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Comptes Rendus Mathématique
Volume 335, n° 1
pages 99-104 (2002)
Doi : S1631-073X(02)02429-9
Received : 18 April 2002 ;  accepted : 19 April 2002
Periodic unfolding and homogenization
Éclatement périodique et homogénéisation
 

Doina Cioranescu a , Alain Damlamian b , Georges Griso a
a Université Pierre et Marie Curie (Paris VI), Laboratoire d'analyse numérique, 4, place Jussieu, 75252 Paris cedex 05, France 
b Université Paris XII Val de Marne, Laboratoire d'analyse et de mathématiques appliquées, CNRS UMR 8050, 94010 Créteil cedex, France 

Note presented by Philippe G. Ciarlet

Abstract

A novel approach to periodic homogenization is proposed, based on an unfolding method, which leads to a fixed domain problem (without singularly oscillating coefficients). This method is elementary in nature and applies to cases of periodic multi-scale problems in domains with or without holes (including truss-like structures). To cite this article: D. Cioranescu et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99-104.

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Résumé

Cette Note présente une approche originale des problèmes d'homogénéisation périodique. Basée sur une méthode d'éclatement périodique, elle conduit à un problème limite à coefficients non oscillants sur un domaine fixe. En comparaison avec les méthodes classiques, cette approche passe par des démonstrations relativement élementaires, et son champs d'application inclut le cas périodique multi-échelle ainsi que le cas des domaines perforés et des structures réticulées. Pour citer cet article : D. Cioranescu et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99-104.

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