Infinite-order laminates in a model in crystal plasticity

We consider a geometrically nonlinear model for crystal plasticity in two dimensions, with two active slip systems and rigid elasticity. We prove that the rank-one convex envelope of the condensed energy density is obtained by infinite-order laminates. We also determine the polyconvex envelope, leading to anupper and a lower bound on the quasiconvex envelope. The two bounds differ by less than 2%. We finally investigate the immpact of elastic approximations of the model.

This is joint work with Nathan Albin and Sergio Conti.