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.
Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics / Lazzaroni, Giuliano; Rossi, Riccarda; Thomas, Marita; Toader, Rodica. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - STAMPA. - 727:(2016), pp. 012009-012009. (Intervento presentato al convegno 7th International Workshop on MUlti-Rate Processes and HYSteresis, MURPHYS 2014 in conjunction with the 2nd International Workshop on Hysteresis and Slow-Fast Systems, HSFS 2014 tenutosi a Weierstrass Institute for Applied Analysis and Stochastics (WIAS), deu nel 2014) [10.1088/1742-6596/727/1/012009].
Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics
Lazzaroni, Giuliano;
2016
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 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.
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