Section 6: Material modelling in solid mechanics - GAMM 2012

Section 6: Material modelling in solid mechanics 11
ver, 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)
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,
numerical analysis and implementation, Comp. Meth. Appl. Mech. Engrg. Vol. 98, 41-104,