Rate-independent damage in thermo-viscoelastic materials with inertia
Abstract
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
Cite
@article{arxiv.1804.07902,
title = {Rate-independent damage in thermo-viscoelastic materials with inertia},
author = {Giuliano Lazzaroni and Riccarda Rossi and Marita Thomas and Rodica Toader},
journal= {arXiv preprint arXiv:1804.07902},
year = {2018}
}