Inserted: 14 oct 2014
Last Updated: 9 mar 2022
Journal: J. Dynam. Differential Equations
Preprint SISSA 52$/$2014$/$MATE
We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is independent of temperature.
Keywords: elastodynamics, Heat equation, rate-independent systems, energetic solutions, Partial damage, Phase-field models, Local solutions