrich Philipp (TU Berlin) Schedule
Considered is an additive perturbation of a bounded non-negative operator A in a Krein space
with a likewise bounded non-negative operator C from a Schatten-von Neumann ideal of order
p, such that ker C = ker C 2 and 0 is not a singular critical point of C. We show a qualitative
result on the variation of the discrete spectra of the unperturbed and perturbed operator, that
is, given a finite union ∆ of open intervals with 0 /∈ ∆, there exist enumerations (αn) and (βn) of
the discrete eigenvalues of A and B := A + C in ∆ such that
(βn − αn) ∈ ℓ p .

Section 23: Applied operator theory 379
Sign preserving Perturbations of Eigenvalues
Roland Möws (TU Ilmenau), Jussi Behrndt (TU Graz), Carsten Trunk (TU Ilmenau) Schedule
We consider two operators A and B which are self-adjoint in a Krein space (K, [·, ·]) and whose
resolvent difference is one-dimensional, i.e.
dim ran � (A − λ) −1 − (B − λ) −1� = 1, λ ∈ ρ(A) ∩ ρ(B).
It is well-known that the algebraic eigenspace corresponding to a real discrete eigenvalue of A
(or B), equipped with [·, ·], is a Krein space. The main result is the following: Assume that there
exists a domain Ω ⊂ C in which A (or, equivalently, B) has similar spectral properties as a
definitizable operator and that A satisfies a certain minimality condition. Moreover, let λ1 and λ2
be two discrete eigenvalues of A in Ω ∩ R such that (λ1, λ2) ⊂ ρ(A) and [·, ·] is positive definite on
both ker(A−λ1) and ker(A−λ2). Then there exists a (discrete) eigenvalue µ of B in (λ1, λ2) such
that [·, ·] is not negative definite on the algebraic eigenspace corresponding to µ. In particular, if
µ is a simple eigenvalue with a corresponding eigenvector f, then [f, f] > 0.
The result is applied to a class of Sturm-Liouville problems with an indefinite weight function.
Zeros of Nevanlinna functions with one negative square
Henrik Winkler (TU Ilmenau) Schedule
A generalized Nevanlinna function Q(z) with one negative square has precisely one generalized
zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation
defined by Qτ(z) = (Q(z) − τ)/(1 + τQ(z)), τ ∈ R ∪ {∞}, is a generalized Nevanlinna
function with one negative square. Its generalized zero of nonpositive type α(τ) as a function of τ
defines a path in the closed upper halfplane. Various properties of this path are studied in detail.
A perturbation approach to differential operators with indefinite weights
Jussi Behrndt (TU Graz), Friedrich Philipp (TU Berlin), Carsten Trunk (TU Ilmenau) Schedule
In many situations differential operators with indefinite weight functions can be regarded as perturbations
of nonnegative selfadjoint operators in Krein spaces. In this talk we first provide an
abstract result on bounded additive perturbations and apply it afterwards to Sturm-Liouville and
second order elliptic partial differential operators with indefinite weights on unbounded domains.
S23.2: Partial Differential Operators Tue, 16:00–18:00
Chair: Sergey Belyi S1|03–107
Weak Neumann implies Stokes
Horst Heck (TU Darmstadt) Schedule
When studying the Navier-Stokes equations, one of the basic models in fluid dynamics, a thorough
understanding of the (linear) Stokes equation is very helpful. In particular, the property
of maximal L p -regularity is a very powerful tool in order to treat the nonlinear equation. In this
presentation we show that the existence of the Helmholtz projection in L q (Ω) is sufficient for the
maximal L p -regularity of the Stokes operator, provided the domain Ω ⊂ R n is smooth enough.
The presented result is a joint work with M. Geissert, M. Hieber, and O. Sawada.
Schrödinger operators with interactions on hypersurfaces
Vladimir Lotoreichik (TU Graz) Schedule

380 Section 23: Applied operator theory
In the talk we plan to present a new approach to the definition of self-adjoint Schrödinger operators
with δ and δ ′ interactions on hypersurfaces. This approach uses operator extension theory via quasi
boundary triples. Within our approach we prove results concerning spectral and scattering theory
of Schrödinger operators with interactions on hypersurfaces.
A comparison with the approach based on quadratic forms will be given. The quadratic form
for δ ′ interactions was not constructed so far and the question of its construction was posed as
an open problem by Pavel Exner in 2008. In the talk it will be also presented our solution of that
problem.
The talk is based on a joint work with Jussi Behrndt (Graz University of Technology) and
Matthias Langer (University Strathclyde).
Spectra of selfadjoint elliptic differential operators, Robin-to-Dirichlet maps, and an
inverse problem of Calderón type
Jussi Behrndt, Jonathan Rohleder (TU Graz) Schedule
In this talk we consider selfadjoint operator realizations of an elliptic differential expression of the
form
n� ∂ ∂
Lu = − ajk u + au
∂xj ∂xk
j,k=1
on a bounded or unbounded domain Ω with certain local or nonlocal Robin type boundary conditions.
We will discuss the connections between the behaviour of a corresponding Robin-to-Dirichlet
maps on the boundary of Ω at its discontinuities and the point, absolutely continuous, and singular
continuous spectra of the operator realization. As an application, we present a mild uniqueness
result for the Calderón or Gelfand inverse problem corresponding to L.
Selfadjoint elliptic differential operators on domains with non-compact boundary
Christian Kühn (TU Berlin) Schedule
We consider a uniformly elliptic differential expression L of second order on an open set Ω in R n
with a non-compact boundary. We show selfadjointness of a class of realizations of L in L 2 (Ω).
The talk is based on a joint work with J. Behrndt.
Extensible quasi boundary triples and applications
Till Micheler (TU Berlin), Jussi Behrndt (TU Graz) Schedule
We study extensions of symmetric operators in Hilbert spaces via a generalization of boundary
triple methods and also discuss applications to elliptic partial differential operators on smooth
and rough domains.
S23.3: Applied Operator Theory and Linear Systems Wed, 13:30–15:30
Chair: Andras Batkai S1|03–107
The Elusive Drude-Born-Fedorov Model for Chiral Electromagnetic Media.
Rainer Picard, Henrik Freymond (TU Dresden) Schedule
In a Hilbert space operator setting, covering a comprehensive class of evolutionary equations, as
a particular application various aspects of material laws for Maxwell’s equations are discussed.
In particular, the Drude-Born-Fedorov model for electromagnetic waves in chiral media is investigated
and well-posedness is shown.
Well-posedness and conservativity for linear control systems (Part 1)
Marcus Waurick (TU Dresden) Schedule

Section 23: Applied operator theory 381
We discuss a class of linear control problems in a Hilbert space setting. The aim is to show that
these control problems fit in a particular class of evolutionary equations such that the discussion
of well-posedness becomes easily accessible. We exemplify our findings by a system with unbounded
control and observation operator.
Well-posedness and conservativity for linear control systems (Part 2)
Sascha Trostorff (TU Dresden) Schedule
Using the results obtained in part 1 of the talk, we study conservativity of a certain class of linear
control problems. For this purpose we require additional regularity properties of our solution
operator in order to allow pointwise evaluations of our solution. We apply the results to the linear
control system with unbounded observation and control operators mentioned in the first part of
the talk.
On energy conditions for electromagnetic diffraction by apertures
Matthias Kunik (Universität Magdeburg), Norbert Gorenflo (TFH Berlin) Schedule
The diffraction of light is considered for a plane screen with an open bounded aperture. The
corresponding solution behind the screen is given explicitly in terms of the Fourier transforms
of the tangential components of the electric boundary field on the screen. All components of the
electric as well as the magnetic field vector are considered. We introduce solutions with global
finite energy behind the screen and describe them in terms of two boundary potential functions.
This new approach leads to a decoupling of the vectorial boundary equations on the screen in the
case of global finite energy. For the physically admissible solutions, i.e. the solutions with local
finite energy, we derive a characterisation in terms of the electric boundary fields.
Approximation methods for a class of perturbed paired convolution equations
Michał A. Nowak (AGH University of Science and Technology, Krakow) Schedule
We consider approximation methods for some class of perturbed paired convolution equations (or,
in general, singular equations). Effective error estimates, and simultaneously, decaying properties
for solutions are obtained in terms of some smooth spaces. The talk is based on a joint work with
Petru A. Cojuhari.
Hamiltonians and Riccati equations for unbounded control and observation operators
Christian Wyss, Birgit Jacob (Universität Wuppertal), Hans Zwart (University of Twente, The
Netherlands) Schedule
We consider the control algebraic Riccati equation
A ∗ X + XA − XBB ∗ X + C ∗ C = 0
for the case that A is normal with compact resolvent, B ∈ L(U, H−s) and C ∈ L(Hs, Y ), 0 ≤ s ≤ 1.
Here Hs ⊂ H ⊂ H−s are the usual fractional domain spaces corresponding to A. Under certain
additional assumptions on A, B and C we show the existence of infinitely many solutions X of
the Riccati equation using invariant subspaces of the Hamiltonian operator matrix
� �
∗
A −BB
T =
.
−C ∗ C −A ∗
The first problem is here to make sense of T as an operator on H × H, because BB ∗ and C ∗ C
map from Hs to H−s. Our main tools are then Riesz bases of eigenvectors of T and indefinite
inner products. In general the solutions X will be unbounded, but we also obtain conditions for
bounded solutions.

