Published Paper

Inserted: 14 oct 2014
Last Updated: 9 mar 2022

Journal: J. Dynam. Differential Equations
Volume: 30
Pages: 1311-1364
Year: 2018
Doi: 10.1007/s10884-018-9666-y

Preprint SISSA 52$/$2014$/$MATE

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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: elastodynamics, Heat equation, rate-independent systems, energetic solutions, Partial damage, Phase-field models, Local solutions

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