Rate-independent damage in thermo-viscoelastic materials with inertia
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Date
2014-10-15
Journal Title
Journal ISSN
Volume Title
Publisher
SISSA
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.
Description
Keywords
Partial damage, Rate-independent systems, Elastodynamics, Phase-field models, Heat equation, Energetic solutions, Local solutions