382 Section 23: Applied operator theory
S23.4: Applied Operator Theory Wed, 16:00–18:00
Chair: Jussi Behrndt S1|03–107
Shape Preservation of Evolution Equations
András Bátkai (Loránd Eötvös University Budapest) Schedule
Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce
a definition of shape preserving operator semigroups and analyze their fundamental properties.
In particular, we prove that the class of shape preserving semigroups is preserved by
perturbations and taking limits. These results are applied, among others, to partial delay differential
equations.
Sectorial realizations of Stieltjes functions
Sergey Belyi (Troy University) Schedule
A class of Stieltjes functions with a special condition is considered. We show that a function
belonging to this class can be realized as the impedance function of a singular L-system with
a sectorial state-space operator. We provide an additional condition on a given function from
this class so that the state-space operator of the realizing L-system is α-sectorial with the exact
angle of sectoriality α. Then these results are applied to L-systems based upon a non-self-adjoint
Schrödinger operator.
The talk is based on a joint work with Yu. Arlinskiĭ and E. Tsekanovskiĭ.
On trace norm estimates
Johannes Brasche (TU Clausthal) Schedule
Let E and P be nonnegative quadratic forms in a Hilbert space H and suppose that E and the
sum E + bP is densely defined and closed for every b > 0. Let Hb be the selfadjoint operator
associated to E + bP . We present estimates for the trace norm of
(Hb + 1) −1 − lim
b ′ (Hb ′ + 1)−1
−→∞
In particular, we present a criterion in order that these trace norms tend to zero with maximal
rate, i.e. as fast as O(1/b). We illustrate our results with the aid of point interaction Hamiltonians.
On determining the domain of the adjoint operator
Michal Wojtylak (Jagiellonian University, Cracow) Schedule
A theorem that is of aid in computing the domain of the adjoint operator will be presented. It may
serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally
normal operator or for H–selfadjointness of an H–symmetric operator.
Parabolic Variational and Quasi-Variational Inequalities with Gradient Constraints
Carlos N. Rautenberg (Universität Graz), Michael Hintermüller (HU Berlin) Schedule
A class of nonlinear parabolic quasi-variational inequality (QVI) problems with gradient type
constraints in function space is considered. Problems of this type arise, for instance, in the mathematical
modelization of superconductors and elasto-plasticity. The paper addresses existence,
regularity and approximation results based on monotone operator theory, Mosco convergence and
C0 semigroup methods. Numerical tests involving the p-Laplacian operator with several nonlinear
constraints are provided.

Section 23: Applied operator theory 383
On a class of quadratic operator pencils with normal coefficients
Friedrich Philipp (TU Ilmenau), Vladimir Strauss (Universidad Simón Bolívar, Caracas),
Carsten Trunk (TU Ilmenau) Schedule
A standard description of damped small oscillations of a continuum or of small oscillations of a
pipe carrying steady-state fluid is done via
T ¨z + R ˙z + V z = 0, (1)
where z is a function with values in a Hilbert space and V and R are unbounded operators. A
classical approach is to investigate solutions of the form u(t) = e tλ φ0, and to transform, under
some additional assumptions, the equation in (1) into
L(λ)φ0 := (λ 2 I + λE + F )φ0 = 0
with bounded operators E and F . We will investigate the operator polynomial L with the coefficients
E = AC and F = C 2 , where C is a bounded normal operator in a Hilbert space H and A
is a bounded selfadjoint operator which commutes with C. If there exists a bounded operator Z1
which is an operator root, i.e., a solution of
Z 2 + ACZ + C 2 = 0,
then L(λ) = λ 2 + λAC + C 2 decomposes into linear factors
L(λ) = (λI − � Z1)(λI − Z1),
where � Z1 = −AC − Z1.
In our talk we will give sufficient conditions for the existence of an operator root. For this we
will investigate the companion operator (or linearizer) of the operator polynomial L which turns
out to be a normal operator in some Krein space. We will then apply recent results from the
spectral theory of normal operators in Krein spaces.

384 Section 24: History of mechanics
Section 24: History of mechanics
Organizers: Lothar Gaul (Universität Stuttgart), Erwin Stein (Leibniz Universität Hannover)
S24.1: Analysis of deformation, friction, damage and failure Thu, 13:30–15:30
Chair: Erwin Stein S1|03–223
On the History of the Mechanical Theory of Material Modelling
Albrecht Bertram (Universität Magdeburg) Schedule
We consider the last 50 years of development of material theory which are characterized by
radical disputes and changes of paradigms. We are still far from being able to consider this as a
finalized and practical theory. Two main lines of approaches shall be demonstrated, namely the
history or heredity functionals, and the inner-variables or state theories. Since both approaches
suffer from fundamental deficiencies, none of them really achieved global acceptance. And for a
long time it remained unclear how the two lines could be mutually related.
This was changed in 1972 by Nolls New Theory of Simple Materials [1], in which a third
approach was suggested, and one of the former sets could be imbedded into the other. The gain
of generality was, however, accompanied by a loss of simplicity, so that this theory is used only
by very few singu-lar groups within our community.
During the last 40 to 50 years many new flowering branches of material theory like finite
plasticity, viscoplasticity, or continuum damage mechanics have been successfully created, but
a globally ac-cepted general theory is still lacking. The tree of material theory has gained an
overwhelming variety of branches, while its trunk still remains conceptually unclear. If we enlarge
our frame and include thermodynamics into our considerations, then we have to state that also
here the lack of a general theory leads to undesirable effects like, e.g., that for each and every
new constitutive model the thermodynamical consistency has to proven anew without being able
to just refer to a general representation. There remains still a good deal of work to be done.
[1] Noll, W.: A new mathematical theory of simple materials. Arch. Rational Mech. Anal. 48,
1-50 (1972)
Einige Bemerkungen zur Geschichte der Plastizitätstheorie
Otto T. Bruhns (Universität Bochum) Schedule
Die Geschichte der Materialgleichungen und damit auch die Entwicklung der heutigen Materialtheorie
als einer Methode zur Beschreibung des Verhaltens von Materialien ist eng mit der
Entwicklung der Kontinuumstheorie auf der einen Seite sowie mit der beginnenden Industrialisierung
gegen Ende des 19. Jahrhunderts verknüpft.
Während einerseits durch Cauchy, Euler, Leibniz u.a. Begrifflichkeiten wie das Kontinuum,
Spannungen und Verzerrungen, deformierbare Körper eingeführt und die mathematischen Methoden
zu ihrer Beschreibung bereitgestellt wurden, hat erst der Druck der Industrialisierung mit
dem Bedürfnis nach immer neueren, zugleich aber auch verlässlich sicheren, Entwicklungen dazu
geführt, dass neben der Beschreibung eines elastischen Verhaltens fester Körper auch dem realen
Verhalten im Zustand des Versagens eher entsprechende Modelle wie z.B. das eines elastischplastischen
Verhaltens eingeführt wurden.
Vor diesem Hintergrund will der Vortrag in die Geschichte der Plastizitätstheorie einführen
und dabei schlaglichtartig auch die Beiträge des Darmstädter Absolventen Heinrich Hencky beleuchten,
der vor nicht ganz 100 Jahren hier seine wissenschaftliche Laufbahn begonnen hat.

Section 24: History of mechanics 385
Prandtl-Tomlinson-Model: History and Applications in Friction, Plasticity and Nano
Technologies
Valentin L. Popov (TU Berlin) Schedule
One of the most popular models in nano tribology widely used as the basis for many investigations
of frictional mechanisms on the atomic scale is the so-called TTomlinson model“. The name
TTomlinson modelïs, however, historically incorrect: The paper by Tomlinson that is often cited
in this context [1] did not contain the model known as the TTomlinson modeländ suggests an
adhesive contribution to friction. In reality it was Ludwig Prandtl who suggested in 1928 this
model to describe the plastic deformations in crystals [2]. Following some other researchers we
therefore call this model the PPrandtl-Tomlinson-Model“, while the truly correct name should
be just Prandtl model. The original paper by Ludwig Prandtl was written in German and was
not accessible for a long time for the largest part of international tribological community. In this
paper, Ludwig Prandtl considered not only the simplest deterministic form of the model consisting
of a point mass driven in a periodic potential, but also the influence of thermal fluctuations.
He was the first ttribologist“who came to the conclusion that thermal fluctuations should lead
to a logarithmic dependency of the frictional force on velocity. The success of the model as well
as its variations and generalizations is due to the fact that it is the simplest usable model of a
tribological system. Results concerning the basic properties of the Prandtl-Tomlinson-Model are
scattered over many publications and are summarized shortly in [3]. Extensions and variations
of the Prandtl model are widely used for understanding such processes as plasticity, including
dislocations (Frenkel-Kontorowa model), elastic instabilities, control of friction by chemical and
mechanical means as well as in designing of nano drives and handling of single molecules.
[1] G.A. Tomlinson, Phil. Mag, 1929, v.7, p.905.
[2] L. Prandtl, Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM, 1928,
Vol. 8, p. 85-106..
[3] V.L. Popov. Contact Mechanics, Springer, 2011.
Some Remarks on the History of Fracture Mechanics
Dietmar Gross (TU Darmstadt) Schedule
After a short overview on the history of fracture mechanics, some important milestones are considered
in detail. They include among others Griffith’s energy criterion and Irwin’s concept of
K-factors. Enlightened is also the context of these early developments with the state of the art of
solid mechanics at that time.
On Fröhlich’s Result for Boussinesqs Problem
A.P.S. Selvadurai, William Scott Professor and James McGill Professor (McGill University)
Schedule
Boussinesqs solution to the action of a concentrated normal force on the surface of an isotropic
elastic halfspace has been a problem of fundamental interest to theory of elasticity with applications
to contact mechanics and specifically geomechanics. Boussinesqs solution can be obtained
in a variety of ways starting with Kelvins solution to the problem of the interior loading of an
infinite space by concentrated force. The linearity of the governing equations lends itself to the
additional procedures based on integral transform techniques and potential theory. An extension
to Boussinesqs result was proposed in by O.K. Fröhlich in 1937. The concentration factor introduced
by Fröhlich is visualized as a procedure for examining the pattern of load transfer from

