Variational analysis of unilateral contact problem for thermo-piezoelectric materials with friction

This paper deals with the mathematical analysis of quasi-static unilateral contact problem with friction between a thermo-piezoelectric body and a conductive foundation. The material is assumed to have thermo-electro-elastic behavior and the contact is modeled by the Signorini’s law, the condition of dry friction and a regularized electrical conductivity condition. The effects of frictional heating and thermal conductivity on the mechanisms of material are taken into account. To prove the existence of a weak solution to the problem, an incremental formulation obtained by using an implicit time scheme is studied. Several estimates on the incremental solutions are given, which allow us to pass to the limit by using compactness results.