Prof. Dr. Hans Georgund Liselotte Hahn Stiftung

Lehrstuhl fur Technische Mechanik

5. GAMM-Seminar on

Multiscale Material

Modeling

Kaiserslautern, 30.06.-01.07.2011

Book of Abstracts

1

Lageplan

Haltestelle

Rotunde, Geb. 57

Restaurant

Uni Ost

Raum 208/210

Sommerhaus

2

3

Programm

Donnerstag, 30.06.

09.00 - 09.20 Eroffnung

09.20 - 10.00 S. Ricker, H. Andra, S. Frei, M. Kabel, F. Krzikalla, I. Shyklar, A. Zemi-tishMulti-Scale Simulation of Viscoelastic Fiber-Reinforced Composites

10.00 - 10.40 A. Bertram, T. HoffmannIdentifikation und Validierung eines kristall-plastischen Modells aufMakro- und Mikroebene

10.40 - 11.20 R. Kazakeviciute-Makovska, H. SteebHierarchical structure and multi-scale mechanics of fibrous protein ma-terials

11.20 - 12.00 S. KnellNumerical modeling of the transient response of material grades at themicron-scale

12.00 - 13.40 Mittagspause im Restaurant Sommerhaus

13.40 - 14.20 S. Lin, T.A. Langhoff, T. BohlkeHomogenization of Mechanical Properties of Pyrolytic Carbons Basedon Domain Orientation Distribution Function by Combining DifferentImage Processing Techniques

14.20 - 15.00 K.-H. Sauerland, R. MahnkenTwoscale FE Simulation of Coated Forming Tools under Thermo-Mechanical Loading

15.00 - 15.40 Md. Khalaquzzaman, R. Muller, B.-X. XuMultiscale simulation of piezoelectric materials using configurationalforce theory

15.40 - 16.10 Kaffeepause

16.10 - 16.50 F. Hildebrand, S. Mauthe, C. MieheA Partial Relaxation Approach to Laminate Formation and Evolutionin Martensitic CuAlNi at Large Strains

16.50 - 17.30 D. Schrading, S. DiebelsAnisotropic Cosserat modelling of the regular honeycomb structure

17.30 Treffen des GAMM Fachausschusses

19.00 Abendessen

4

Freitag, 01.07.

09.00 - 09.40 C. Linder, C. MieheModeling fracture in piezoelectric ceramics with embedded strong dis-continuities and an account for polarization saturation

09.40 - 10.20 S. Wulfinghoff, T. BohlkeDislocation Transport and Production by Line Length Increase in SingleCrystals

10.20 - 11.00 A. Attaran, S. GrohA molecular dynamics study of crack/void interaction in α-Iron

11.00 - 11.40 M. Klassen, R. MullerMaterial Modelling and Optimization on Microstructure Level of Di-electric Elastomer Actuators

11.40 Abschlussdiskussion

12.00 Mittagsbuffet

5

Abstracts

Multi-Scale Simulation of Viscoelastic

Fiber-Reinforced Composites

Sarah Ricker1, Heiko Andra1, Stefan Frei1, Matthias Kabel1, FabianKrzikalla2, Inga Shyklar1, and Aivars Zemitis1

1 Department of Flow and Material Simulation,Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern,Germany

2 Department of Geophysics,Stanford University, Stanford, USA

Abstract. The mechanical properties of fiber-reinforced polymers dependon the fiber volume fraction, the local fiber-orientation, the geometrical andelastic properties of the fibers as well as on the viscoelastic polymer matrix. Inthe work at hand, a chain of numerical procedures to compute the full macro-scopic mechanical composite properties is presented, which is based on thegeometrical and viscoelastic properties of the single constituents. To this end,a fast, robust, and locally refined tetrahedral meshing of statistical volumeelements representing complex microstructures is applied, see [1]. In contrastto other approaches, here a voxel-based ansatz is used, which in particular issuitable for images resulting from 3D computer tomography. For these statis-tical volume elements the so-called µFE-simulation is applied by the softwareFeelMath (Finite Elements for elastic Materials and Homogenization), whichhas been developed at Fraunhofer ITWM. Therein, all time-dependend co-efficients of the anisotropic elasticity tensor, which only can be determinedpartially in experimental settings, are predicted. The results of these micro-scopic simulations are compared to appropriate measurements and theoreticalresults. Conclusions for the simplified calculation of viscoelastic properties forcomposites based on purely elastic µFE-simulation are drawn, for more detailssee [2]. Finally, the estimated macroscopic material properties are applied tothe dimensioning of components with locally varying fiber-orientations. Inour numerical examples the commercial software ABAQUS is used.

