Computational homogenization of transientchemo-mechanical processes based on a variational minimization principle

We present a variational framework for the computational homogenization of chemo-mechanical processes of soft porous materials. The multiscale variational framework is based on a minimization principle with deformation map and solvent flux acting as independent variables. At the microscopic scale we assume the existence of periodic representative volume elements (RVEs) that are linked to the macroscopic scale via first-order scale transition. In this context, the macroscopic problem is considered to be homogeneous in nature and is thus solved at a single macroscopic material point. The microscopic problem is however assumed to be heterogeneous in nature and thus calls for spatial discretization of the underlying RVE. Here, we employ Raviart–Thomas finite elements and thus arrive at a conforming finite-element formulation of the problem. We present a sequence of numerical examples to demonstrate the capabilities of the multiscale formulation and to discuss a number of fundamental effects.