Analysis of a Frictional Unilateral Contact Problem for Piezoelectric Materials with Long-Term Memory and Adhesion

摘要

This paper deals with the study of a mathematical model that describes a frictionalcontact between a piezoelectric body and an obstacle. The material behavior is described with anelectro-elastic constitutive law with long memory and the contact is modelled with Signorini conditionsassociated with the non-local friction law in which the adhesion between the contact surfaces is takeninto account. We establish a variational formulation of the model in the form of a system involving thedisplacement, stress, electric displacement, electric potential and adhesion field. Under the assumptionthat the coefficient of friction is small enough, we prove the existence of a unique weak solution to theproblem. The proof is based on arguments of variational inequalities, nonlinear evolutionary equationswith monotone operators, differential equations and the Banach fixed-point theorem.