Rank-one convexity implies polyconvexity in isotropic planar\n incompressible elasticity

2016/09/05 by Ionel‐Dumitrel Ghiba, Ghiba, Ionel-Dumitrel, Robert J. Martin +3
Engineering · Computer Science · #Elasticity and Material Modeling #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics

paper · pdf · doi:10.48550/arxiv.1609.01339

Abstract

We study convexity properties of energy functions in plane nonlinear\nelasticity of incompressible materials and show that rank-one convexity of an\nobjective and isotropic elastic energy W on the special linear group\n\SL(2) implies the polyconvexity of W.\n

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