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Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case
We show that, in the two-dimensional case, every objective, isotropic and isochoric energy function that is rank-one convex on GL + (2) is already polyconvex on GL + (2). Thus, we answer in the negative Morrey's conjecture in the subclass of isochoric nonlinear energies, since polyconvexity implies quasi-convexity. Our methods …