Finite element approximation and numerical analysis of thermoelectroelastic frictional contact problem with frictional heating

In this paper, we consider a static frictional contact problem including frictional heat generation and heat transfer across the contact surface. The contacting body is modeled by a linear thermo-electroelastic constitutive law and a heat conductor and electrically insulator foundation. The contact is modeled with Signorini's conditions, Tresca's friction law combined with regularized conditions for frictional heating and heat transfer across the contact interface. Under appropriate hypotheses, an existence and uniqueness result is proved, error estimates and a finite element approximation are derived. Moreover, a successive iteration technique is used to solve numerically the thermo-electroelastic problem and a convergence result is established. Finally, the obtained results are illustrated by a numerical example.