Dynamic thermoviscoelastic problem with friction and damage |
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| Institution: | 1. CWI – Centrum Wiskunde & Informatica, Amsterdam, the Netherlands;2. Faculty of Aerospace Engineering, Delft University of Technology, Delft, the Netherlands;3. DIAM, Delft University of Technology, Delft, the Netherlands;1. Institute of Mathematics, University of Kassel, Heinrich-Plett Str. 40, 34132 Kassel, Germany;2. DICATAM–Sezione di Matematica, University of Brescia, Via Valotti 9, 25133 Brescia, Italy;3. Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy |
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| Abstract: | In this paper we present a model of dynamic frictional contact between a thermoviscoelastic body and a foundation. The thermoviscoelastic constitutive law includes a temperature effect described by the parabolic equation with the subdifferential boundary condition and a damage effect described by the parabolic inclusion with the homogeneous Neumann boundary condition. Contact is modeled with bilateral condition and is associated to a subdifferential frictional law. The variational formulation of the problem leads to a system of hyperbolic hemivariational inequality for the displacement, parabolic hemivariational inequality for the temperature and parabolic variational inequality for the damage. The existence of a unique weak solution is proved by using recent results from the theory of hemivariational inequalities, variational inequalities, and a fixed point argument. |
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| Keywords: | Nonlinear thermoviscoelastic material Subdifferential frictional condition Damage Temperature Variational inequality Hemivariational inequality |
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