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

Article type: Research Article

Authors: Sab, K.

Affiliations: C.E.R.A.M. – Ecole Nationale des Ponts et Chaussees, Central IV, 1 Avenue Montaigne, 93167 Noisy-Le-Grand Cedex, France

Note: [] Correspondence to: K. Sab, C.E.R.A.M. – Ecole Nationale des Ponts et Chaussees, Central IV, 1 Avenue Montaigne, 93167 Noisy-Le-Grand Cedex, France.

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.

DOI: 10.3233/ASY-1994-9402

Journal: Asymptotic Analysis, vol. 9, no. 4, pp. 311-336, 1994