References

1 V. Schulz, H. Andra and K. Schmidt: Robuste Netzgenerierung zur Mikro-FE-Analyse mikrostrukturierter Materialien. NAFEMS Magazin, 2, 28–30 (2007)

2 H. Andra, M. Kabel, F. Krzikalla and V. Schulz: Numerical Homogeniza-tion of Viscoelastic Fiber-Reinforced Composites. In: Proc. NAFEMS-

Seminar: “Fortschritte in der Simulation von Composites”, Wiesbaden,Germany, April 2011

6

Identifikation und Validierung eines kristall-

plastischen Modells auf Makro- undMikroebene

Albrecht Bertram1 and Thorsten Hoffmann

Lehrstuhl fur Festigkeitslehre, Institut fur Mechanik,Otto-von-Guericke University, Magdeburg, Germany

Zusammenfassung Fur Mikro-Makro-Modelle besteht ein Mangel an ver-lasslichen Identifikations- und Validierungsmethoden. Zur Entwicklung derar-tiger Methoden konnen sowohl Experimente auf der polykristallinen Makro-ebene als auch auf der einkristallinen Mikroebene genutzt werden. In dieserPrasentation werden Experimente beschrieben, die auf beiden Ebenen durch-gefuhrt werden [1]. Alle Proben stammen von gewalzten Blechen des unle-gierten Tiefziehstahls DC04. Parallel zu den experimentellen Untersuchungenwerden Finite-Elemente Rechnungen unter Verwendung eines kristallplasti-schen Materialmodells [2] durchgefuhrt. Im ersten Teil dieser Prasentationwird eine Identifikation und Validierung des Materialmodells auf der Grund-lage klassischer makroskopischer Scher- [3] und Zugversuche vorgestellt. Imzweiten Teil werden die Moglichkeiten der Nutzung von makroskopischen undmikroskopischen Eindringversuchen zur Identifikation und Validierung unter-sucht. Mit den Berechnungen kann gezeigt werden, dass auf der Makroebeneangepasste Materialmodelle der Kristallplastizitat auch auf der Mikroebe-ne realistische Ergebnisse liefern [4]. Anhand von Sensitivitatsstudien ist esmoglich, einige fur die Eindringversuche wichtige Einflussfaktoren zu ermit-teln. Schließlich werden die bestehenden Probleme bezuglich einer Identifika-tion aufgezeigt.

References

1 T. Hoffmann: Identifikation und Validierung eines kristallplastischen Mo-

dells auf Makro- und Mikroebene, Diss. (online), OvGUMagdeburg, (2011).2 A. Bertram: Elasticity and Plasticity of Large Deformations. Springer-Verlag, Berlin, 2008

3 S. Bouvier, H. Haddadi, P. Levee, C. Teodosiu: Simple shear tests: Ex-perimental techniques and characterization of the plastic anisotropy ofrolled sheets at large strains, J. Mater. Process. Technol., 172, 96–103(2006).

4 T. Hoffmann, J. Kalisch, A. Bertram, S. Shim, J. Z. Tischler, H. Bei, B. C.Larson: Experimental identification and validation of models in micro andmacro plasticity. In: Proc. 1st Int. Conf. Mat. Mod., pp. 136–145, , Tech.Mech. 30(1-3), 2010.

7

Hierarchical structure and multi-scale

mechanics of fibrous protein materials

R. Kazakeviciute-Makovska and H. Steeb

Institute of Mechanics,Ruhr-University Bochum, Germany

Abstract. Fibrous proteins are composed of chains which may be cross-linked leading to the formation of fibrous structural materials with consid-erable mechanical properties (strength, rigidity, stability, etc.). Furthermore,the mechanical properties and biocompatibility of these materials may betailored for specific functions. This makes fibrous protein materials particu-larly attractive in a variety of biomaterial and tissue engineering applications[1,2]. The origin of research in the field of elasticity of fibrous protein ma-terials can be traced back to Flory [3]. Recent studies concentrate on thestructure-property relationships relating the intrinsic multi-level structure ofthese materials to the mechanical and thermal properties observed at variouslength and time scales [1,2].

