Computational Homogenization of Materials with Microstructures based on Incremental Variational Formulations

Abstract

The paper presents incremental minimization principles for the broad class of standard dissipative materials at finite strains. Starting with a minimization principle for the local constitutive material response we define a minimization problem for the incremental boundaryvalue problem of standard dissipative solids. The existence of this principle allows the determination of micro-structure developments in non-stable dissipative materials based on a convexification analysis. Finally, we propose a minimization principle for the boundary-value problem of homogenization in heterogeneous microstructures.