This talk is devoted to the analysis of systems coupling
rate-independent processes with rate-dependent
ones and inertial effects in a general framework. A notion of solution
combining ideas used for
generalized gradient flows and energetic solutions of rate-independent
processes is introduced and existence
results are obtained via suitable minimizing movement schemes.   The
abstract results are applied to problems arising in damage, delamination
or plasticity. This is joint work with Riccarda Rossi (U Brescia).