Abstract
This work uses the energetic formulation of rate-independent systems that is based on the stored-energy functionals E and the dissipation distance D. For sequences (E_k) and (D_k) we address the question under which conditions the limits q of solutions q_k satisfy a suitable limit problem with limit functionals E and D, which are the corresponding Gamma-limits.
We derive a sufficient condition, which is essential to guarantee that q solves the limit problem. In particular, this condition holds if certain joint recovery sequences exist.
Moreover, we show that time-incremental minimization problems can be used to approximate the solutions. A first example involves the numerical approximation of functionals using finite-element spaces. A second example shows that the stop and the play operator convergece if the yield sets converge in the sense of Mosco.
The third example deals with a problem developing microstructure in the limit.