WIAS Preprint No. 2025, (2014)

Rate-independent damage in thermo-viscoelastic materials with inertia


  • Lazzaroni, Giuliano
  • Rossi, Riccarda
    ORCID: 0000-0002-7808-0261
  • Thomas, Marita
    ORCID: 0000-0001-6771-0742
  • 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.

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