A bilateral contact problem with nonlocal friction, damage and adhesion

We consider a bilateral contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The process is quasistatic and the contact is modelled with a general nonlocal friction law in which the adhesion of contact surfaces is taken into account. We derive a variational formulation of the problem and, under smallness assumptions, we establish an existence and uniqueness theorem of a weak solution, including a regularity result. We also study the dependence of the solution on the data.