In the present contribution, we discuss different multi-scale models of fi-brous proteins and apply these models to describe superelasticity, self-healingand other properties of proteinaceous biomaterials such as α-keratin fibers,silk fibers and the whelk egg capsule biomembrane. The phenomenologicalmodel for such materials have been proposed in [4,5]. The current work makesan attempt to correlate the macroscopic predictions of this model to the in-herent hierarchical structure of fibrous protein materials.

References

1 M. J. Buehler: Theoretical and computational hierarchical nanomechan-ics of protein materials: Deformation and fracture, Progress in Materials

Science, 53(8), 1101–1241 (2008).2 M. J. Buehler, S. Keten, T. Ackbarow: Multiscale mechanics of biologicaland biologically inspired materials and structures, Acta Mechanica Solida

Sinica, 23(6), 1–13 (2010).3 P. J. Flory: Theory of elastic mechanisms in fibrous proteins, Journal ofthe American Chemical Society, 78(20), 5222–5235 (1956).

4 R. Kazakeviciute-Makovska, H. Steeb: Micromechanical bases of supere-lastic behavior of certain biopolymers. In: Mechanics of Generalized Con-

tinua, Advanced Structured Materials (eds H. Altenbach, G. Maugin &V. Erofeev), pp. 175–192, Springer, 2011.

5 R. Kazakeviciute-Makovska, H. Steeb: Superelasticity and self-healing ofproteinaceous biomaterials, Procedia Engineering (accepted), (2011).

8

Numerical modeling of the transient response

of material grades at the micron-scale

Sascha Knell

Fraunhofer Institute for High-Speed Dynamics – Ernst-Mach-Institut,Eckerstrasse 4, 79104 Freiburg, Germany

Abstract. Many material grades, e.g., ceramics, composites, etc., show adistinct structure at the micron-scale. The qualitative and quantitative anal-ysis of the processes at the micron-scale of the aforenamed material gradesform the basis for the understanding and the modeling of their macroscopicmaterial response. In the case of shock loading, the experimental analysis ofthe micron-scale processes, particularly localized failure, proves to be difficultif not impossible. In contrast, numerical modeling enables the direct spatialand temporal analysis of the aforementioned processes.

In this contribution, a combined explicit, linear, FE-based simulation ap-proach proposed by the author in [1] is presented and its applicability for thetask outlined above is demonstrated. The bulk deformations of the single con-stituents of the material grades are modeled with simplicial, i.e., triangularor tetrahedral, continuum elements. The adopted continuum element formu-lation is the finite calculus formulation proposed by Onate et al. [2] whichwas extended in [1] with regard to its applicability to moderately anisotropicmaterials with internal phase interfaces. Localized failure at phase interfacesis modeled by “initially rigid” cohesive elements. The adopted cohesive el-ement formulation, also proposed in [1], is predicated on the linear variantof the “time continuous” formulation from Papoulia et al. [3]. However, theadopted formulation avoids some issues and shortcomings of the underlyingformulation. The analysis and the demonstration of the applicability of thecombined approach is conducted on the basis of spallation simulations ofgeneric Al2O3-ceramic RVEs.

References

1 S. Knell: A numerical modeling approach for the transient response of

solids at the mesoscale. PhD thesis, Fraunhofer Verlag, in Press, 2011.2 E. Onate, J. Rojek, R. L. Taylor, O. C. Zienkiewicz: Finite calculus for-mulation for incompressible solids using linear triangles and tetrahedra.International Journal for Numerical Methods in Engineering, 59, 1473–1500, (2004).

3 K. D. Papoulia, C.-H. Sam, S. A. Vavasis: Time continuity in cohesivefinite element modeling. International Journal for Numerical Methods in

Engineering, 58, 679–701, (2003).

