III. Numeric Modelling and Simulation - CRP Henri Tudor

Catalogue of services « Advanced Materials & Structures » 

III. 

Numeric Modelling and Simulation 

The use of mathematical and numerical modelling to assist with design, to research new functionalities 

and to optimise materials, processes and structures (industrialists, health and environment) has become a 

principal component of RDI, both academically and industrially. The AMS department, through its modelling 

and numerical simulation Unit, covers the following topics: 

• inverse modelling: coupling experiment-modelling, identification of behavioural laws by inverse methods, 

integration of proposed approaches in computer code of finite elements; 

• structural vibration and structural integrity (structural health monitoring): active and passive damping of 

vibrations in the structures; 

• modelling and simulation of manufacturing processes (forming, lamination); 

• homogenisation methods of heterogeneous materials: the micromechanical models (Mori Tanaka, selfconsistent) 

are available within the unit to outline the electro-thermo-mechanical behaviour of materials; 

• multiscale modelling: developing coupling methods from the molecular to the macro level; 

• modelling the behaviour composite materials in fatigue; 

• phenomenological modelling of shape memory alloys: phase transformation, multiphysics coupling, 

microstructure characterisation, micromechanical modelling; 

• data reduction models for detecting damage using the stochastic subspace method. 

The main investigative methods are the numerical simulations using industry codes (Ansys, Abaqus, CASTEM) 

and specific numerical codes (C++, Matlab, Fortran, etc). 

In the field of materials, more specifically, these activities are an approach which is complementary to a 

continuity of services offered by the department through its materials unit; namely, the development of 

micromechanical constitutive laws for materials (polymers, nanocomposites, ceramics) according to their 

microstructures and loading conditions. 

Some of the projects undertaken by the modelling and simulation unit are presented in this section. 

Numeric Modelling and Simulation

III.1. 

Improve material performances and engineering 

design cycle using simulations and computational 

tools 

Modelling and Simulation Services at the Centre de Recherche Public Henri Tudor are devoted to the development 

of new methodologies and simulation tools for supporting a broader interpretation of materials, structures and 

engineering processes. We offer to our customers a fast bring to market innovative products through: 

1. Advanced Numerical Methods: FEM, X-FEM (eXtended Finite Element Method) and EMFG (Element Mesh Free Galerkin) 

Method and BEM (Boundary Element Method) 

2. Nonlinear multi-scale modeling and simulation of material and structure to design innovative, multifunctional and 

optimal materials and structures 

3. Homogenisation: Estimation of Material Effective Properties: Conventional Micro-Mechanics Methods (Eshelby Based 

Methods) 

4. Phenomenological Modelling and Material Constitutive Modelling and FEM Implementation 

5. Ab. initio and Molecular Dynamics simulations 

6. Statistical Modelling of Heterogeneous Materials: Statistical Micro-Mechanical Method and Statistical Macro- 

Mechanical (Monte Carlo) Method 

7. Material by Design Strategies (Optimisation) 

8. Adaptive (Smart) Structures for Vibration and Noise Control: Innovative solutions for analysis and control, including 

passive-active vibration damping 

9. Advanced techniques for the material parameter identification by inverse methods: Experiment-Modelling Coupling 

10. Advanced numerical techniques for damage and health monitoring of material and structures 

11. Advanced numerical techniques to model composite structures behaviour of statics and dynamics in linear and nonlinear 

domains (damage), in time and frequency domains 

12. Structural Dynamics (vibration) and Instabilities (Buckling) 

13. Crack Propagation and Delamination in Composite Materials 

14. Advanced techniques for data acquisition, management, treatment and analysis 

15. Advanced methods to model dynamical systems and control systems 

16. Advanced techniques for data filtering, information retrieval, statistical data mining, and data compression and 

representation 


III.1.1. 

