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Author: Mielke, Alexander × Subject: balanced-viscosity solutions × Subject: rate-independent systems ×

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    Variational approaches and methods for dissipative material models with multiple scales
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Mielke, Alexander
    In a first part we consider evolutionary systems given as generalized gradient systems and discuss various variational principles that can be used to construct solutions for a given system or to derive the limit dynamics for multiscale problems. These multiscale limits are formulated in the theory of evolutionary Gamma-convergence. On the one hand we consider the a family of viscous gradient system with quadratic dissipation potentials and a wiggly energy landscape that converge to a rate-independent system. On the other hand we show how the concept of Balanced-Viscosity solution arise as in the vanishing-viscosity limit. As applications we discuss, first, the evolution of laminate microstructures in finite-strain elastoplasticity and, second, a two-phase model for shape-memory materials, where H-measures are used to construct the mutual recovery sequences needed in the existence theory.