Abstract
AbstractWe show that in the two‐dimensional case, every objective, isotropic and isochoric energy function which is rank‐one convex on GL+(2) is already polyconvex on GL+(2). Thus we negatively answer Morrey's conjecture in the subclass of isochoric nonlinear energies, since polyconvexity implies quasiconvexity. Our methods are based on different representation formulae for objective and isotropic functions in general as well as for isochoric functions in particular. We also state criteria for these convexity conditions in terms of the deviatoric part of the logarithmic strain tensor. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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