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.