Balanced-Viscosity solutions to infinite-dimensional multi-rate systems

Abstract

We consider generalized gradient systems with rate-independent and rate-dependent dissipation potentials. We provide a general framework for performing a vanishing-viscosity limit leading to the notion of parametrized and true Balanced-Viscosity solutions that include a precise description of the jump behavior developing in this limit. Distinguishing an elastic variable u having a viscous damping with relaxation time epsalpha and an internal variable z with relaxation time eps we obtain different limits for the three cases alphain(0,1), alpha=1 and alpha>1. An application to a delamination problem shows that the theory is general enough to treat nontrivial models in continuum mechanics.