Thermomechanical Modeling of Microstructure Evolution Caused by Strain-Induced Crystallization

The present contribution deals with the thermomechanical modeling of the strain-induced crystallization in unfilled polymers. This phenomenon significantly influences mechanical and thermal properties of polymers and has to be taken into consideration when planning manufacturing processes as well as applications of the final product. In order to simultaneously capture both kinds of effects, the model proposed starts by introducing a triple decomposition of the deformation gradient and furthermore uses thermodynamic framework for material modeling based on the Coleman–Noll procedure and minimum principle of the dissipation potential, which requires suitable assumptions for the Helmholtz free energy and the dissipation potential. The chosen setup yields evolution equations which are able to simulate the formation and the degradation of crystalline regions accompanied by the temperature change during a cyclic tensile test. The boundary value problem corresponding to the described process includes the balance of linear momentum and balance of energy and serves as a basis for the numerical implementation within an FEM code. The paper closes with the numerical examples showing the microstructure evolution and temperature distribution for different material samples.

Multiscale FEM simulations of cross-linked actin network embedded in cytosol with the focus on the filament orientation

The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks that are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill-Mandel macrohomogeneity condition for bridging 2 scales: the macroscopic scale that is related to the cell level and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel-Ogden β-model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors, and enables a novel finite element implementation. The elements with the neo-Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely, its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior.