Analysis of a dynamic contact problem for electro-viscoelastic materials with tresca's friction

We consider a mathematical model which describes the dynamic process of contact between two electro-viscoelastic bodies with damage. The contact is bilateral and is modeled with Tresca's friction law. The damage of the materials caused by elastic deformations. We derive a variational formulation for the model which is in the form of a system involving the displacement field, the electric potential and the damage. Then we provide the existence of a unique weak solution to the model. We also study the finite element approximations of the problem and derive error estimates. Finally, we present numerical simulation results in the study of a two-dimensional example.