Relaxation in multi-mode plasticity with a rate-potential

The energy criterion of path stability for incremental nonlinear materials with rate potential (J. Mech. Phys. Solids 40 (1992) 1227) is applied to multi-mode plasticity. Due to the corner effect, the quasi-convexity of the rate potential can be violated, while it is still bounded from below. A simple example shows that a check of the acoustic tensor on the fundamental path is not sufficient in that case. The problem is relaxed by approximate sequential lamination computed on a grid (SIAM J. Numer. Anal. 36 (1999) 1621) using the monotone chain algorithm (Inform. Proc. Lett. 9 (1979) 216) on discrete rank-one-directions, resulting in the discrete Young measure of the equivalent bifurcated solutions.