Hybrid impotent–incompatible eigenstrain based homogenization

Abstract

SUMMARY We present a constitutive framework for a periodic heterogeneous medium with minimal number of internal variables. The method is based on a variant of the transformation field analysis (TFA) where eigenstrains are discretized using C 0 continuous approximation in matrix dominated mode of deformation, hereafter referred to as impotent eigenstrain mode, whereas in multiphase mode of deformation, the eigenstrains are approximated using the usual C − 1 approximation. The delay in the onset of inelastic response and the eigenstrain induced anisotropy in a microphase, both characteristic to averaging methods, are alleviated by introducing an eigenstrain upwinding scheme and by enhancing constitutive laws of microphases. The proposed formulation has been verified against a direct numerical simulation. The method has been found to be very accurate in predicting an overall material response at a computational cost comparable with the phenomenological modeling of a periodic heterogeneous medium. Copyright © 2013 John Wiley & Sons, Ltd.