Analytical Aspects of Relaxation in Crystal Plasticity

Carolin Klust
University Regensburg

Abstract: Modern mathematical models in plasticity lead to nonconvex variational problems, for which the standard methods of the calculus of variations are not applicable. In this contribution a geometrically nonlinear model for crystal elastoplasticity in two dimensions with one active slip system is considered. Instead of using the simplified assumption of rigid elasticity, we admit a finite energy that penalizes elastic deformations that are different form rigid body rotations. The main question is whether the rigid case is a good approximation to the one with elastic energy, if the yield stress is small compared to the elastic constants. It is shown that in the model without hardening the macroscopic energy is trivial, i.e. it vanishes identically on the set of interest. On the other hand good approximations can be achieved, when linear hardening is included into the model.