On the Signorini’s Contact Problem with Non-local Coulomb’s Friction in Thermo-Piezoelectricity

Abstract

This paper deals with the quasi-static frictional contact problem between a thermo-piezoelectric body and a rigid foundation. The body’s material is modelled with a linear thermo–electro-elastic constitutive laws. The contact is described with a temperature depends Signorini conditions and a version of Coulomb’s friction law with slip dependent coefficient of friction. We derive a variational formulation for the model, it is a coupled system for the displacements, the electric potential and the temperature. We then prove, under some smallness assumptions of the friction coefficient, existence of weak solution to the problem. Finally, we study the continuous dependence of solutions on friction coefficient and on displacement and temperature initial data.