386 Section 24: History of mechanics
surface loads to the interior of the halfspace. The historical details that lead to the introduction
of the concentration factor are scant although it is widely used in the area of soil mechanics problems
associated with tillage induced soil compaction. The purpose of this paper is to examine
the concentration factor in terms of geomechanics of an elastic continuum and to identify the
precise conditions that are satisfied by the distribution of stresses and strains that accommodate
the concentration factor.
S24.2: Interaction of experiment, theory and numerics Thu, 16:00–18:00
Chair: Lothar Gaul S1|03–223
Experimentierkunst in der Mikromechanik
Dierk Raabe (MPI Düsseldorf) Schedule
Der Vortrag gibt einen Überblick über die Entwicklung der Experimentierkunst in der Mikromechanik.
Zwei Gebiete werden vorgestellt. Zum Ersten wird die Entwicklung mikromechanischer
Versuche besprochen beginnend mit einfachen Eindringversuchen bis hin zu in-situ Zugversuchen
innerhalb eines Elektronenmikroskops. Zum Zweiten werden die strukturanalytischen Verfahren
der Abbildung von Gitterfehlern von der optischen Mikroskopie über Raster- und Transmissionselektronenmikroskopie
bis hin zur atomaren Analytik dargestellt.
Parameter Identification in Continuum Mechanics: From Hand-Fitting to Stochastic
Modelling
Rolf Mahnken, Kai-Uwe Widany, Nicole Nörenberg (Universität Paderborn) Schedule
The correct determination of material parameters for constitutive equations is an important issue
for predictive simulation, both in industry and research. Its history is strongly related to the
achievements in constitutive modelling beginning with the celebrated Hooke’s law. This contribution
addresses various topics on parameter identification on the basis of experimental data.
Starting from hand-fitting procedures different identification procedures illustrated by simple examples
are outlined. Then particular aspects of the least squares approach are illustrated such
as optimization, local minima, sensitivity analysis, consequences of instabilities. Uniform small
strain problems and non-uniform large strain problems are considered. For the latter, finite element
results are incorporated into the optimization process, where for efficiency and reliability
the concept of goal oriented error estimators for adaptive mesh refinement is considered. Main
shortcomings of experimental data are scattering and measurement errors on the one side, and
limited repetitions of experiments on the other side, which ensues an uncertainty to the predictive
simulations. In order to obtain a broader range of experimental data for statistically distributed
material parameters the concept of stochastic modelling is outlined. The different concepts and
methodologies are illustrated by various examples in the field of continuum mechanics.
Gibbs–Appell Equations of Motion: History and Perspective
Ulrike Zwiers (Hochschule Bochum) Schedule
The so-called Gibbs–Appell equations of motion, independently discovered and developed by the
American physicist Josiah Willard Gibbs (1839–1903) and the French mathematician Paul Émile
Appell (1855–1930) in the late 19th century, represent presumably the simplest and most versatile
formulation of analytical mechanics discovered so far. Based on Gauss’ principle of least
constraints and the use of quasi-coordinates, the approach is applicable to both holonomic and
nonholonomic systems, including variable mass systems and systems subject to high-order nonholonomic
constraints.
Despite their elegance and wide field of applicability, many textbooks on engineering mecha-

Section 24: History of mechanics 387
nics present the Gibbs-Appell equations only as contents of secondary importance, provided that
they are covered at all. The contribution at hand discusses the advantages but also the disadvantages
associated with the Gibbs-Appell approach by means of illustrative examples and in view
of its historical development and recent advances.
Historic development of the knowledge of shock and blast waves
Torsten Döge, Norbert Gebbeken (Universität der Bundeswehr München) Schedule
The historic development of the scientific knowledge of shock and blast waves is given. The overview
starts in the 17 th century and goes to the first half of the 20 th century. Groundbreaking works
of outstanding scientists, like Galilei, Torricelli, Pascal, von Guericke, Boyle, Hooke,
Newton, Daniel Bernoulli, Euler, Lagrange, Gay-Lussac, Poisson, Laplace, Navier,
Carnot, Mayer, Stokes, Thomson, Clausius, Maxwell, Riemann, Boltzmann,
Rankine, Hugoniot, Mach, Rayleigh, Taylor, Bethe and Weyl, and their relations are
presented and discussed.
Especially the development of sound wave velocity, equation of state for gases, balance equations
and the occurrence of discontinuities (shocks) is regarded.

388 List of Participants
List of Participants
A
Aßmann, Ute S19.4 Wed 16:20–16:40
Abali, B. Emek S6.6 Wed 15:10–15:30
Abdelrahman, Mahmoud S14.3 Wed 14:10–14:30
Abdulaziz, Ali S11.5 Thu 14:30–14:50
Abels, Helmut S14.3 Wed 15:10–15:30
Adamyan, Vadim S23.1 Tue 13:30–13:50
Afendikov, Andrey S14.4 Wed 17:00–17:20
Agiasofitou, Eleni S6.11 Thu 16:20–16:40
Aigner, Mario S9.2 Tue 17:40–18:00
Akindeinde, Saheed Ojo S19.3 Wed 14:50–15:10
Aksel, Nuri
Al-Baldawi, Ammar S9.5 Thu 15:10–15:30
AL-Kinani, Raad S6.8 Wed 16:20–16:40
Alber, Hans-Dieter Me3 Mon 17:40–18:00
Alber, Oliver S5.3 Wed 17:40–18:00
Albrecht, Daniel S2.1 Tue 15:10–15:30
Aldudak, Fettah S10.2 Tue 17:00–17:20
Alexandru Marius, Rizescu S16.2 Tue 17:40–18:00
Alin-Cosmin, Tot S12.3 Wed 14:30–14:50
Allaire, Gregoire Plenary Fri 08:30–09:30
Altenbach, Holm
Altmann, Robert S18.4 Wed 13:30–13:50
Alves de Sousa, Ricardo Yr Me2 Tue 11:20–11:40
Amirtham , Rajagopal S8.8 Thu 17:40–18:00
Ams, Alfons
Ansorge, Rainer
Antos, Pavel S10.3 Wed 14:10–14:30
Arghir, Mariana S2.4 Wed 16:00–16:40
Arne, Walter S22.3 Thu 15:10–15:30
Arnold, Martin S1.6 Thu 13:30–14:10
Arrieta, Andres S4.4 Wed 16:40–17:00
Arslan, Eray S4.7 Thu 16:00–16:40
Asmus, Andreas S12.2 Tue 16:40–17:00
Avakian, Artjom
Avsarkisov, Victor S10.2 Tue 16:20–16:40
Awrejcewicz, Jan S1.3 Tue 17:40–18:00
Aydin, Aycan Özlem S6.2 Tue 14:30–14:50
B
Bátkai, András S23.4 Wed 16:00–16:20
Böhlke, Thomas Me1 Mon 17:15–17:40
Böl, Markus

List of Participants 389
Böttcher, Kai S13.3 Wed 17:40–18:00
Bühler, Stefan S12.1 Tue 14:10–14:30
Bürger, Raimund S18.2 Tue 16:00–16:20
Baars, Albert
Baaser, Herbert
Babolian, Maziar
Bach, Karolina S5.4 Thu 13:50–14:10
Baier, Tobias Me2 Mon 17:20–17:40
Balke, Herbert
Ballmann, Josef Prandtl Mon 13:30–14:30
Balzani, Claudio S3.3 Wed 15:10–15:30
Balzani, Daniel S3.2 Tue 16:00–16:20
Bamer, Franz S4.6 Thu 14:10–14:30
Banas, Lubomir S18.7 Thu 13:50–14:10
Banuls, Maria Carmen S17.1 Tue 13:30–14:10
Baodong, Shi S6.1 Tue 14:50–15:10
Bare, Zoufine S8.7 Thu 15:10–15:30
Bargmann, Swantje S8.1 Tue 14:10–14:30
Barnard, Richard S19.2 Tue 17:00–17:20
Baron, Eugeniusz S8.8 Thu 17:00–17:20
Bartel, Thorsten S6.5 Wed 13:30–14:10
Bartels, Alexander S6.4 Tue 17:20–17:40
Barthold, Franz-Joseph S19.3 Wed 14:10–14:30
Bastian, Peter
Bauer, Marcus S12.1 Tue 14:30–14:50
Bauer, Maria S22.2 Tue 16:40–17:00
Baum, Ann-Kristin S20.1 Tue 13:30–13:50
Bayerschen, Eric
Becker, Christian S1.4 Wed 14:50–15:10
Becker, Christian S7.1 Tue 13:30–13:50
Becker, Wilfried
Beckmann, Carla S8.3 Tue 17:40–18:00
Behn, Carsten S2.2 Tue 17:40–18:00
Behnke, Ronny S6.4 Tue 17:00–17:20
Behrndt, Jussi S23.1 Tue 15:10–15:30
Beitelschmidt, Michael S1.7 Thu 16:00–16:20
Belyi, Sergey S23.4 Wed 16:20–16:40
Benner, Peter
Berezhnyi, Maksym S8.2 Tue 17:40–18:00
Berger, Thomas Yr Ma2 Tue 10:00–10:25
Berthelsen, Rolf
Bertram, Albrecht S24.1 Thu 13:30–14:10
Betsch, Peter
Beyn, Wolf-Juergen S17.2 Tue 16:40–17:00
Bian, Xin Yr Me3 Tue 10:40–11:00
Bidier, Sami

390 List of Participants
Bientinesi, Paolo
Billmaier, Maximilian S4.1 Tue 14:50–15:10
Birk, Sebastian S17.5 Thu 13:30–13:50
Birken, Philipp S18.3 Wed 13:30–13:50
Bischoff, Stefan S12.2 Tue 16:00–16:20
Bloßfeld, Wolfgang Moritz S7.1 Tue 13:50–14:10
Bluhm, Joachim
Boeck, Thomas S11.6 Thu 16:00–16:20
Boettcher, Konrad S11.4 Wed 16:00–16:20
Boger, Markus S11.2 Tue 17:20–17:40
Bolea Albero, Antonio S2.6 Thu 16:40–17:00
Bolten, Matthias S17.6 Thu 16:40–17:00
Borin, Dmitry S13.3 Wed 17:20–17:40
Borsch, Sebastian S6.4 Tue 16:20–16:40
Bothe, Dieter
Boukellif, Ramdane S3.3 Wed 14:50–15:10
Boyaci, Aydin S5.2 Wed 15:10–15:30
Bozovic, Nemanja S17.5 Thu 13:50–14:10
Bröcker, Christoph S6.6 Wed 13:30–13:50
Brändli, Silvan S7.3 Tue 16:00–16:20
Brüls, Olivier Plenary Tue 08:30–09:30
Brands, Dominik
Brasche, Johannes S23.4 Wed 16:40–17:00
Braun, Julian S14.1 Tue 14:10–14:30
Braun, Stefan S9.2 Tue 17:20–17:40
Breiten, Tobias S17.4 Wed 16:00–16:20
Bremer, Hartmut
Brenner, Andreas S18.1 Tue 15:10–15:30
Brommundt, Eberhard S5.1 Tue 13:30–13:50
Bronowicki, Przemyslaw Max S11.4 Wed 17:20–17:40
Brouwer, Jens S18.1 Tue 13:30–13:50
Bruhns, Otto S24.1 Thu 14:10–14:30
Brylka, Barthel S6.8 Wed 16:40–17:00
Buchacz, Andrzej S7.8 Thu 17:20–17:40
Buerger, Johannes Yr Ma3 Tue 10:20–10:40
Bui, Tinh Quoc S3.4 Wed 16:00–16:20
Burlayenko, Vyacheslav S3.4 Wed 16:40–17:00
C
Canfield, Peter S11.4 Wed 17:40–18:00
Cantrak, Djordje S10.3 Wed 13:30–13:50
Carvalho Leite, Alexandre S20.2 Tue 17:20–17:40
Caylak, Ismail S6.2 Tue 15:10–15:30
Cekus, Dawid S20.6 Thu 17:20–17:40
Chan, Allan
Chaudhry, Aqeel Afzal