9

Homogenization of Mechanical Properties of

Pyrolytic Carbons Based on DomainOrientation Distribution Function by

Combining Different Image ProcessingTechniques

S. Lin, T.-A. Langhoff, and T. Bohlke

Chair for Continuum MechanicsInstitute of Engineering MechanicsDepartement of Mechanical EngineeringKarlsruhe Institute of Technology (KIT), Germany

Abstract. By using experimental characterizationmethods like high-resolutiontransmission electron microscopy (HRTEM) with selected-area electron diffrac-tion [1] the microstructure of pyrolytic carbon (PyC) can be described as aset of coherent domains having different orientations. The aim of the presen-tation is to estimate the mechanical properties on the submicron scale takinginto account statistical information extracted from HRTEM images based ona segmentation technique.

With a specific filter preprocessing and Fourier Transform, the approachof spectral density function [2] can be morphologically applied to model thedomain orientation distribution function. Locally, every domain with a homo-geneous orientation of the graphene planes can be extracted by using texturesegmentation method based on Local Binary Patterns [3] to identify thesedomains. Both approaches indicate that the orientation distribution of thenormal direction of the graphene layers can be modeled by von Mises-Fisherdistributions. This facilitates the description of the microstructure based ononly one concentration parameter at least for highly textured materials [4].The estimated parameter can be used to homogenize the elastic and thermalproperties of PyC on the submicron scale by means of first- and second-orderbounds.

References

1 B. Reznik, D. Gerthsen, W. Zhang, K. Huttinger: Texture changes in thematrix of an infiltrated in a carbon fiber felt studied by polarized lightmicroscopy and selected area electron diffraction, Carbon, 41(2), 376–380(2003).

2 D. Yavuz, N. C. Geckinli, N. C. Geockinti: Discrete Fourier Transforma-

tion and Its Applications to Power Spectra Estimation. Elsevier, Cam-bridge, 1983.

10

3 T. Ojala, M. Pietikainen: Unsupervised texture segmentation using fea-ture distributions, Pattern Recognition, 32(3), 477–486 (1999).

4 T. Bohlke, K. Jochen, R. Piat, T.-A. Langhoff, I. Tsukrov, B. Reznik:Elastic properties of pyrolytic carbon with axisymmetric textures, Tech-nische Mechanik, 30, 343–353 (2010).

11

Twoscale FE Simulation of Coated Forming

Tools under Thermo-Mechanical Loading

Kim-Henning Sauerland1 and Rolf Mahnken1

Chair of Engineering Mechanics (LTM),University of Paderborn, Paderborn, Germany

Abstract. In industrial hybrid-forming processes workpieces are heated upbefore forming in order to reduce the forming forces. In the process underinvestigation [1] a simultaneous coupling between thermal and mechanicaltreatment of the workpiece enables to produce components with graded prop-erties, particularly with regard to tailored material properties and geometricalshape. In these forming processes the forming tools are subjected to cyclicthermal shock loading conditions which can result into damage and failure.For improvement of the tool service life coated forming tools with multilay-ered coating systems are considered to be applied in future.

This contribution shows the actual state of work for the development of atwoscale FE model for the simulation of the multilayered coated forming tool.Within this model the three-dimensional model of the forming tool builds themacromodel. On the macrolevel the multilayered coating is discretized withone element over the coating thickness. The mesomodel of the coating con-siders the actual layer design with particular coating layers. The macro-mesoscale transition is realized with a Taylor-assumption. As the microscale isnot considered in our model, the constitutive equations are formulated onthe mesoscale. The meso-macro scale transition is done using volume averag-ing procedures. Furthermore, a damage model is included for particular layers[2]. The scalar damage variable is used in a thermo-mechanical coupled modelfor simulation of a reduced heat transfer through a partially damaged layer.

References

1 K. Steinhoff, U. Weidig, B. Scholtes, W. Zinn: Innovative Flexible MetalForming Processes based on Hybrid Thermo-Mechanical Interaction. SteelRes. Int., 76, pp. 154–159 (2005).

2 R. Mahnken, M. Schlimmer: Simulation of Strength Difference in Elasto-Plasticity for Adhesive Materials. Int. J. Numer. Meth. Engng, 63, pp.1461–1477 (2005).

