Hemivariational inequality approach to the dynamic viscoelastic sliding contact problem with wear

The dynamic contact problem of sliding contact with wear between a viscoelastic body and a foundation is formulated as a hemivariational inequality. The contact is modeled with a general normal damped response condition which is nonmonotone, possibly multivalued and has the subdifferential form. We establish the existence of weak solutions by using a surjectivity result for a class of pseudomonotone operators. We also deliver conditions under which the solution of the evolution inclusion associated with the hemivariational inequality is unique.