Calculus of Variations and Geometric Measure Theory

G. Lazzaroni - R. Rossi - M. Thomas - R. Toader

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

created by lazzaroni on 21 Oct 2014
modified on 13 Jul 2016


Published Paper

Inserted: 21 oct 2014
Last Updated: 13 jul 2016

Journal: Journal of Physics: Conference Series
Volume: 727
Pages: 012009
Year: 2016

Preprint SISSA 53$/$2014$/$MATE

Proceedings of MURPHYS-HSFS-2014


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 Roubicek (Math. Methods Appl. Sci. 32 825–862, 2009, and SIAM J. Math. Anal. 40 256–297, 2010) with the methods from Lazzaroni-Rossi-Thomas-Toader (WIAS-Preprint 2025, 2014). The present analysis encompasses, differently from Roubicek 2010, the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike Lazzaroni-Rossi-Thomas-Toader 2014, a nonconstant heat capacity and a time-dependent Dirichlet loading.