We consider the dynamic process of an elastic body in unilateral frictional contact with a rigid foundation. Friction is modelled with the Coulomb law with a coefficient that depends on the slip velocity. To allow for velocity discontinuities we use the elastodynamic (hyperbolic) framework. Nevertheless, this does not lead to a well-posed problem. To remedy this, we perturb the solution of the elastodynamic problem in a thin layer next to the contact boundary. This is a generalisation of an approach previously studied in a one-dimensional case. We establish existence and uniqueness results for the perturbed and regularised problem and provide an interpretation of this perturbation.