12

Multiscale simulation of piezoelectric materials

using configurational force theory

Md. Khalaquzzaman1, Ralf Muller1, and Baixiang Xu1

Lehrstuhl fur Technische Mechanik,Fachbereich Maschinenbau und Verfahrenstechnik,Technische Universitat Kaiserslautern, Kaiserslautern

Abstract. Computational homogenization has become increasingly impor-tant in determining the macroscopic material response of inhomogeneousmaterials, e.g. piezoelectric materials. In this work, two-scale classical (first-order) homogenization of an electro-mechanically coupled material using aFE2-approach is discussed. The homogenized coefficients of the elastic, piezo-electric and dielectric tensors for small strain are explicitly formulated, aswell as the homogenized remanent strain and remanent polarization [1]. Dif-ferent representative volume elements (RVEs) are used to capture the do-main microstructure of the piezoelectric material. Two different schemes areconsidered: in the first case, domain wall movement is not allowed; in thesecond case the movement of the domain walls is taken into account usingconfigurational forces at the domain walls [3]. Based on the multiscale modeland the homogenized configurational force [2], the mode-I crack problem inpiezoelectric material is simulated. The effect of the applied electric field onconfigurational forces at the crack tip has been extensively investigated. Theconfigurational force at the crack tip is lower in the case of evolving domainmicrostructure than that of fixed domain microstructure.

References

1 M. Khalaquzzaman, S. Ricker & R. Muller: Computational Homogeniza-tion of Piezoelectric Materials using FE2, PAMM, 10, 417–418 (2010).

2 S. Ricker, J. Mergheim, P. Steinmann & R. Muller: A Comparison ofDifferent Approaches in the Multi-Scale Computation of ConfigurationalForces, Journal of Fracture, 166(1-2), 203-214 (2010).

3 D. Schrade, R. Muller, D. Gross, T. Utschig, V. Y. Shur & D. C. Lu-pascu: Interaction of domain walls with defects in ferroelectric materials,Mechanics of Materials, 39(2), 161–174 (2007).

13

A Partial Relaxation Approach to Laminate

Formation and Evolution in MartensiticCuAlNi at Large Strains

F. Hildebrand1, S. Mauthe1, and C. Miehe1

Institut fur Mechanik (Bauwesen), Lehrstuhl I, Universitat StuttgartPfaffenwaldring 7, 70550 Stuttgart, Germany

Abstract. The modeling of laminate formation and evolution in Shape Mem-ory Alloys plays a crucial role in the prediction of their extraordinary thermo-mechanical properties. When considering only two martensitic variants, therelated free energy functions are of two-well nature and existence of solutionsis not guaranteed for related boundary value problems. Full relaxation bymeans of rank-one convexification restores existence of solutions, however, itis not suited to model the dissipative hysteretic bahavior that is typical forphase transformations. Recently, a partial relaxation approach was suggestedby [1] that combines the relaxation of elastic variables with the dissipativeevolution of dissipative variables.

Starting from a non-convex large strain free energy function describinga mixture of two orthorhombic martensitic variants of CuAlNi, we carryout its full relaxation by use of a full and a reduced grid-search algorithm.Building on these results, we suggest a suitable partial relaxation approachand formulate a related incremental variational framework. We illustrate allsteps with numerical results and show the good agreement of the partialrelaxation simulations with the experiments of [2].

References

1 T. Bartel, K. Hackl: Mat. Sci. Eng. A-Struct. 481, 371–375 (2008) .2 A. Abeyaratne, C. Chu, R. James: Phil. Mag. A. 73, 457–497 (1996) .

