Infinite-order laminates in a model in crystal plasticity

Zusammenfassung

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-1 convex envelope of the condensed energy density is obtained by infinite-order laminates, and express it explicitly via the (2)F(1) hypergeometric function. We also determine the polyconvex envelope, leading to upper and lower bounds to the quasiconvex envelope. The two bounds differ by less than 2%.