A dynamic contact model for viscoelastic plates

We introduce a mathematical model that describes the evolution of a viscoelastic plate in frictionless contact with a deformable foundation. The process is dynamic, the contact is with normal compliance and is modelled with a subdifferentiable boundary condition. We derive a variational formulation of the problem which has the form of a second-order evolutionary hemivariational inequality for the displacement field. Then, we establish the existence of a weak solution to the model.