Hemivariational inequalities modeling dynamic contact problems with adhesion

This paper deals with the mathematical modelling of viscoelastic frictional contact processes in mechanics which involve adhesion. The model consists of a coupled system of the hemivariational inequality of hyperbolic type for the displacement and the ordinary differential equation for the bonding field. The frictional forces are derived from nonconvex superpotentials through the generalized Clarke subdifferential. The properties of the body are described by a modified Kelvin–Voigt constitutive law. The existence of weak solution to the problem is proved by embedding it into a class of second order evolution inclusions and by applying a surjectivity result for multivalued pseudomonotone operators. We also establish a result on the regularity of weak solution to the model. Finally, examples of subdifferential boundary conditions which include the functions of d.c. type are provided.