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arXiv · 1508.05721

On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor

David Yang Gao·Patrizio Neff·Ionel Roventa·Christian Thiel
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Abstract

We present a sufficient condition under which a weak solution of the Euler-Lagrange equations in nonlinear elasticity is already a global minimizer of the corresponding elastic energy functional. This criterion is applicable to energies $W(F)=\widehat{W}(F^TF)=\widehat{W}(C)$ which are convex with respect to the right Cauchy-Green tensor $C=F^TF$, where $F$ denotes the gradient of deformation. Examples of such energies exhibiting a blow up for $\det F\to0$ are given.

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David Yang Gao, Patrizio Neff, Ionel Roventa, Christian Thiel. 2015-08-24. On the convexity of nonlinear elastic energies in the right Cauchy-Green tensor. https://arxiv.org/abs/1508.05721

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