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Mathematics > Analysis of PDEs

arXiv:1804.07902 (math)
[Submitted on 21 Apr 2018]

Title:Rate-independent damage in thermo-viscoelastic materials with inertia

Authors:Giuliano Lazzaroni, Riccarda Rossi, Marita Thomas, Rodica Toader
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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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.07902 [math.AP]
  (or arXiv:1804.07902v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.07902
Related DOI: https://doi.org/10.1007/s10884-018-9666-y

Submission history

From: Riccarda Rossi [view email]
[v1] Sat, 21 Apr 2018 06:50:40 UTC (70 KB)
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