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arXiv · 1609.01339

Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity

Ionel-Dumitrel Ghiba·Robert J. Martin·Patrizio Neff
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Abstract

We study convexity properties of energy functions in plane nonlinear elasticity of incompressible materials and show that rank-one convexity of an objective and isotropic elastic energy $W$ on the special linear group $\mathrm{SL}(2)$ implies the polyconvexity of $W$.

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Ionel-Dumitrel Ghiba, Robert J. Martin, Patrizio Neff. 2016-09-05. Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity. https://arxiv.org/abs/1609.01339

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