Tools 

• In-house Finite Element code (F90): Hipperdang 

• In-house Finite Element code for Composite Structures (F90): MUL2 

• In-house Composite material Laboratory Python Code 

• In-house X-FEM code (C++) 

• In-house Statistical Homogenisation Code 

• In-house periodic Homogenisation Code 

• In-house XEFG Meshless code (Fortran 90) 

• Molecular Dynamics code (Fortran and C++) (Sandia Labs) 

• Cristal Plasticity code (Fortran 77) (Los Alamos Nat. lab) 

• In-house Boundary Element Code (Fortran 90) 

• In-house Monte Carlo Simulation Code (Fortran 90) 

• In-house codes (Finite element, Multiscale, Homogenization, Multifield Modelling of Multilayered structures ) 

• High expertise on Commercial Finite Element codes like Abaqus, Ansys, CASTEM and NASTRAN 

• Proficient use of scientific software like Matlab, Simulink, Scilab and of programming languages like, Fortran, C, C++ 

and Python 

• Knowledge and experience in free open source software 

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Service Sectors 

• Material Suppliers: Increasing demands in theoretical understanding of more and more realistic materials (nanoclusters, 

amorphous phases, …) and materials phenomena (radiation damage, hydrogen storage, ion conductivity, 

brittleness, hardness) require efficient numerical techniques as well as multi-scale modeling that connect micro 

calculations with meso- and macroscopic concepts. 

• Health and biomaterials: Across the scales, from nano to macro, computational methods have been applied that link 

atomistic to mesoscopic to continuum length-scles and hereby provide insight into the material properties of key 

components of living systems. 

• Medical Industry: computational geometry, combinatorial optimization methods, and multi-scale approaches) has led 

to more efficient and more stable algorithms for image analysis and image processing for such tasks as segmentation, 

classification, restoration, registration, tracking or reconstruction. 

• Aerospace Industry: Numerical analyses of composite space structures are becoming absolutely necessary. We offer 

advanced capabilities mechanical solvers to model space composite structures behaviour in statics and structural 

dynamics in linear and non-linear domains (damage), in time and frequency domains, also with large models and large 

amount of data management. 

• Process Industry: We offer industrials assistance to better understand, control, optimize their process through 

techniques from data mining and automatic control engineering and the use of classical statistic tools or others tools 

called intelligent such as neural networks, fuzzy logic, genetic algorithms. 

• Public sector: we offer assistance to acquire, manage and analyse data and can propose some trainings in scientific 

programming. 


Our project highlights 

Composites and Adaptive Structures: Simulation, 

Experimentation and Modelling 

FP6 Project Coordinated under the NMP Priority (FP6-2003-NMP-TI3/G3) 

The principal aim of this FP6 STREP project is developing a vibration control technology to enable higher performance, 

less energy consuming and lighter weight structural systems. Vibration control technology involves reducing 

detrimental vibration in flexible structures by active and passive procedures. The project goal is to define the «best» 

models and techniques permitting to model, simulate, and validate the new development for a more efficient vibration 

control. The final research action will be devoted to a full scale testing of the obtained numerical and laboratory 

results. The development of vibration control systems will allow to extend the areas of application of multi-functional 

composite materials based on the advanced knowledge of vibration response. 


Figure 1: Active vibration control using experimentation and modelling 

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Multiscale Modelling of Nano-Reinforced 

The research activity concerns modeling of polymer clay nanocomposites for a Multiscale approach. Nanocomposites 

designed by incorporating nano-sized second phase into polymers have attached a lot of attention due to the new 

extraordinary opportunities that such materials offer. The multiscale modeling strategy is employed to account for 

the hierarchical morphology of the nanocomposites: at a lengthscale of thousands of microns, the structure is one of 

high aspect ratio inclusions within a matrix; at the lengthscale of microns, the clay inclusion is either; exfoliated clay 

sheets of nanometer level thickness or stacks of parallel clay sheets separated from one another by interlayer galleries 

of nanometer level height, and the matrix, if semi-crystalline, consists of fine lamella, oriented with respect to the 

polymer/nanoclay interfaces. 

Figure 2: Automatic microstructure generation 


Figure 3: FEM modelling of nanoclay reinforeced composites 

Design of composite materials 

The objective of this research activity is the design of heterogeneous composite materials with an optimal given 

physical properties.The physical properties of basic materials (metals, polymers, etc.) can be improved in specific 

or all directions by simply introducing heterogeneities with specific physical properties, shape and orientation. The 

properties of the resultant heterogeneous composite materials depend also on the distribution of the heterogeneities. 

The evaluation of the macroscopic effective properties of these heterogeneous materials is of prime importance due 

to their considerable technological importance. Due to the complex morphological characteristics as well as structural 

distributions of both the matrix and the fillers, many micromechanics models have been proposed to evaluate the 

effective properties of composite heterogeneous materials. For instance, statistical continuum approaches take 

into account the distribution, shape and orientation of the composite constituents through correlation functions. 