14

Anisotropic Cosserat modelling of the regular

honeycomb structure

Daniel Scharding1 and Stefan Diebels1

1 Chair of Applied Mechanics, Department of Material Science,Saarland University, Saarbrucken, Germany

Abstract. Polymer and metal foams have established as state-of-the-art en-gineering materials e. g. in automotive and aerospace industry. The mainreasons for that are their high stiffness and good damping properties againstthe background of low weight. Apart from that the mechanical behaviourhas to be denoted very complex because it is dominated by the underlyingmicro-topology.Despite the wide-ranging use of foams as construction materials the ques-tion of their computational treatment is not completely cleared yet. But thenecessity for numerical computations exists because finite element computa-tions replaced expensive experimental series during the process of productdevelopement.As an example a regular honeycomb-structure will be investigated as a fullresolution micro-model in finite element computations to provide referencedata for a subsequent parameter identification [3]. The goal of the parameteridentification procedure will be to determine the extended set of materialparameters contained in an extended continuum theory.The linear Cosserat theory [1-3] can reproduce the microstructure’s behavioron a macroscopic level by the introduction of additional rotational degreesof freedom and a corresponding couple stress tensor. Therefore the linearCosserat theory will be used to perform the homegenization.Another important aspect will be the observed dependency of the honeycomb-structure’s mechanical behaviour from it’s orientation towards the appliedload [4]. An approach will be shown how to incorporate this aspect into thelinear Cosserat theory.

References

1 E. Cosserat, F. Cosserat, Theorie des corps deformables. A. Hermann etfils, Paris, 1909

2 R. de Borst: Simulation of strain localization: a reappraisal of the Cosseratcontinuum, Engineering Computations, 8, 317–332 (1991).

3 S. Diebels, H. Steeb: The size effect in foams and it’s theoretical andnumerical investigation. In: Proceedings of the Royal Society London A

458, pp. 1–15, 20024 C. Tekoglu, P. R. Onck: Size effects in the mechanical behaviour of cellularsolids. Journal of Material Science, 40, 5911–5917 (2005).

15

Modeling fracture in piezoelectric ceramics

with embedded strong discontinuities and anaccount for polarization saturation

Christian Linder and Christian Miehe

Institute of Applied Mechanics, University of Stuttgart, Stuttgart, Germany

Abstract. In this work new finite elements, capable of modeling fracture inpiezoelectric ceramics, are shown. Such materials which are commonly usedin smart systems in the form of actuators or sensors are prone to defectsin the form of cracks represented by strong discontinuities, i.e. jumps in thedisplacement field. Those are modeled in a discrete way with the possibilityof their propagation through the individual finite elements without the needof remeshing or refinement strategies. Originated for purely mechanical basedmaterials and commonly referred to as the strong discontinuity approach [1, 2]an extension to account for the electromechanical coupling and the additionalappearance of jumps in the electric potential is made [3]. From a constitutivepoint of view the influence of polarization saturation is investigated whencomparing the obtained numerical results with experimental results availablein the literature [4] in the form of tension tests and three point bending tests.

References

1 J. C. Simo, J. Oliver, F. Armero: An analysis of strong discontinuitiesinduced by strain-softening in rate-independent inelastic solids, Comput.

Mech., 12, 277–296 (1993).2 C. Linder, F. Armero: Finite elements with embedded strong discontinu-ities for the modeling of failure in solids, Int. J. Numer. Methods Engrg.,72, 1391–1433 (2007).

3 C. Linder, D. Rosato, C. Miehe: New finite elements with embeddedstrong discontinuities for the modeling of failure in electromechanical cou-pled solids, Comput. Methods Appl. Mech. Engrg., 200, 141–161 (2011).

4 S. Park, C.-T. Sun: Fracture criteria for piezoelectric ceramics, J. Am.

Ceram. Soc., 78, 1475–1480 (1995).

16

Dislocation Transport and Production by Line

Length Increase in Single Crystals

Stephan Wulfinghoff and Thomas Bohlke

Chair for Continuum Mechanics, Institute of Engineering Mechanics,Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.

Abstract. The ContinuumDislocation Dynamics Theory suggested by Hoch-rainer et al. and Sandfeld et al. [1, 2] is embedded in the classical continuumcrystal plasticity framework at small strains. The theory is based on a gener-alized higher-dimensional dislocation-density tensor (a kinematical quantity)and its evolution equation. The solution allows to compute the evolutionof the orientation-dependent and total dislocation density, the geometricallynecessary dislocations and the average curvature of the dislocations. The as-sociated evolution equations are kinematically coupled to crystal plasticityvia the Orowan-equation.Due to the higher dimensionality, the simulation of complex geometries is ex-tensive. However, a homogenization procedure yields a theory which is bettersuited for the numerical treatment and will mainly be addressed.To close the set of mechanical and dislocation equations, constitutive laws forthe dislocation based hardening effects are identified. The variational formof the global work balance and the weak form of the dislocation problem canbe specified allowing to derive a closed set of field equations.

