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.

The development of new type of hydrogels featuring enhanced properties is a recent topic and of particular interest for a wide range of industrial applications, especially in biomedical sector. The present contribution focuses on the mutliscale modeling of hydrogels that are treated by the enzymatic mineralization and thus enriched with calcium phosphate. More specifically, the calcium phosphate forms spherical or honeycomb structures in the hydrogel matrix, which significantly improves effective material properties such as stiffness and strength. The chosen multiscale finite element method (FEM) homogenization strategy uses the Hill–Mandel macrohomogeneity condition for bridging two scales: the macroscopic boundary value problem (BVP) simulates the specimen behavior, whereas the microscopic BVP investigates the representative volume element (RVE) depicting the heterogeneous multiphase microstructure. The approach proposed uses the Ogden model to simulate the hydrogel and the neo‐Hooke model for the calcium phosphate phase. It varies the RVE type and the macroscopic tests in order to study the influence of the microstructure on the effective behavior and uses experimental data to determine missing microscopic material parameters. Chosen numerical examples demonstrate the applicability of the numerical tool for the estimation of the optimal microscopic arrangement of phases.