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Description:
We develop a global-in-time variational approach to the time-discretization of rate-independent processes. In particular, we investigate a discrete versionof the variational prin-ciple based on theweighted energy-dissipation functionalintroduced in [13]. We prove theconditional convergence of time-discrete approximate minimizers to energetic solutions of thetime-continuous problem. Moreover, the convergence result is combined with approximationand relaxation. For a fixed partition the functional is shown to have an asymptotic developmentby€-convergence (cf. [1]) in the limit of vanishing viscosity.