Quasistatic frictional wear in electro-elasto-viscoplastic materials with unilateral constraints

We investigate a mathematical model for wear-induced quasistatic frictional contact between a moving foundation and a piezoelectric body. Archard’s law governs the evolution of the wear function. Takingdamage effects into account, the electro-elasto-viscoplastic constitutive law is used. In order to accountfor foundation wear, the model takes into consideration both a regularized Coulomb’s law of dry frictionand a normal compliance condition with unilateral constraints. A parabolic inclusion with homogeneousNeumann boundary conditions describes the evolution of damage. We provide a variational formulation for the model, which is represented as a system that includes the wear field, damage field, electric potential field,and displacement field. Arguments based on differential equations, elliptic variational inequalities, parabolicinequalities, and the Banach fixed point theorem have been used to demonstrate the existence and uniquenessof a result.