Rate-independent damage in thermo-viscoelastic materials with inertia
- Lazzaroni, Giuliano
- Rossi, Riccarda
- Thomas, Marita
- Toader, Rodica
2010 Mathematics Subject Classification
- 35Q74 74H20 74R05 74C05 74F05
- Partial damage, rate-independent systems, elastodynamics, phase-field models, heat equation, energetic solutions, local solutions
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.
- J. Dynam. Differential Equations, 30 (2018), pp. 1311--1364, DOI 10.1007/s10884-018-9666-y .