Dynamic thermoviscoelastic problem with friction and damage. (February 2015)

• Record Type: Journal Article
• Authors: Gasiński, Leszek; Ochal, Anna
• Is Part Of: Nonlinear analysis. Volume 21(2015)
• Page Start: 63
• Page End: 75
• Publication Date: 2015-02
• Subjects: Nonlinear thermoviscoelastic material -- Subdifferential frictional condition -- Damage -- Temperature -- Variational inequality -- Hemivariational inequality; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.06.004
• Languages: English
• ISSNs: 1468-1218

Abstract

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.