Analysis of a frictional contact problem with wear and damage between two thermo-viscoelastic bodies

We consider a mathematical model which describes the bilateral contact problem with wear and damage between two thermo-viscoelastic bodies. The contact is frictional and bilateral, which results in the wear and damage of the contacting surface. The evolution of the wear function is described by Archard’s law. The evolution of the damage is described by a differential inclusion of parabolic type. We establish a variational formulation for the model and we prove the existence of a unique weak solution. The proof is based on a classical existence and uniqueness result for parabolic inequalities, the theory of differential equations and a fixed point argument.