Balanced-Viscosity solutions to infinite-dimensional multi-rate systems
- Mielke, Alexander
- Rossi, Riccarda
2020 Mathematics Subject Classification
- 35Q74 47J30 49J40 49J45 49J52 74D10 74R99
- Balanced-Viscosity solution, reparametrized solutions, energy-dissipation principle, generalized gradient systems, delamination model
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 $eps^alpha$ and an internal variable $z$ with relaxation time $eps$ we obtain different limits for the three cases $alpha in (0,1)$, $alpha=1$ and $alpha>1$. An application to a delamination problem shows that the theory is general enough to treat nontrivial models in continuum mechanics.