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.