Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case

Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff

We show that in the two-dimensional case, every objective, isotropic and isochoric energy function which is rank-one convex on ${\mathrm{GL}}^{+}(2)$ is already polyconvex on $\mathrm{…