Symmetry groups in nonlinear elasticity: an exercise in vintage mathematics

Annie Raoult

doi:10.3934/cpaa.2009.8.435

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2009, Volume 8, Issue 1: 435-456. Doi: 10.3934/cpaa.2009.8.435

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Symmetry groups in nonlinear elasticity: an exercise in vintage mathematics

Annie Raoult^1,

1.
Laboratoire MAP5, Université Paris Descartes and CNRS, 45 rue des Saints Pères, 75006 Paris

Received: February 29, 2008

Revised: July 31, 2008

Published: December 2008

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Abstract

This manuscript aims at characterizing energy densities and constitutive laws of transversely isotropic materials, orthotropic elastic materials and materials with non orthogonal families of fibers. It makes explicit references to results that are scattered over the literature and, although said to be well-known, are not always easy to locate. Direct proofs that are thought to be new and simplified expressions of constitutive laws for materials with two preferred directions are given.

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Mathematics Subject Classification: 74A20, 74B20, 74E10.

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