  We deal with quasistatic evolution problems in plasticity with softening, in
the framework of small strain associative elastoplasticity. The presence of a
nonconvex term due to the softening phenomenon requires a nontrivial extension
of the variational framework for rate-independent problems to the case of a
nonconvex energy functional. We argue that, in this case, the use of global
minimizers in the corresponding incremental problems is not justified from the
mechanical point of view. Thus, we analize a different selection criterion for
the solutions of the quasistatic evolution problem, based on a viscous
approximation. This leads to a generalized formulation in terms of Young
measures, developed in the first part of the paper. In the second part we apply
our approach to some concrete examples.