Inversely, this methodology can also be used to compute the optimal microstructure leading to the best effective 

properties. Further the optimization algorithm can be chosen depending on the studied microstructure. In case of 

composite with a known heterogeneity shape (fibers, spheres, ..), genetic algorithms are the most used. However, 

Reverse Monte Carlo optimization is more desirable for microstructures where the shape of the fillers (heterogeneities) 

is unknown. 

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Figure 4: 2D microstructure of composite with a given thermal conductivity optimized using a genetic algorithm 

Viscous Effects Investigated by Applied Numerics and 

Experimental Nanoindentation 

In this project, material parameter identification using nanoindentation testing together with the subsequent solution 

of an inverse problem is investigated. In this method, the difference between experimental measurements and 

finite element modeling results of the indentation test are minimized using gradient-based numerical optimization. 

After successful implementation of a sensitivity analysis based on direct differentiation, required for an efficient 

calculation of the gradients used in the optimization algorithm, the reliability of the method has been assessed 

through so-called virtual experimental curves, where the experimental input data are replaced by finite element 

modeling results of the same experiment. In that case, the exact material parameters are known, and the accuracy of 

the material identification procedure can be assessed. This also gives the possibility to analyze noisy data generated 

by superposition of a controlled random noise on the virtual experimental curves in order to assess the effect of 

noise on the material parameters obtained. Using an approximation of the second order gradient, the stability of the 

identification procedure was monitored in order to define appropriate experimental load histories. It was found that a 

suitable load history, which includes periods of constant load, can decouple the response of some material parameters. 

However, a strong coupling between several parameters remains. 


Figure 5: Scheme of the uniaxial indentation test and axisymmetric finite element model of the indentation test 

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Figure 6: Flowchart of the identification algorithm 

Blank shape design of high precision thin metallic parts obtained 

by stampin 

The main objective of this project is to build a numerical approach for the determination of the blank and tools 

geometries used to produce by stamping a thin metallic precision part, knowing the 3D CAD geometry of the desired 

part. The purpose of the present procedure is to replace an expensive and time consuming experimental trial and error 

method. Two numerical approaches have been proposed, the first is regarding the determination of the blank shape. 

An estimation of the blank shape can be given using the Inverse Approach. Update of the blank shape will then be 

continued by iterations combining heuristic optimization algorithms and incremental stamping codes. The second 

approach is based on precise finite element models and springback compensation algorithm. The numerical approaches 

are tested in the case of a special stamping process where the parts are pressed in one or more steps using a manual 

press, without blank holder and by the mean of complex shape tools. 


Figure 7: Flowchart of the numerical procedure for blank shape design 

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Functionally Graded Materials Multi-Scale Modelling, Design and 

Optimisation 

The aim of the project is to develop advanced and accurate micro- and macro-scale modelling for simulation, design and 

optimisation of FGMs and lightweight structural components with high thermo-mechanical capabilities. The following 

specific objectives are proposed: 1- development of advanced models of FGM composites as well as computational 

approaches for the simulation of the effective thermo-mechanical properties; 2- development of accurate theories for 

the design of FGMs-based structures; 3- development of adequate 

models to accurately predict the temperature field and the effect 

of temperature on the material properties; 4- multi-objective 

optimisation of FGMs and FGMs-based structures; 5- development 

of a multi-scale simulation, design and optimisation software tool 

that efficiently utilises the information generated by the multiscale 

modelling. The following scientific results are expected: 

extension of homogenisation and advanced multi-scale modelling 

of FGM composites; accurate description of heat transfer within 

FGMs; higher than classical order modelling of FGMs and FGMs-based 

structures and the development of a systemic and comprehensive 

software tool for the analysis, design and optimisation of FGMs 

Figure 8: Sketch of FGM material 

and structures made of FGMs 

Low cycle fatigue life of nickel-based superalloy valve membranes 

under non-proportional cyclic loading 

In this project, a numerical model for low cycle fatigue damage analysis of valve membranes was developped. The 

isotropic and non-linear kinematic hardening laws of Lemaître–Chaboche, which define both the cyclic hardening 

and the ratchetting phenomenon, are adopted. The model for prediction of the number of cycles to crack initiation 

is based on a combination between Manson–Coffin relationship and Jiang–Sehitoglu fatigue parameter. The applied 

cyclic loading consists in a load pressure imposed to the internal face of the membrane and a vertical displacement of 

its hub section. The experimental results and numerical simulation predictions in terms of number of cycles to failure 

turned out to be in good concordance. Thus, numerical predictions are confirmed by microscopic observations made 

on membranes failed during testing. 