List of Participants 391
Chen, Zhaoyu S6.4 Tue 16:40–17:00
Chiroiu, Veturia S12.4 Wed 16:20–16:40
Christian, Boehm S19.2 Tue 17:40–18:00
Cibis, Thomas Martin S14.2 Tue 17:00–17:20
Cimarelli, Andrea S13.4 Thu 13:30–13:50
Clanet, Christoph Plenary Wed 08:30–09:30
Class, Andreas G. S10.3 Wed 14:50–15:10
Clever, Debora S19.5 Thu 14:10–14:30
Conti, Sergio
Cremers, Daniel S21.1 Tue 13:30–14:10
Cvetkovic, Ljiljana
Czarnecka, Sylwia
D
Döge, Torsten S24.2 Thu 17:20–17:40
Düll, Wolf-Patrick S14.4 Wed 16:40–17:00
Düster, Alexander
Dally, Tim S6.5 Wed 14:10–14:30
Dargazany, Roozbeh S6.4 Tue 17:40–18:00
Daschiel, Gerti S13.2 Wed 14:50–15:10
De Angelis, Elisabetta S10.1 Tue 13:30–13:50
de Payrebrune, Kristin S5.2 Wed 13:50–14:10
de Silva, Tina S4.4 Wed 17:20–17:40
Debeleac, Carmen S14.2 Tue 16:40–17:00
Denk, Robert
Denzer, Ralf S7.2 Tue 13:50–14:10
Dereich, Steffen S15.1 Wed 14:50–15:10
Dickopf, Thomas S22.2 Tue 16:20–16:40
Didinska, Evgenia S11.1 Tue 14:50–15:10
Diebels, Stefan
Dieringer, Rolf S4.3 Wed 14:10–14:30
Diop, El Hadji S21.2 Tue 16:20–16:40
Dirks, Hendrik S21.2 Tue 17:00–17:20
Dirksen, Frank Yr Me1 Tue 11:40–12:00
Dittmar, Ina S11.3 Wed 14:10–14:30
Dmitrieva, Irina S14.6 Thu 16:20–16:40
Dobberschütz, Sören S14.6 Thu 16:00–16:20
Dohnal, Fadi
Dolzmann, Georg Plenary Fri 12:00–13:00
Dondl, Patrick
Dostal, Leo S15.1 Wed 13:30–13:50
Dreyer, Michael
Dreyer, Wolfgang
Duchmann, Alexander S13.4 Thu 13:50–14:10
Dumitrache, Alexandru S9.1 Tue 14:50–15:10
Dumitrescu, Horia S9.3 Wed 14:30–14:50

392 List of Participants
Duong, Xuan Thang S7.3 Tue 17:20–17:40
E
Eberhard, Peter S1.4 Wed 13:30–14:10
Eberhardt, Oliver S6.11 Thu 16:00–16:20
Eckelsbach, Stefan S22.1 Tue 14:10–14:30
Eckstein, Manuel
Ehlers, Wolfgang
Ehret, Alexander S2.5 Thu 13:30–14:10
Eichfelder, Gabriele S16.3 Wed 13:30–13:50
Eidel, Bernhard S8.2 Tue 16:00–16:20
Eisenschmidt, Kathrin S11.1 Tue 13:30–13:50
El Jarbi, Mustapha S16.2 Tue 16:20–16:40
Emamy, Nehzat S11.2 Tue 16:00–16:20
Emmrich, Etienne
Engert, Sonja S13.5 Thu 16:20–16:40
Engwer, Christian Yr Me3 Tue 10:20–10:40
Erbts, Patrick S7.3 Tue 16:40–17:00
Ergenzinger, Christian S1.7 Thu 16:20–16:40
Espig, Mike S17.1 Tue 14:30–14:50
Ethiraj, Gautam S7.6 Wed 17:20–17:40
F
Faßbender, Heike
Fabregat-Traver, Diego S17.3 Wed 14:30–14:50
Fahlbusch, Nina-Carolin S4.4 Wed 17:00–17:20
Farwig, Reinhard
Faulwasser, Timm Yr Ma3 Tue 11:40–12:00
Feng, Fan S18.5 Wed 16:00–16:20
Fidlin, Alexander
Fiege, Sabrina S16.4 Wed 16:40–17:00
Fischer, Katrin S22.1 Tue 14:50–15:10
Flaßkamp, Kathrin S20.3 Wed 14:30–14:50
Fleischhauer, Robert S8.8 Thu 16:20–16:40
Flockerzi, Dietrich
Fornasier, Massimo S17.3 Wed 13:30–13:50
Forster-Heinlein, Brigitte S21.4 Wed 17:00–17:20
Fouego, Marcisse S19.5 Thu 14:50–15:10
Franke, Matthias S20.4 Wed 16:00–16:20
Franze, Andreas S5.4 Thu 14:30–14:50
Friedmann, Elfriede S13.2 Wed 14:30–14:50
Friedmann, Elfriede S14.5 Thu 15:10–15:30
Fritzen, Felix Yr Me2 Tue 11:00–11:20
Frohnapfel, Bettina S13.2 Wed 15:10–15:30
Frommer, Andreas S17.4 Wed 17:40–18:00
Frunzulica, Florin S9.3 Wed 14:10–14:30

List of Participants 393
Fuchs, Vilmar S7.7 Thu 13:30–13:50
Furer, Dmytro S15.2 Wed 16:00–16:20
G
Göllner, Thea S16.1 Tue 15:10–15:30
Götschel, Sebastian S19.1 Tue 15:10–15:30
Götz, Marco Yr Me1 Tue 10:20–10:40
Günther, Andreas S19.1 Tue 13:30–14:10
Günther, Christina S6.1 Tue 15:10–15:30
Garloff, Jürgen S17.6 Thu 16:20–16:40
Gatti, Davide S13.1 Tue 13:50–14:10
Gaul, Lothar
Gaulke, Diana S11.4 Wed 17:00–17:20
Gaus, Nicole S5.1 Tue 14:50–15:10
Gautam, Sachin Singh
Gawinecki, Jerzy S14.1 Tue 14:50–15:10
Gehring, Nicole S20.5 Thu 13:50–14:10
Geissert, Matthias S14.3 Wed 13:30–13:50
Gekle, Stephan S11.6 Thu 16:20–16:40
Gellmann, Roman S7.4 Tue 16:20–16:40
Georgiev, Ivan
Georgievskii, Dimitri S6.6 Wed 14:50–15:10
Germain, Sandrine S6.11 Thu 16:40–17:00
Gerzen, Nikolai Yr Me1 Tue 10:40–11:00
Ghareeb, Nader S20.5 Thu 15:10–15:30
Gippert, Sabrina S18.4 Wed 13:50–14:10
Gitter, Kurt S13.3 Wed 17:00–17:20
Gizewski, Carsten S9.6 Thu 17:20–17:40
Glavas, Vedran S8.1 Tue 14:50–15:10
Gligor, Anamaria S2.4 Wed 16:40–17:00
Gluege, Rainer S8.5 Wed 16:40–17:00
Gobbert, Matthias S17.3 Wed 14:50–15:10
Goldmann, Joseph S7.6 Wed 16:40–17:00
Gompper, Gerhard Me2 Mon 16:20–16:40
Gondhalekar, Ravi Yr Ma3 Tue 11:20–11:40
Goodarzi, Mehdi S6.1 Tue 13:30–13:50
Gorb, Yuliya S14.5 Thu 14:30–14:50
Gottschalk, Hanno S15.2 Wed 16:40–17:00
Gräf, Manuel S21.3 Wed 15:10–15:30
Grüne, Lars S20.3 Wed 13:30–13:50
Graf, Matthias S4.8 Thu 17:20–17:40
Graf, Wolfgang
Graichen, Knut S20.3 Wed 13:50–14:10
Granados, Albert S7.8 Thu 16:00–16:20
Grasedyck, Lars S17.2 Tue 16:00–16:20
Graupeter, Thomas S22.2 Tue 17:20–17:40

394 List of Participants
Gravenkamp, Hauke S12.2 Tue 16:20–16:40
Griesmaeir, Roland S21.3 Wed 14:10–14:30
Griewank, Andreas S16.4 Wed 16:00–16:20
Große-Wöhrmann, Andre S22.3 Thu 14:30–14:50
Groll, Rodion S10.1 Tue 15:10–15:30
Gross, Dietmar S24.1 Thu 14:50–15:10
Grußler, Christian S20.6 Thu 16:20–16:40
Grundel, Sara S22.4 Thu 16:20–16:40
Grundl, Kilian S1.5 Wed 16:00–16:20
Gruttmann, Friedrich
Guenther, Stefan S21.2 Tue 17:20–17:40
Gueven, Ibrahim S7.1 Tue 14:10–14:30
Guhlke, Clemens S6.7 Wed 16:40–17:00
Gundermann, Thomas S13.3 Wed 16:00–16:20
Guran, Ardeshir S5.4 Thu 13:30–13:50
H
Hömberg, Dietmar S19.6 Thu 16:00–16:40
Häberle, Kai S7.5 Wed 14:10–14:30
Hürkamp, André S8.8 Thu 16:40–17:00
Hütter, Geralf S3.3 Wed 14:30–14:50
Habermehl, Kai S16.3 Wed 14:10–14:30
Hackbarth, Axel S20.3 Wed 14:10–14:30
Hackl, Klaus
Haddad Khodaparast, Hamed Yr Me1 Tue 10:00–10:20
Hagedorn, Peter
Hahn, Andreas S11.5 Thu 14:10–14:30
Hahnenkamm, Anton S12.1 Tue 14:50–15:10
Hanisch, Tanja
Hanke, Hauke S8.7 Thu 13:30–13:50
Hankeln, Frederik S6.12 Thu 16:00–16:20
Hardenacke, Volker S3.5 Thu 14:10–14:30
Hardt, Steffen
Hartmaier, Alexander Me3 Mon 17:20–17:40
Hartmann, Dirk Yr Me3 Tue 10:00–10:20
Hartmann, Stefan
Hebel, Jochen S4.2 Tue 16:40–17:00
Heck, Horst S23.2 Tue 16:00–16:20
Hedrih , Katica R. (Stevanovic) S5.2 Wed 14:50–15:10
Heeren, Behrend S21.4 Wed 16:20–16:40
Heffel, Eduard S5.3 Wed 16:00–16:20
Heidlauf, Thomas S2.2 Tue 16:40–17:00
Heiland, Jan Yr Ma2 Tue 11:10–11:35
Heinemann, Christian S3.2 Tue 17:00–17:20
Heinen, Dennis S21.4 Wed 16:40–17:00
Heinz, Sebastian S6.1 Tue 14:30–14:50

