Multiple scales and Gamma limits in rate-independent material models

Many rate-independent evolution systems can be described by an energy strorage functional and a dissipation functional. Thus, there is a similar geometric structure like in gradient flows; but now the dissipation is positively homogeneous of degree 1 and not 2 like for gradient flows. These functionals may depend on small parameters, for instance due to a periodic inhomogeneities, singular perturbations, regularizing terms or due to numerical discretization. We present abstract conditions that guarantee the convergence of solutions of these problems for the parameter going to 0 to the solutions associated with the limit functionals obtained as suitable Gamma limits. Application to a two-scale homogenization for elastoplasticity is discussed. (The talk is based on joint work with Michael Ortiz, Ulisse Stefanelli, Tomas Roubicek and Aida Timofte.)