Figure 9A: Factors influencing the fatigue life of the analysed component 

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Figure 9B: FEM modelling and fatigue life estimation of the supervalve membrane 


Figure 10: Evolution of the normal stress for a pressure of 100 bars 

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Piezoelectric transducers for vibration and structural Health 

Monitoring 

The overall aim of this research topic is to explore the possibility of developing unidirectional piezoelectric actuator/ 

sensor which is necessary for various applications require enforcing the unidirectionality of the piezoelectric 

properties. 

Figure 11A: Multiscale modelling of adaptive structures 

The proposed methodology 

Figure 11B: Estimation of the effective properties of macrofiber components 

Fatigue and fatigue damage of Honeycomb sandwich structures 

In this project, an analytical analysis and a numerical model of a typical four-point bending test on a honeycomb 

sandwich panel are proposed. The honeycomb core is modelled as a single solid layer of equivalent material properties. 

Analytical and numerical (finite element) homogenization approaches are used to compute the effective properties of 

the honeycomb core. A general kinematic model (unified formulation) has been adopted and used for the modelling 

of honeycomb sandwich panel submitted to the bending test. A comparative study of major classes of representative 

theories has been considered. Qualitative and quantitative assessments of displacement, stress have been presented 

and discussed. 

Modélisation / simulation numérique 


Figure 12: Effective properties of honeycomb composite materials 

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In parallel, static and fatigue behaviours of honeycomb sandwich composites, made of aramide fibres and aluminium 

cores, are investigated through four-point bending tests. Damage and failure modes are reported and discussed. Global 

and local parameters were considered to evaluate the fatigue life of the analysed sandwich composites. Effects of 

core densities and the cell orientation (L or W) on the maximum load and on the damage processes (initiation and 

evolution) are also investigated. 

Figure 13: Typical fatigue damages in honeycomb sandwich structures 

Crack Propagation in Solid Oxide Fuel Cells (SOFC) 

The major drawback of SOFC technology is the high operating temperature that can lead to complex materials 

degradation problems and major developments are still required to reach the performance where SOFC technology 

can be widely commercialized. We Develop and demonstrate the feasibility of an integrated, predictive computerbased 

tool for fuel cell design and reliability/durability analysis. We are focused to characterize SOFC failure modes 

thermomechanical failure analysis models, interdependency between structural issues and electrochemical/thermal 

transport phenomena. 


Figure 14: Modelling of crack propagation in solid oxide fuel cells 

AMBIENT : 

Towards reliable and accurate ambient simulations 

The main objective of this research activity is the implementation of a partition of unity- related finite element 

method for mechanical simulations in ambient space. The main feature that is expected here is an independent 

description of a) the geometry of the object - for instance, its boundaries may be represented with level-sets and b) 

the mesh used as a description of the functional space in which the solution is sought. In other words, the mesh is 

not expected to be conforming to the object’s boundaries. This has many advantages. Mesh generation is for instance 

greatly simplified because it has not to cope with conformity along interfaces. In the case of shape optimization, 

the geometry of an object may be changed without re-meshing. For objects where no explicit description is available 

(as are results of MRI scan for instance*) the technique will allow to perform simulations without having to build 

an explicit geometrical model. Additionally, one must be able to represent accurately internal boundaries (between 

dissimilar materials or between different models), which is possible with partition of unity methods like the XFEM. 

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Figure 15: Example of ambient simulations 

Modelling of a typical car seat 

The development of a model for the determination of the pressure distribution in a typical car seat is proposed. The 

major challenge is the implementation of the constitutive model of the foam. Indeed, foams cannot be considered as 

being linearly elastic, and the constants describing their mechanical behaviour are not generally available. A suitable 

material model and the parameters of this model have to be determined from mechanical experiments. Particular 

attention will be focused on the modelling of the material behaviour of the foam and the influence of the pre-stressing 

of the trim. Considering the rather complicated constitutive behaviour of the foam and the shape of the seat, a 

numerical, finite element model will be used rather than an analytical model. The car seat is considered as a block 

partially enveloped in a trim under pretension. The results are validated through experimental data obtained from an 

experimental set-up developed. 