References

1 T. Hochrainer, M. Zaiser and P. Gumbsch, March 2007. A three-dimen-sional continuum theory of dislocation systems: kinematics and mean-field formulation. Phil. Mag. 87 (8-9), 1261–1282.

2 S. Sandfeld, T. Hochrainer, M. Zaiser and P. Gumbsch, 2010. NumericalImplementation of a 3D Continuum Theory of Dislocation Dynamics andApplication to Microbending. Phil. Mag. 90,

17

A molecular dynamics study of crack/voidinteraction in α-Iron

A. Attaran and S. Groh

Institute of Mechanics and Fluid DynamicsTechnische Universitat Bergakademie FreibergLampadiusstrasse 4, D-09596 Freiberg, Germany

{Abdolhamid.Attaran,Sebastien.Groh}@imfd.tu-freiberg.de

Abstract. A study on crack/void interaction using molecular dynamics (MD)simulation technique is presented. The material of interest is α-Iron modeledwith an Embedded Atom Method (EAM) - cohesive rule. Three distributionsof void were considered: (i) void positioned at varying distance normal to thecrack tip, (ii) void inserted at varying distances along the crack-tip and (iii)void placed in such a way that dislocations nucleated at the crack tip reachedthe void when moving. The data obtained for the different configurations werecompared to the one obtained in a void free specimen.

Depending on the configuration, elastic shielding or anti-shielding wasobserved as a function of the temperature and strain rate. The increase intemperature augmented the shielding effect in all the configurations. Theanti-shielding effect was detected in the first configuration. This effect dimin-ished as the void was moving away from the crack tip.

18

Material Modelling and Microstructural

Optimization of Dielectric ElastomerActuators

M. Klassen1, B. X. Xu1, and R. Muller1

Lehrstuhl fur Technische Mechanik,Fachbereich Maschinenbau und Verfahrenstechnik,Technische Universitat Kaiserslautern, Kaiserslautern

Abstract. Actuators demand a coupling between different physical fields.One of the most common coupling in the design of actuators is the interactionbetween an electric and a mechanic field. Through this coupling a mechanicaldeformation is controlled by an electric signal. One of the most well knownmaterials, in which the direct coupling takes place, are piezoelectric ceramics.In the last years dielectric elastomer actuators (DEAs) appeared as a newconcept for the realization of actuators. In contrast to piezoelectric actuators,DEAs realize large deformations and low forces. The deformation and forcerange is close to natural muscles.In this work the numerical modelling and implementation for DEAs will bepresented. Since DEAs realize large deformations, the modelling takes placein the context of the nonlinear continuum mechanics theory. Furthermore,electrostatic definitions, with the introduction of the Maxwell stress tensor,are taken into account. For the mechanical part the Neo-Hooke and the Yeohmaterial model are implemented in the numerical simulation.One important aspect which is also treated is the stability of DEAs. Sincethe electric field increases as the actuator is compressed, a collapse of thestructure is possible. For this purpose an analytical study is provided for thecomparison with the numerical implementation.Another aspect in this work is an idea for improving the compression of DEAsby microstructural modifications. For this objective numerical simulation arerealized in which inclusions are incorporated in the numerical model. Severaltypes of inclusions are analysed with regard to the behaviour of the actuator.

References

1 Mueller, R.; Xu, B. X.; Gross, D.; Lyschik, D.; Schrade, D.; Klinkel,S.: Deformable dielectrics - optimization of heterogeneities, InternationalJournal of Engineering Science, 48, 647–657 (2010).

1 Xu, B. X.; Mueller, R.; Klassen, M.; Gross, D.: On electromechanical sta-bility analysis of dielectric elastomer actuators, Applied Physics Letters,97, 162908 (2010).

