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 [1, 2] with the methods from Lazzaroni/Rossi/Thomas/Toader [3]. The present analysis encompasses, differently from [2], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [3], a nonconstant heat capacity and a time-dependent Dirichlet loading.
Highlights
This note deals with the analysis of a model for partial damage, where the rateindependent, 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
Energetic solutions for rate-independent processes coupled with rate-dependent effects In this note we discuss the existence of solutions for an evolutionary model of 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
We will further contribute to the analysis initiated in [2] by pointing out that the existence result therein can be extended to the case in which the evolution for the internal variable is unidirectional, as in the context of the damage model
Summary
We will further contribute to the analysis initiated in [2] by pointing out that the existence result therein can be extended to the case in which the evolution for the internal variable is unidirectional (i.e., monotone nonincreasing), as in the context of the damage model. We consider the solutions to carefully devised incremental problems and give the time-discrete version of the energetic formulation, consisting of the semistability, the weak momentum and enthalpy equations, and the (discrete) mechanical and total energy inequalities.
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