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

Bernard Dacorogna

doi:10.3934/dcdsb.2001.1.257

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2001, Volume 1, Issue 2: 257-263. Doi: 10.3934/dcdsb.2001.1.257

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

Bernard Dacorogna^1,

1.
Department of Mathématics, EPFL, 1015 Lausanne

Revised: October 31, 2000

Published: April 2001

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Abstract

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: 83C40.

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