19

Teilnehmer

Heiko Andra Abteilung fur Stromungs- und MaterialsimulationFraunhofer ITWM, Kaiserslautern

Abdolhamid Attaran Institut fur Mechanik und FluiddynamikTU Bergakademie Freiberg, Freiberg

Franz-Josef Barth Lehrstuhl fur Technische MechanikTechnische Universitat Kaiserslautern, Kaiserslautern

Albrecht Bertram Institut fur Mechanik,Otto-von-Guericke-Universitat, Magdeburg

Stefan Diebels Lehrstuhl fur Technische MechanikUniversitat des Saarlandes, Saarbrucken

Stefan Frei Abteilung fur Stromungs- und MaterialsimulationFraunhofer ITWM, Kaiserslautern

Felix Fritzen Institut fur Technische MechanikKarlsruher Institut fur Technologie (KIT), Karlsruhe

Oliver Goy Lehrstuhl fur Technische MechanikTechnische Universitat Kaiserslautern, Kaiserslautern

Dietmar Gross Fachgebiet FestkorpermechanikTechnische Universitat Darmstadt, Darmstadt

Felix Hildebrandt Institut fur MechanikUniversitat Stuttgart, Stuttgart

Matthias Kabel Abteilung fur Stromungs- und MaterialsimulationFraunhofer ITWM, Kaiserslautern

Rasa Kazakeviciute- Lehrstuhl fur KontinuumsmechanikMakovska Ruhr-Universitat Bochum, BochumMd. Khalaquzzaman Lehrstuhl fur Technische Mechanik

Technische Universitat Kaiserslautern, KaiserslauternMarkus Klassen Lehrstuhl fur Technische Mechanik

Technische Universitat Kaiserslautern, KaiserslauternSascha Knell Fraunhofer Institut fur Kurzzeitdynamik - Ernst-

Mach-Institut, FreiburgNatalia Konchakova Lehrstuhl fur Technische Mechanik

Technische Universitat Kaiserslautern, KaiserslauternCharlotte Kuhn Lehrstuhl fur Technische Mechanik

Technische Universitat Kaiserslautern, KaiserslauternTom-Alexander Langhoff Institut fur Technische Mechanik

Karlsruher Institut fur Technologie (KIT), KarlsruheSong Lin Institut fur Technische Mechanik (Kontinu-

umsmechanik)Karlsruher Institut fur Technologie (KIT), Karlsruhe

Christian Linder Micromechanics of Materials Group (SimTech)Universitat Stuttgart, Stuttgart

20

Ralf Muller Lehrstuhl fur Technische MechanikTechnische Universitat Kaiserslautern, Kaiserslautern

Carolin Plate Lehrstuhl fur Technische MechanikTechnische Universitat Kaiserslautern, Kaiserslautern

Sarah Ricker Abteilung fur Stromungs- und MaterialsimulationFraunhofer ITWM, Kaiserslautern

Christian Sator Lehrstuhl fur Technische MechanikTechnische Universitat Kaiserslautern, Kaiserslautern

Kim-Henning Sauerland Lehrstuhl fur Technische MechanikUniversitat Paderborn, Paderborn

Daniel Scharding Lehrstuhl fur Technische MechanikUniversitat des Saarlandes, Saarbrucken

Ulrike Schmidt Lehrstuhl fur Technische MechanikUniversitat Erlangen, Erlangen

Regina Schmitt Lehrstuhl fur Technische MechanikTechnische Universitat Kaiserslautern, Kaiserslautern

Johannes Spahn Abteilung fur Stromungs- und MaterialsimulationFraunhofer ITWM, Kaiserslautern

Bob Svendsen Institut fur WerkstoffmechanikRWTH Aachen, Aachen

Stephan Wulfinghoff Institut fur Technische Mechanik (Kontinu-umsmechanik),Karlsruher Institut fur Technologie (KIT), Karlsruhe

Bai-Xiang Xu Lehrstuhl fur Technische MechanikTechnische Universitat Kaiserslautern, Kaiserslautern

Tobias Zangmeister Abteilung fur Stromungs- und MaterialsimulationFraunhofer ITWM, Kaiserslautern

Bernd Zastrau Institut fur Mechanik und FlachentragwerkeTechnische Universitat Dresden, Dresden