Balanced-Viscosity Solutions to Infinite-Dimensional Multi-Rate Systems

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 εα and an internal variable z with relaxation time ε we obtain different limits for the three cases α∈ (0 , 1) , α= 1 and α> 1 . An application to a delamination problem shows that the theory is general enough to treat nontrivial models in continuum mechanics.