Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension

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May 2001, 1(2): 257-263. doi: 10.3934/dcdsb.2001.1.257

Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension

1.	Department of Mathématics, EPFL, 1015 Lausanne, Switzerland

Revised November 2000 Published February 2001

Abstract
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We consider hyperelastic stored energy functions in $\mathbb{R}^{n\times n}$ that are isotropic. We give necessary and sufficient conditions for the ellipticity of such functions. The present article is essentially a review of recent results on the subject.

Keywords: hyperelastic stored energy functions..

Mathematics Subject Classification: 83C4.

Citation: Bernard Dacorogna. Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 257-263. doi: 10.3934/dcdsb.2001.1.257

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