Figure 16A: Characterization of the hyperelastic behavior of forms 


Figure 16B and 16C: Finite element modelling and experimentation - validation of a typical car seat 

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Thermoforming of polymeric sheets: Modeling and finite element 

simulations 

In this research activity, a temperature and strain rate dependent model for the thermoforming process of amorphous 

polymer materials is proposed. The polymeric sheet is heated at a temperature above the glass transition temperature 

then deformed to take the mold shape by the means of an applied pressure. The applied process temperature is taken 

uniform throughout the sheet and its variation is due only to the adiabatic heating. The behavior of the polymeric 

material is described by a micromechanically-based elastic-viscoplastic model. The simulations are conducted for the 

poly(methyl methacrylate) using the finite element method. The polymer sheet thickness and the orientation of the 

polymer molecular chains show an important dependence on the process temperature, the applied pressure profile, and 

the contact forces with the mold surface 

Figure 17: Modelling of a thermoforming process 


Design of stents for enhanced endurance and flexibility 

The aim of this project is to develop new designs for biomedical stents with special focus on optimizing deliverability 

and reducing long-term complications occasioned by unexpected in vivo failure of the stent due to high-cycle fatigue. 

Two types of metallic platforms commonly used for manufacturing stents will be considered: AISI 316L stainless steel 

and medical-grade Nitinol. Developing auxetic designs, which appears to be a very recent trend in stent design, will 

also investigated. 

Figure 18: Finite element modelling of medical stents 

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Urban water management 

This project aims to have more detailed and more accurate information concerning the water consumption in 

Luxembourg. We help if it needed communes to acquire and collect measurements over their drinking water network 

and manage these data in a database. We analyse data about water consumption provided by our partners (communes 

and syndicates) in order to establish some precise characteristics such as typical daily curves for example and the 

influence of factors like the day of week, the season, the type of zone (urban, commercial, industrial, agricultural…). 

The second goal is to carry out an advanced algorithm based on forecasting and optimization to control a water 

network. The final goal is to transfer these developments to industrial robotic automation company and to design 

offices or consulting engineers involving in water network construction. 

Figure 19: Optimization and control methodologies 


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Figure 20: Modelling and simulation of data using statistical methods 


Figure 21: Data analysis and signal processing 

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Selected Publications 

• Active control of nonlinear vibration of sandwich piezoelectric beams: A simplified approach Computers & Structures, 

Volume 86, Issues 3-5, February 2008, Pages 386-397 

• On low cycle fatigue life of nickel-based superalloy valve membranes under non-proportional cyclic loading. 

International Journal of Fatigue, Volume 30, Issue 7, July 2008, Pages 1160-1168 

• Numerical evaluation of the equivalent properties of Macro Fiber Composite (MFC) transducers using periodic 

homogenization. International Journal of Solids and Structures, Volume 47, Issue 24, 1 December 2010, Pages 3272- 

3285 

• Finite element implementation including sensitivity analysis of a simple finite strain viscoelastic constitutive law. 

Computers & Structures, Volume 88, Issues 13-14, July 2010, Pages 825-836 

• A numerical method for the optimal blank shape design. Materials & Design, 

• Statistical continuum theory for the effective conductivity of fiber filled polymer composites: Effect of orientation 

distribution and aspect ratio. Composites Science and Technology, Volume 70, Issue 3, March 2010, Pages 510-517 

• Study of interface influence on crack growth: Application to Solid Oxide Fuel Cell like materials design, Materials & 

Design, Volume 31, Issue 3, March 2010, Pages 1033-1041 

• A novel finite element for global and local buckling analysis of sandwich beams, Composite Structures, Volume 90, 

Issue 3, October 2009, Pages 270-278 

• Multi-scale nonlinear modelling of sandwich structures using the Arlequin method composite Structures, Volume 92, 

Issue 2, January 2010, Pages 515-522 


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III. Numeric Modelling and Simulation - CRP Henri Tudor

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