List of Participants 395
Helbig, Martin S3.1 Tue 15:10–15:30
Held, Alexander S1.1 Tue 14:10–14:30
Helfen, Cecile S8.8 Thu 16:00–16:20
Heller, Dominik
Hellmich, Christian S4.7 Thu 17:20–17:40
Hempel, Nico S6.2 Tue 14:10–14:30
Hempel, Philipp S6.2 Tue 14:50–15:10
Henneberg, Dimitri S8.7 Thu 14:10–14:30
Hertel, Ida S15.2 Wed 16:20–16:40
Hertel, Kai S18.5 Wed 16:20–16:40
Herzog, Roland Ma1 Mon 16:40–17:00
Hesch, Christian S4.1 Tue 13:50–14:10
Hess, Martin S18.5 Wed 16:40–17:00
Hetzler, Hartmut
Higgins, Natalie S12.2 Tue 17:00–17:20
Hildebrand, Felix Me3 Mon 16:40–17:00
Himmel, Martin
Hinze, Michael S11.6 Thu 16:40–17:00
Hladik, Ondrej
Hochbruck, Marlis Plenary Fri 11:00–12:00
Hochlenert, Daniel S5.1 Tue 13:50–14:10
Hochrainer, Thomas S8.6 Thu 13:30–14:10
Hofacker, Martina S3.4 Wed 16:20–16:40
Hoffmann, Norbert S12.3 Wed 13:50–14:10
Hofreither, Clemens S18.1 Tue 14:50–15:10
Hohe, Jörg S8.2 Tue 17:00–17:20
Hollborn, Stefanie S14.6 Thu 16:40–17:00
Holtermann, Raphael S6.3 Tue 17:00–17:20
Homayonifar, Malek S8.6 Thu 14:30–14:50
Horcicka, Michael
Hossain, Mokarram S6.8 Wed 17:20–17:40
Hosseinzadeh, Arash S10.1 Tue 13:50–14:10
Hriberek, Matja S9.6 Thu 17:00–17:20
Hu, Han S4.1 Tue 14:10–14:30
Hu, Miao S11.1 Tue 15:10–15:30
Huckle, Thomas S17.5 Thu 15:10–15:30
Huidong, Yang S7.3 Tue 17:00–17:20
Hysing, Johan Shu-Ren
I
Ievdokymov, Mykola S6.7 Wed 17:40–18:00
Ihlemann, Jörn
Ilchmann, Achim S20.1 Tue 13:50–14:10
Iqbal, Naveed S7.7 Thu 13:50–14:10
Itskov, Mikhail S6.4 Tue 16:00–16:20
Ivanović, Dečan S9.1 Tue 14:30–14:50

396 List of Participants
J
Jöchen, Katja S8.2 Tue 16:40–17:00
Jänicke, Ralf S7.1 Tue 14:30–14:50
Jablonski, Philipp-Paul S4.1 Tue 13:30–13:50
Jacob, Birgit Plenary Thu 09:30–10:30
Jaegle, Felix S11.2 Tue 17:00–17:20
Jahn, Mischa S7.5 Wed 13:50–14:10
Jakirlic, Suad S9.5 Thu 13:30–14:10
Janda, Oliver
Janez, Lupe S10.4 Wed 17:20–17:40
Jarre, Florian
Jędrysiak, Jarosław S4.3 Wed 13:30–14:10
Jeltsch, Rolf
Jian, Dandan S13.5 Thu 16:00–16:20
John, Michael S9.2 Tue 16:40–17:00
Joná, Pavel S9.1 Tue 14:10–14:30
Joulaian, Meysam S8.5 Wed 16:00–16:20
Judt, Paul S3.3 Wed 14:10–14:30
Juhre, Daniel S8.4 Wed 14:30–14:50
Juhre, Daniel S16.2 Tue 16:00–16:20
Junker, Philipp Me3 Mon 17:00–17:20
Juraszek, Janusz
Juretzka, Carsten
Jurisits, Richard S5.2 Wed 14:30–14:50
K
Körner, Claudia S5.2 Wed 13:30–13:50
Köster, Marius
Kühn, Christian S23.2 Tue 17:00–17:20
Kürschner, Patrick S17.4 Wed 16:20–16:40
Kaźmierczak, Magda S4.6 Thu 14:30–14:50
Kalisch, Jan S8.1 Tue 14:30–14:50
Kaliske, Michael
Kallendorf, Christina S11.5 Thu 13:50–14:10
Kaltenbacher, Barbara
Kaltenbacher, Manfred S12.1 Tue 13:30–14:10
Kamlah, Marc
Kancheva, Elena Vladimirova
Kandler, Ute S17.3 Wed 13:50–14:10
Karabelas, Elias S18.2 Tue 16:20–16:40
Karcher, Christian
Kavaliou, Klim S18.8 Thu 16:00–16:20
Kawohl, Bernd
Kazeev, Vladimir S17.1 Tue 14:10–14:30
Kebriaei, Reza S6.5 Wed 14:50–15:10

List of Participants 397
Kecskemethy, Andres
Keeling, Stephen S21.3 Wed 13:30–14:10
Keip, Marc-Andre
Kelbin, Olga S14.3 Wed 13:50–14:10
Keller, Florian Me2 Mon 16:40–17:00
Kern, Dominik S4.8 Thu 16:00–16:20
Khalaquzzaman, Md S8.5 Wed 16:20–16:40
Khan , Muhammad Sabeel S6.3 Tue 16:00–16:20
Khoromskaya, Venera S17.1 Tue 14:50–15:10
Khoromskij, Boris
Khotenko, Olena
Khrabustovskyi, Andrii S8.3 Tue 17:20–17:40
Khromov, Oleg S11.5 Thu 15:10–15:30
Khruslov, Evgen S8.3 Tue 16:00–16:40
Khujadze, George S12.1 Tue 15:10–15:30
Kiefer, Björn S7.6 Wed 16:00–16:40
Kienzler, Reinhold
Kilian, F. Johannes S1.3 Tue 16:20–16:40
Kiryan, Dmitry S1.2 Tue 17:00–17:20
Kitavtsev, Georgy Ma3 Mon 16:30–17:00
Klapproth, Corinna S18.5 Wed 17:00–17:20
Klawonn, Axel S17.5 Thu 14:10–14:30
Klein, Benedikt S9.4 Wed 16:00–16:20
Klinge, Sandra S8.4 Wed 13:30–13:50
Klusemann, Benjamin Yr Me2 Tue 10:40–11:00
Kluwick, Alfred S9.2 Tue 17:00–17:20
Knüppel, Torsten S20.5 Thu 13:30–13:50
Knees, Dorothee S14.1 Tue 14:30–14:50
Knoll, Carsten S20.4 Wed 16:20–16:40
Kobert, Maria S18.1 Tue 13:50–14:10
Koch, David S7.1 Tue 14:50–15:10
Koch, Michael S1.5 Wed 16:40–17:00
Kochmann, Dennis Yr Me2 Tue 10:00–10:20
Koller, Daniela S16.1 Tue 14:30–14:50
Kolling, Stefan
Kollmann, Markus S19.1 Tue 14:50–15:10
Kolmeder, Sebastian S2.3 Wed 14:10–14:30
Kolodziej, Jan Adam S18.4 Wed 14:10–14:30
Kolpakov, Alexander G. S8.3 Tue 17:00–17:20
Koltai, Péter S20.4 Wed 17:40–18:00
Kolupaev, Vladimir A. S6.10 Thu 15:10–15:30
Komo, Christian S14.4 Wed 16:00–16:20
Konchakova, Natalia S3.4 Wed 17:00–17:20
Kondratenko, Yuriy S16.2 Tue 17:20–17:40
Konyukhov, Alexander
Kosmas, Odysseas S18.5 Wed 17:20–17:40

