Analysis and Numerical Approximation of an Electro-Elastic Frictional Contact Problem

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and a conductive foundation. A non linear electro-elastic constitutive law is used to model the piezoelectric material. The unilateral contact is modelled using the Signorini condition, nonlocal Coulomb friction law with slip dependent friction coefficient and a regularized electrical conductivity condition. Existence and uniqueness of a weak solution is established. A finite elements approximation of the problem is presented, a priori error estimates of the solutions are derived and a convergent successive iteration technique is proposed.