a quasi-static contact problem with friction in electro viscoelasticity with long-term memory body with damage and thermal effects.

In this paper, we consider a mathematical model that describes the quasi-static process of contact between a piezo electric body and a deformable foundation. a nonlinear thermo-electro-viscoelastic constitutive law with long term memory and damage is used and the contact is described with the normal compliance condition and a version of coulomb’s law of friction. we derive variational formulation for the model which is in the form of a system involving the displacement field, the electric potential field, the temperature field and the damage field, existence and uniqueness of a weak solution of the problem is proved. the proof is based on arguments of time-dependent variational inequalities, parabolic inequalities, differential equations and fixed points.