398 List of Participants
Kostic, Vladimir S17.3 Wed 14:10–14:30
Kotyczka, Paul S20.4 Wed 16:40–17:00
Kowalczyk, Wojciech
Krämer, Stephan S6.10 Thu 14:50–15:10
Krüger, Melanie S4.1 Tue 14:30–14:50
Krüger, Thomas
Krajsek, Kai S21.1 Tue 14:50–15:10
Kralovec, Christoph S4.3 Wed 14:30–14:50
Krasnov, Dmitry S9.6 Thu 16:00–16:40
Kratochvil, Jan S4.5 Thu 15:10–15:30
Krause, Robert S2.6 Thu 17:00–17:20
Kraynyukova, Nataliya
Kressner, Daniel S17.2 Tue 17:40–18:00
Kreuzer, Edwin
Krichler, Martin S13.3 Wed 16:20–16:40
Krumbein, Andreas S9.1 Tue 13:30–14:10
Kruse, Roland S2.2 Tue 16:00–16:20
Kruse, Sebastian S18.3 Wed 14:10–14:30
Kruzik, Martin
Krysko, Anton S5.1 Tue 14:30–14:50
Kuhl, Ellen S2.6 Thu 16:00–16:40
Kuhlmann, Hendrik Christoph S9.2 Tue 16:00–16:20
Kuhn, Charlotte S3.2 Tue 16:20–16:40
Kuijper, Arjan S21.2 Tue 16:40–17:00
Kummer, Florian S11.3 Wed 13:50–14:10
Kunik, Matthias S23.3 Wed 14:30–14:50
Kunis, Susanne Ma2 Mon 17:30–18:00
Kurz, Armin S13.4 Thu 14:50–15:10
Kurzeja, Patrick S8.4 Wed 14:50–15:10
Kutschke, Andreas S6.10 Thu 14:10–14:30
Kutyniok, Gitta S21.4 Wed 17:20–17:40
Kutyniok, Gitta S17.6 Thu 16:00–16:20
L
Lübke, Martin S11.3 Wed 15:10–15:30
Labisch, Daniel
Lahmer, Tom S7.4 Tue 16:00–16:20
Landgraf, Ralf S6.11 Thu 17:00–17:20
Lang, Holger S1.6 Thu 15:10–15:30
Langer, Ulrich S19.4 Wed 16:00–16:20
Laouar, Roudouane S9.5 Thu 14:50–15:10
Larsson, Ragnar S3.1 Tue 13:30–14:10
Lazar, Markus S6.7 Wed 16:00–16:40
Lazuka, Jaroslaw
Lazzaroni, Giuliano S8.7 Thu 13:50–14:10
Leben, Leslie S23.1 Tue 14:10–14:30

List of Participants 399
Lehmann, Eva S6.3 Tue 16:20–16:40
Leithäuser, Christian S19.1 Tue 14:30–14:50
Leitz, Thomas S7.7 Thu 14:10–14:30
Lenhof, Bernd S7.2 Tue 14:10–14:30
Lenzen, Frank S21.3 Wed 14:50–15:10
Leyendecker, Sigrid S1.1 Tue 13:30–14:10
Li, Bo Yr Me3 Tue 11:20–11:40
Li, Weiguo S6.12 Thu 17:20–17:40
Liebscher, Martin
Lincke, Anne S19.4 Wed 17:20–17:40
Linder, Christian S3.1 Tue 14:10–14:30
Linke, Julia S13.3 Wed 16:40–17:00
Lion, Alexander S6.2 Tue 13:30–14:10
Litak, Grzegorz
Litvinenko, Alexander Yr Ma1 Tue 10:20–10:40
Lohkamp, Richard S6.3 Tue 17:40–18:00
Lohse, Christian S1.7 Thu 17:20–17:40
Lorenz, Maike S14.4 Wed 17:20–17:40
Lorenz, Michael S5.4 Thu 15:10–15:30
Lotfi, Marjan
Lotoreichik, Vladimir S23.2 Tue 16:20–16:40
Lu, Daixing S7.7 Thu 15:10–15:30
Lu, Shuai S19.6 Thu 16:40–17:00
Lubkoll, Lars S19.6 Thu 17:00–17:20
Luchscheider, Vera S4.6 Thu 13:30–13:50
Ludwig, Hanna
Ludwig, Lars S18.3 Wed 13:50–14:10
Luginsland, Tobias S10.4 Wed 17:00–17:20
Lumei, Calin S12.3 Wed 15:10–15:30
Luttmann, Andreas
Lvov, Ivan S4.7 Thu 17:00–17:20
M
Ma, Chen S11.4 Wed 16:20–16:40
Möws, Roland S23.1 Tue 14:30–14:50
Müller, Björn S11.2 Tue 16:20–16:40
Müller, Matthias
Müller, Ralf S7.2 Tue 13:30–13:50
Müller, Sebastian S3.2 Tue 17:20–17:40
Müller, Viktor S8.2 Tue 17:20–17:40
Müller, Wolfgang S4.4 Wed 16:00–16:40
Müller-Hoeppe, Dana S8.7 Thu 14:30–14:50
Müllner, Markus S9.1 Tue 15:10–15:30
Müllner, Thomas S12.3 Wed 14:10–14:30
Münker, Tobias S17.4 Wed 17:20–17:40
Maas, Ramona S2.2 Tue 17:00–17:20

400 List of Participants
Mabuma, Joffrey S2.1 Tue 14:50–15:10
Mach, Thomas S17.4 Wed 16:40–17:00
Mack, Werner
Mahmood, Saqib S13.4 Thu 13:30–13:50
Mahnken, Rolf S24.2 Thu 16:40–17:00
Maier, Christian S1.5 Wed 16:20–16:40
Majcher, Krzysztof S4.6 Thu 13:50–14:10
Majzner, Michał S6.9 Thu 14:50–15:10
Malessa, Christian S1.5 Wed 17:00–17:20
Maringer, Johannes S15.1 Wed 14:10–14:30
Markert, Bernd
Markert, Richard
Markzac, Rogerio
Marschall, Holger S11.5 Thu 14:50–15:10
Martens, Wolfram S5.1 Tue 15:10–15:30
Marti, Kurt
Materna, Daniel S16.3 Wed 14:30–14:50
Mattern, Steffen S4.2 Tue 16:00–16:20
Matthes, Michael Yr Ma2 Tue 10:45–11:10
Matvienko, Oleg S10.4 Wed 16:40–17:00
Matz, Daniel S9.3 Wed 15:10–15:30
Mauthe, Steffen S6.1 Tue 13:50–14:10
McBride, Andrew Me1 Mon 16:25–16:50
Mehmood, Ahmer
Mehrmann, Volker S20.1 Tue 14:10–14:30
Melcher, Andreas S7.8 Thu 16:20–16:40
Menshikov, Yuri S22.4 Thu 17:20–17:40
Menshykov, Oleksandr S3.4 Wed 17:20–17:40
Menzel, Andreas
Mester, Rudolf
Meysonnat, Pascal S13.1 Tue 13:30–13:50
Michael, Christian S20.2 Tue 16:40–17:00
Micheler, Till S23.2 Tue 17:20–17:40
Miedlar, Agnieszka S17.2 Tue 17:00–17:20
Miehe, Christian Me1 Mon 16:00–16:25
Mielke, Alexander S14.1 Tue 13:30–14:10
Mierzwiczak, Magdalena S18.3 Wed 14:30–14:50
Miller, Urs S5.3 Wed 16:40–17:00
Min, Chen S6.10 Thu 13:50–14:10
Ming, Pingbing Ma3 Mon 17:00–17:30
Mirwaldt, Thomas S1.7 Thu 16:40–17:00
Mladenova, Clementina S1.2 Tue 16:00–16:20
Modersitzki, Jan S21.2 Tue 17:40–18:00
Mohr, Dirk S3.5 Thu 15:10–15:30
Montalvo-Urquizo, Jonathan S4.4 Wed 17:40–18:00
Moran, Sean S8.6 Thu 14:10–14:30

List of Participants 401
Morciano, Alessandra
Mosler, Jörn
Mousavi, Roozbeh S11.2 Tue 16:40–17:00
Muhirwa, Luc N. S20.4 Wed 17:00–17:20
Munteanu, Ligia S6.12 Thu 16:20–16:40
Munz, Claus-Dieter
Muravey, Lionid
N
Němec, Tomá S11.1 Tue 13:50–14:10
Nörenberg, Nicole S6.11 Thu 17:20–17:40
Naß, Martin S19.3 Wed 15:10–15:30
Naetar, Wolf S19.5 Thu 15:10–15:30
Nagórko, Wiesław
Nastac, Silviu S14.2 Tue 16:20–16:40
Nastase, Adriana S16.1 Tue 14:10–14:30
Naumann, Andreas S22.2 Tue 17:00–17:20
Naumov, Maxim Ma2 Mon 16:30–17:00
Necasova, Sarka S13.1 Tue 14:10–14:30
Nedelkovski, Igor
Neff, Patrizio
Neitzel, Ira S19.3 Wed 13:30–14:10
Nesenenko, Sergiy
Neumüller, Martin S18.8 Thu 16:40–17:00
Neumann, Rudolf
Nguyen, An Danh S3.5 Thu 13:50–14:10
Niederhöfer, Florian S1.6 Thu 14:10–14:30
Niessner, Herbert S10.3 Wed 14:30–14:50
Nold, Andreas S9.2 Tue 16:20–16:40
Nopparat, Pochai S18.2 Tue 16:40–17:00
Nowak, Michał A. S23.3 Wed 14:50–15:10
O
Ober-Blöbaum, Sina S22.1 Tue 13:30–14:10
Oberhuber, Bernhard S1.3 Tue 16:40–17:00
Odenbach, Stefan
Of, Günther S18.4 Wed 14:30–14:50
Orlik, Julia S8.7 Thu 14:50–15:10
Osman, Muhammad S4.7 Thu 16:40–17:00
Osorio Nesme, Anuhar S9.6 Thu 17:40–18:00
Ostrowski, Piotr S6.9 Thu 15:10–15:30
Ostwald, Richard S6.5 Wed 15:10–15:30
Otten, Denny S18.8 Thu 17:00–17:20
Ozhoga-Maslovskaja, Oksana S3.2 Tue 17:40–18:00
P

