Rate-independent damage in thermo-viscoelastic materials with inertia

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Date
2014
Volume
2025
Issue
Journal
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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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.

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Keywords
Partial damage, rate-independent systems, elastodynamics, phase-field models, heat equation, energetic solutions, local solutions
Citation
Lazzaroni, G., Rossi, R., Thomas, M., & Toader, R. (2014). Rate-independent damage in thermo-viscoelastic materials with inertia (Vol. 2025). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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