A more fundamental approach to damaged elastic stress-strain relations

Abstract

For many engineering problems it can be assumed that the damaged material elastic response at a fixed damage state is linear and hyperelastic. With this assumption, a systematic and rigorous approach for formulating damaged elastic stress-strain relations is presented. The approach is based on the Fourier series representations of two naturally defined damage orientation distribution functions and on a theorem on elasticity tensors, and developed resorting neither to the notion of effective stress (strain) nor to the hypothesis of strain (stress) equivalence nor to that of elastic energy equivalence. The proposed approach is finally illustrated by applying it to initially isotropic materials and to unidirectional fiber-reinforced composites.