402 List of Participants
Płaczek, Marek S7.3 Tue 17:40–18:00
Pach, Martin Yr Ma1 Tue 11:20–11:40
Pandey, Anamika S15.1 Wed 14:30–14:50
Pannek, Jürgen Yr Ma3 Tue 10:40–11:00
Pantangi, Pradeep S10.1 Tue 14:10–14:30
Pearson, John Ma1 Mon 16:20–16:40
Pertschik, Konstantin
Peschka, Dirk Me2 Mon 17:40–18:00
Peter, Thomas S21.3 Wed 14:30–14:50
Peters, Ivo Me2 Mon 17:00–17:20
Petrisor , Silviu Mihai S1.7 Thu 17:40–18:00
Pfaff, Sebastian
Pfeiffer, Friedrich
Pham, Thanh Chung S4.6 Thu 14:50–15:10
Philipp, Anne
Philipp, Friedrich S23.1 Tue 13:50–14:10
Picard, Rainer S23.3 Wed 13:30–13:50
Pieper, Konstantin S19.1 Tue 14:10–14:30
Pinnau, Rene S19.2 Tue 17:20–17:40
Pippig, Michael S17.3 Wed 15:10–15:30
Pitsch, Heinz Plenary Thu 08:30–09:30
Plate, Carolin S3.1 Tue 14:50–15:10
Pollak, Thilo S9.4 Wed 17:40–18:00
Poloni, Federico S20.1 Tue 14:50–15:10
Ponsiglione, Marcello Ma3 Mon 16:00–16:30
Popov, Valentin L. S24.1 Thu 14:30–14:50
Potapov, Vadim S4.8 Thu 16:20–16:40
Prange, Corinna S3.3 Wed 13:30–13:50
Prechtl, Gerhard S4.8 Thu 16:40–17:00
Preusser, Tobias
Prieling, Doris S11.4 Wed 16:40–17:00
Prignitz, Rodolphe S18.1 Tue 14:10–14:30
Prill, Dennis S5.3 Wed 17:00–17:20
Probst, Axel S9.3 Wed 13:30–14:10
Procházka, Pavel S13.4 Thu 14:10–14:30
Prohl, Andreas
Prygorniev, Oleksandr S8.5 Wed 17:40–18:00
Prytula, Mykola S12.4 Wed 16:40–17:00
Q
Quarti, Michael S13.2 Wed 14:10–14:30
Quintana-Orti, Enrique S.
R
Röbenack, Klaus S20.3 Wed 15:10–15:30
Röhrle, Oliver S2.3 Wed 15:10–15:30

List of Participants 403
Röhrnbauer, Barbara S2.5 Thu 14:30–14:50
Rösch, Arnd
Rösner, Malte S20.6 Thu 16:40–17:00
Rückert, Jens S18.2 Tue 17:00–17:20
Rüffer, Björn S20.4 Wed 17:20–17:40
Rütten, Markus S13.5 Thu 17:40–18:00
Raabe, Dierk S24.2 Thu 16:00–16:40
Rademacher, Andreas S22.3 Thu 14:10–14:30
Rafa, Józef
Raghunath, Rathan
Raguz, Andrija S14.5 Thu 14:50–15:10
Raina, Arun S3.3 Wed 13:50–14:10
Raisch, Jörg Plenary Fri 09:30–10:30
Rammerstorfer, Franz
Ranjbar, Maedeh
Rasool, Raheel S9.4 Wed 17:20–17:40
Rasuo, Bosko S9.3 Wed 14:50–15:10
Rauschenberger, Philipp S11.1 Tue 14:10–14:30
Rautenberg, Carlos S23.4 Wed 17:20–17:40
Ravnik, Jure
Reble, Marcus Yr Ma3 Tue 11:00–11:20
Reese, Stefanie S2.3 Wed 13:30–14:10
Regener, Benjamin S8.5 Wed 17:20–17:40
Reips, Louise S19.6 Thu 17:40–18:00
Reisner, Timo S11.3 Wed 14:30–14:50
Reiss, Julius S9.4 Wed 16:20–16:40
Reiter, Thomas 1 Tue 18:30–18:50
Reiterer, Stefan S19.4 Wed 17:40–18:00
Reshniak, Viktor S18.4 Wed 14:50–15:10
Reuter, Uwe Yr Me1 Tue 11:00–11:20
Rheinbach, Oliver S22.2 Tue 16:00–16:20
Richter, Thomas Yr Me3 Tue 11:40–12:00
Ricken, Tim
Ricoeur, Andreas
Riedeberger, Donald S13.1 Tue 15:10–15:30
Riedlbauer, Daniel S7.5 Wed 14:50–15:10
Rieger, Florian
Rinne, Klaus Friedrich Me2 Mon 16:00–16:20
Rist, Ulrich S13.4 Thu 14:30–14:50
Rohleder, Jonathan S23.2 Tue 16:40–17:00
Rosenbaum, Benjamin Yr Ma1 Tue 10:40–11:00
Rosenthal, Dietmar S2.3 Wed 14:30–14:50
Rosic, Bojana Yr Ma1 Tue 11:00–11:20
Rosteck, Andreas S10.2 Tue 16:00–16:20
Rothe, Steffen S6.8 Wed 17:40–18:00
Rottmann, Matthias S17.6 Thu 17:00–17:20

404 List of Participants
Roy, Shyamal S6.12 Thu 17:40–18:00
Rozgic, Marco S16.1 Tue 14:50–15:10
Rozloznik, Miroslav
Rushchitsky, Jeremiah S12.4 Wed 16:00–16:20
Rutzmoser, Johannes S1.1 Tue 15:10–15:30
Ryzhkov, Oleksandr S12.3 Wed 14:50–15:10
S
Sänger, Nicolas S1.3 Tue 17:00–17:20
Sülü, İsmail Yasin S4.5 Thu 14:30–14:50
Saak, Jens S20.1 Tue 15:10–15:30
Saal, Jürgen S14.4 Wed 16:20–16:40
Sachs, Ekkehard Ma1 Mon 17:40–18:00
Sack, Uli S6.7 Wed 17:00–17:20
Sadigh Behzadi, Armin S18.1 Tue 14:30–14:50
Sadigh Behzadi, Shadan S18.3 Wed 14:50–15:10
Sadiki, Amsini S10.1 Tue 14:30–14:50
Salcher, Patrick S4.6 Thu 15:10–15:30
Sander, Manuela
Santarelli, Claudio S10.4 Wed 16:00–16:20
Sauerland, Kim-Henning S8.4 Wed 15:10–15:30
Sawyer, William S17.5 Thu 14:50–15:10
Sbeiti, Mohamad S7.8 Thu 16:40–17:00
Schäfer, Carsten
Schänzel, Lisa S6.8 Wed 16:00–16:20
Schüler, Thorsten S6.6 Wed 14:30–14:50
Schürg, Marco S4.2 Tue 17:00–17:20
Schaal, Christoph S12.2 Tue 17:20–17:40
Schagerl, Martin
Schauer, Marco S12.2 Tue 17:40–18:00
Schauer, Volker S7.8 Thu 17:00–17:20
Schaufler, Alexander S7.1 Tue 15:10–15:30
Scheider, Ingo S3.1 Tue 14:30–14:50
Schenke, Maik S22.3 Thu 14:50–15:10
Scheunemann, Lisa S8.1 Tue 15:10–15:30
Schidlowski, Sergej
Schieche, Bettina S18.8 Thu 17:20–17:40
Schieck, Berthold
Schiehlen, Werner S1.3 Tue 16:00–16:20
Schiela, Anton S19.5 Thu 14:30–14:50
Schillings, Claudia Yr Ma1 Tue 10:00–10:20
Schlömerkemper, Anja S8.1 Tue 13:30–14:10
Schmidt, Bastian S19.4 Wed 16:40–17:00
Schmidt, Bernd
Schmidt, Ingo S7.7 Thu 14:50–15:10
Schmidt, Marcus

List of Participants 405
Schmidt, Thomas S2.1 Tue 14:30–14:50
Schmitt, Joachim S6.10 Thu 14:30–14:50
Schmitt, Regina S6.7 Wed 17:20–17:40
Schmitzer, Bernhard S21.1 Tue 14:10–14:30
Schmoll, Robert S1.6 Thu 14:30–14:50
Schneider , Reinhold S17.1 Tue 15:10–15:30
Schneider, Rene S18.6 Wed 16:00–16:20
Schneidt, Andreas S6.5 Wed 14:30–14:50
Schnepp, Johannes S6.12 Thu 17:00–17:20
Scholle, Markus S6.12 Thu 16:40–17:00
Scholz, Andreas S1.1 Tue 14:30–14:50
Scholz, Lena S20.1 Tue 14:30–14:50
Schröder, Dirk
Schröder, Jörg Me1 Mon 16:50–17:15
Schröder, Wolfgang
Schröppel, Christian S18.6 Wed 16:20–16:40
Schulz, Volker Ma1 Mon 16:00–16:20
Schumacher, Katrin
Schuricht, Friedemann
Schwartpaul, Kai S4.5 Thu 14:10–14:30
Schwarz, Alexander S9.4 Wed 16:40–17:00
Schweitzer, Marcel S17.6 Thu 17:40–18:00
Sedlacek, Matous S17.5 Thu 14:30–14:50
Seemann, Wolfgang
Seifried, Robert S20.2 Tue 17:00–17:20
Selig, Tilman
Selvadurai, Patrick S24.1 Thu 15:10–15:30
Sergey, Lurie S6.9 Thu 14:30–14:50
Setzer, Simon S21.1 Tue 15:10–15:30
Shahid, Mubeen S6.3 Tue 17:20–17:40
Shakhno, Stepan S16.4 Wed 16:20–16:40
Shamolin, Maxim V. S1.2 Tue 16:20–16:40
Shan, Wenzhe S8.2 Tue 16:20–16:40
Shevchuk, Illya S11.3 Wed 13:30–13:50
Shneider, Vladimir S3.5 Thu 14:30–14:50
Shuai, Yan S18.2 Tue 17:20–17:40
Shunqi, Zhang S20.2 Tue 16:20–16:40
Shutov, Alexey S6.3 Tue 16:40–17:00
Sichau, Adrian S16.1 Tue 13:30–13:50
Siebert, Ralf S1.1 Tue 14:50–15:10
Siegl, Benjamin
Simeon, Bernd
Simon, Jaan-Willem S6.8 Wed 17:00–17:20
Simon, Moritz S19.4 Wed 17:00–17:20
simoncini, Valeria Ma1 Mon 17:20–17:40
Sinclair, Andrew

