On Variational Based Scale-Bridging of Inelastic Composites

The paper discusses formulations for the theoretical and numerical analysis of inelastic composites with scale separation. The basic underlying structure is a canonical variational setting in the fully nonlinear range based on incremental energy minimization. We focus on formulations of strain–driven homogenization for representative composite aggregates with emphasis on the development of canonical families of algorithms based on Lagrange and penalty functionals to cover alternative boundary constraints of (i.) linear deformations, (ii.) periodic deformations and (iii.) uniform tractions. As a key result, we present a compact matrix formulation for homogenization covering introduced alternative boundary constraints. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)