Section 6: Material modelling in solid mechanics - GAMM 2012

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10 Section 6: Material modelling in solid mechanics 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) 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) 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) Colloidal structures inside solutions are usually considered as rigid bodies or linear springs. Howe-
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,
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Section 6: Material modelling in solid mechanics - GAMM 2012

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