406 List of Participants
Sindern, Andrea S7.5 Wed 14:30–14:50
Siska, David S18.7 Thu 13:30–13:50
Sittner, Petr Me3 Mon 16:00–16:40
Skopin, Emma S14.3 Wed 14:30–14:50
Sodhani, Deepanshu S8.4 Wed 14:10–14:30
Sokolov, Andriy Yr Me3 Tue 11:00–11:20
Sokolovic, Sonja S17.6 Thu 17:20–17:40
Sommer, Oliver S9.5 Thu 14:10–14:30
Soos, Anna
Souckova, Natalie S13.2 Wed 13:30–13:50
Specht, Steffen S7.2 Tue 15:10–15:30
Spelsberg-Korspeter, Gottfried S5.3 Wed 17:20–17:40
Sprenger, Lisa S13.5 Thu 17:00–17:20
Sprenger, Michael S2.2 Tue 17:20–17:40
Springer, Andreas S19.3 Wed 14:30–14:50
Srisupattarawanit, Tarin S22.4 Thu 16:40–17:00
Stahl, Dominik S21.4 Wed 16:00–16:20
Stark, Sebastian S7.4 Tue 16:40–17:00
Starkov, Konstantin S2.6 Thu 17:20–17:40
Stauch, Christian S20.5 Thu 14:10–14:30
Staufer, Peter S1.3 Tue 17:20–17:40
Stavropoulou, Electra S16.1 Tue 13:50–14:10
Steeger, Karl S4.2 Tue 17:20–17:40
Steidl, Gabriele
Stein, Anika S9.4 Wed 17:00–17:20
Stein, Erwin
Stein, Lukas
Stein, Peter
Steinbach, Olaf S18.7 Thu 14:10–14:30
Steinbrecher, Andreas S18.6 Wed 16:40–17:00
Steindl, Alois S5.2 Wed 14:10–14:30
Steiner, Helfried
Steinrück, Herbert S9.5 Thu 14:30–14:50
Stieler, Marleen
Stilgenbauer, Patrik S15.1 Wed 13:50–14:10
Stingl, Michael S16.3 Wed 13:50–14:10
Stoffel, Marcus S4.3 Wed 14:50–15:10
Stojanovic, Mirjana
Stokmaier, Markus S16.2 Tue 17:00–17:20
Stoll, Martin S17.2 Tue 17:20–17:40
Strampe, Malte S2.3 Wed 14:50–15:10
Strein, Sabine S10.1 Tue 14:50–15:10
Stroh, Alexander S13.2 Wed 13:50–14:10
Strubel, Jan
Strzodka, Robert Ma2 Mon 17:00–17:30
Sturm, Kevin S19.6 Thu 17:20–17:40

List of Participants 407
Sturmat, Maike S2.2 Tue 16:20–16:40
Stykel, Tatjana
Suresh Kumar , Kannan S11.3 Wed 14:50–15:10
Svanadze, Maia M. S6.6 Wed 13:50–14:10
Svanadze, Merab S6.9 Thu 13:30–14:10
Svendsen, Bob Me1 Mon 17:40–18:00
T
Törnig, Willi
Türk, Sebastian S13.1 Tue 14:50–15:10
Takači, Ðurđica S18.7 Thu 14:30–14:50
Takacs, Stefan Ma1 Mon 17:00–17:20
Tao, Wu
Tepes-Bobescu, Alina-Sabina S2.4 Wed 17:00–17:20
Thalhammer, Mechthild S18.8 Thu 16:20–16:40
Thess, Andre S9.6 Thu 16:40–17:00
Thien-Nga, LE
Thomas, Marita S14.1 Tue 15:10–15:30
Thongmoon, Montri
Thongtha, Kaboon S16.2 Tue 16:40–17:00
Timmermann, Julia
Tkachuk, Mykola S8.4 Wed 13:50–14:10
Tobias, Steinle S22.1 Tue 14:30–14:50
Tobiska, Lutz
Todres, Russell S4.8 Thu 17:00–17:20
Travnikov, Vadim S13.5 Thu 16:40–17:00
Trenn, Stephan Yr Ma2 Tue 10:25–10:45
Trenn, Stephan S20.3 Wed 14:50–15:10
Tropea, Cameron
Trostorff, Sascha S23.3 Wed 14:10–14:30
Trunk, Carsten S23.4 Wed 17:40–18:00
Truskinovsky, Lev Plenary Thu 11:00–12:00
Tsedendamba, Sarantuya
Tuchkova, Natalia
Tympel, Saskia S13.5 Thu 17:20–17:40
U
Ulbrich, Heinz
Ulbricht, Volker
Ullmann, Sebastian S20.5 Thu 14:30–14:50
Ulmer, Heike S3.2 Tue 16:40–17:00
Ulz, Manfred S8.6 Thu 14:50–15:10
Unger, Gerhard S18.6 Wed 17:00–17:20
Uribe, David S12.3 Wed 13:30–13:50
Uruba, Vaclav S10.3 Wed 13:50–14:10
Uschmajew, André

408 List of Participants
Utz, Tilman S20.5 Thu 14:50–15:10
V
Varnhorn, Werner S14.5 Thu 14:10–14:30
Vasilyev, Vladimir S18.7 Thu 14:50–15:10
Vendl, Alexander S20.6 Thu 17:00–17:20
Vexler, Boris
Villamil, Pedro Daniel S4.5 Thu 14:50–15:10
Vinci, Carlo S7.7 Thu 14:30–14:50
Vladimirov, Ivaylo Yr Me2 Tue 11:40–12:00
Voigt, Axel S11.5 Thu 13:30–13:50
Voigt, Matthias Yr Ma2 Tue 11:35–12:00
von Wagner, Utz S5.4 Thu 14:10–14:30
Vondřejc, Jaroslav S17.4 Wed 17:00–17:20
Vowinckel, Bernhard S10.4 Wed 16:20–16:40
Vu, Duc Khoi S7.4 Tue 17:00–17:20
Vu, Khiêm S6.10 Thu 13:30–13:50
W
Wächtler, Timo S22.1 Tue 15:10–15:30
Wähnert, Philipp Yr Ma1 Tue 11:40–12:00
Wünsche, Michael S7.6 Wed 17:00–17:20
Wackerfuß, Jens
Waclawczyk, Marta S10.2 Tue 16:40–17:00
Waffenschmidt, Tobias S6.9 Thu 14:10–14:30
Wagner, Andreas S4.2 Tue 17:40–18:00
Wagner, Arndt S2.1 Tue 13:30–14:10
Wagner, Nils S4.8 Thu 17:40–18:00
Wagrowska, Monika
Waldherr, Konrad S17.2 Tue 16:20–16:40
Wallaschek, Joerg S5.1 Tue 14:10–14:30
Walther, Andrea S22.4 Thu 16:00–16:20
Walz, Nico-Philipp S1.4 Wed 14:30–14:50
Warys, Pawel S20.6 Thu 17:40–18:00
Wathen, Andy Plenary Mon 14:30–15:30
Waurick, Marcus S23.3 Wed 13:50–14:10
Weber, Martin
Weigand, Bernhard
Weinberg, Kerstin S7.5 Wed 13:30–13:50
Weiss, Jan-Philipp Ma2 Mon 16:00–16:30
Welk, Martin S21.2 Tue 16:00–16:20
Weller, Stephan S11.2 Tue 17:40–18:00
Wendland, Wolfgang S14.5 Thu 13:30–14:10
Wensch, Jörg
Werner, Daniel S2.1 Tue 14:10–14:30
Wessels, Nicola S8.3 Tue 16:40–17:00

List of Participants 409
Widany, Kai-Uwe S4.1 Tue 15:10–15:30
Wiendl, Steffen S5.4 Thu 14:50–15:10
Wieners, Christian S22.3 Thu 13:30–14:10
Wiercigroch, Marian S5.3 Wed 16:20–16:40
Willbold, Carina S20.6 Thu 16:00–16:20
Willenberg, Wolfgang S2.5 Thu 15:10–15:30
Willinger, Bettina S14.2 Tue 16:00–16:20
Willner, Kai S4.5 Thu 13:30–14:10
Wimmer, Johannes S4.2 Tue 16:20–16:40
Winkler, Henrik S23.1 Tue 14:50–15:10
Winkler, Max S19.2 Tue 16:40–17:00
Wirowski, Artur S1.2 Tue 16:40–17:00
Woźniak, Czesław S8.8 Thu 17:20–17:40
Wojnarowski, Józef S20.2 Tue 16:00–16:20
Wojtusch, Janis S1.4 Wed 14:10–14:30
Wojtylak, Michal S23.4 Wed 17:00–17:20
Wolf, Stefan S2.5 Thu 14:50–15:10
Wollscheid, Daniel S6.6 Wed 14:10–14:30
Worrack, Holger S6.11 Thu 17:40–18:00
Worthmann, Karl Yr Ma3 Tue 10:00–10:20
Wozniak, Günter
Wu, Tao S8.5 Wed 17:00–17:20
Wu, Tao S21.1 Tue 14:30–14:50
Wulf, Hans S22.4 Thu 17:00–17:20
Wulfinghoff, Stephan S6.1 Tue 14:10–14:30
Wyss, Christian S23.3 Wed 15:10–15:30
X
Xu, Baixiang S7.4 Tue 17:20–17:40
Y
Y, L
Yalcinkaya, Tuncay Yr Me2 Tue 10:20–10:40
Yang, Yinping S1.6 Thu 14:50–15:10
Yevdokymov, Dmytro S18.6 Wed 17:20–17:40
Yi, Jeong-Hun S2.6 Thu 17:40–18:00
Yousept, Irwin S19.5 Thu 13:30–14:10
Z
Zäh, Dominic
Zalachas, Nicolas S7.2 Tue 14:30–14:50
Zanger, Florian S14.3 Wed 14:50–15:10
Zapara, Maksim S3.5 Thu 13:30–13:50
Zastrau, Bernd
Zehn, Manfred
Zeiler, Christoph S11.1 Tue 14:30–14:50

410 List of Participants
Zeppieri, Caterina Ida Ma3 Mon 17:30–18:00
Zhang, Chuanzeng S3.4 Wed 17:40–18:00
Zhang, Chunli S4.3 Wed 15:10–15:30
Zhang, Xiaoyu S1.7 Thu 17:00–17:20
Zhou, Bei S2.5 Thu 14:10–14:30
Zhu, Peicheng
Ziems, J. Carsten S19.2 Tue 16:00–16:40
Zimmermann, Markus Yr Me1 Tue 11:20–11:40
Zinatbakhsh, Seyedmohammad S7.3 Tue 16:20–16:40
Zinchenko, Andrii S22.4 Thu 17:40–18:00
Zingler, Paul
Zolkiewski, Slawomir S3.5 Thu 14:50–15:10
Zulehner, Walter
Zwecker, Sandro S7.2 Tue 14:50–15:10
Zwiers, Ulrike S24.2 Thu 17:00–17:20