Homogenization of non-linear random media by a duality method. Application to plasticity

Abstract

The homogenization of non-linear elastic media and elasto-piastic media is investigated. It is shown that the results established for periodic media hold also for statistically homogeneous ergodic (S.H.E.) media. The homogenization scheme is based on (i) — a formal analogy between periodic media and S.H.E. media, and, (ii) — the study of the duality in S.H.E. non-linear media. “Explicit” direct and dual definitions of the homogenized properties are provided and illustrated by an example.