Symmetry groups in nonlinear elasticity: an exercise in vintage mathematics

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January 2009, 8(1): 435-456. doi: 10.3934/cpaa.2009.8.435

Symmetry groups in nonlinear elasticity: an exercise in vintage mathematics

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

Received March 2008 Revised August 2008 Published October 2008

Abstract
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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.

Keywords: fibers, symmetry groups, transverse isotropy, constitutive laws, orthotropy, anisotropy, Nonlinear elasticity.

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

Citation: Annie Raoult. Symmetry groups in nonlinear elasticity: an exercise in vintage mathematics. Communications on Pure & Applied Analysis, 2009, 8 (1) : 435-456. doi: 10.3934/cpaa.2009.8.435

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