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

Abstract

We present a variational framework for the computational homogenization ofchemo-mechanical processes of soft porous materials. The multiscale variationalframework is based on a minimization principle with deformation map and solvent fluxacting as independent variables. At the microscopic scale we assume the existence ofperiodic representative volume elements (RVEs) that are linked to the macroscopic scalevia first-order scale transition. In this context, the macroscopic problem is consideredto 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 callsfor spatial discretization of the underlying RVE. Here, we employ Raviart–Thomas finiteelements and thus arrive at a conforming finite-element formulation of the problem. Wepresent a sequence of numerical examples to demonstrate the capabilities of themultiscale formulation and to discuss a number of fundamental effects.