Variational upscaling for modeling state of strain-dependent behavior and stress-induced crystallization in rubber-like materials

The purpose of this paper is to present a general upscaling strategy for deriving macroscopic constitutive laws for rubber-like materials from the knowledge of the network distribution and a mechanical description of the individual chains and of their free energy. The microscopic configuration is described by the position of the cross-links and is not obtained by an affine assumption but by minimizing the corresponding free energy on stochastic large representative volume elements with adequate boundary conditions. This general framework is then approximated by using a microsphere (directional) description of the network. It is presented in a global setting and is extended in order to handle situations with tube-like constraints and stress-induced crystallization.