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Duality relations for nonlinear incompressible two-dimensional elasticity

Published online by Cambridge University Press:  11 July 2007

G. A. Francfort  and
P. M. Suquet
G. A. Francfort
Affiliation:
LPMTM, Université Paris 13, Avenue J. B. Clément, 93430 Villetaneuse, France
P. M. Suquet
Affiliation:
Laboratoire de Mécanique et d'Acoustique, UPR CNRS 7051, 31 Chemin Joseph Aiguier, 13402 Marseille Cedex 20, France
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Abstract

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Keller's phase-interchange relation, which computes the overall conductivity of a two-dimensional checkerboard with alternating conductivity, is revisited in the context of nonlinear incompressible elasticity. A general phase-interchange relation is obtained in a monotone setting through H-convergence and in a convex setting through variational methods. Several Keller-like applications are presented.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 2 , April 2001 , pp. 351 - 369
Copyright
Copyright © Royal Society of Edinburgh 2001