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arXiv · 2004.10287

Hidden convexity in a problem of nonlinear elasticity

Nassif Ghoussoub·Young-Heon Kim·Hugo Lavenant·Aaron Zeff Palmer
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Abstract

We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation of the problem together with its dual formulation, based on measure-valued mappings, which coincides with the original problem under our condition.

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Nassif Ghoussoub, Young-Heon Kim, Hugo Lavenant, Aaron Zeff Palmer. 2020-04-21. Hidden convexity in a problem of nonlinear elasticity. https://arxiv.org/abs/2004.10287

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