<p>In this paper, our main goal is to study a new mathematical model which describes the frictional contact between a foundation and a deformable body which is composed of viscoplastic materials and where the process is considered dynamic. The contact condition on the normal plane is modeled by a unilateral constraint condition for a version of normal velocity in which the memory effect and the adhesion are considered. On the tangential plane a frictional contact condition is governed by the Clarke subdifferential of a locally Lipschitz function, and the evolution of the bonding field is governed by an ordinary differential equation. We formulate this problem as coupled system that consists of two ordinary differential equations and a variational-hemivariational inequality. Then, the existence, uniqueness and continuous dependence of the solution on the data results concerning the abstract system are established. Finally, we use the abstract results to show the existence and uniqueness of the solution to the contact problem.</p>