WIAS Preprint No. 2128, (2015)

Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics


Authors

  • Lazzaroni, Giuliano
  • Rossi, Riccarda
    ORCID: 0000-0002-7808-0261
  • Thomas, Marita
    ORCID: 0000-0001-9172-014X
  • Toader, Rodica

2010 Mathematics Subject Classification

  • 35Q74 74H20 74R05 74C05 74F05

Keywords

  • Partial damage, rate-independent systems, elastodynamics, phase-field models, heat equation, energetic solutions

DOI

10.20347/WIAS.PREPRINT.2128

Abstract

This note deals with the analysis of a model for partial damage, where the rate-independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from [Roubiček M2AS'09, SIAM'10] with the methods from Lazzaroni/Rossi/Thomas/Toader [WIAS Preprint 2025]. The present analysis encompasses, differently from [Roubiček SIAM'10], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [WIAS Preprint 2025], a nonconstant heat capacity and a time-dependent Dirichlet loading.

Appeared in

  • MURPHYS-HSFS-2014: 7th International Workshop on MUlti-Rate Processes and HYSteresis (MURPHYS) & 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS), O. Klein, M. Dimian, P. Gurevich, D. Knees, D. Rachinskii, S. Tikhomirov, eds., vol. 727 of Journal of Physics: Conference Series, IOP Publishing, 2016, pp. 012009/1--012009/20.

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