  This paper is concerned with an approximation scheme for rate-independent
systems governed by a non-smooth dissipation and a possibly non-convex energy
functional. The scheme is based on the local minimization scheme introduced in
[EM06], but relies on local stationarity of the underlying minimization
problem. Under the assumption of Mosco-convergence for the dissipation
functional, we show that accumulation points exist and are so-called
parametrized solutions of the rate-independent system. In particular, this
guarantees the existence of parametrized solutions for a rather general
setting. Afterwards, we apply the scheme to a model for the evolution of
damage.
