Numerical analysis of a dynamic viscoplastic contact problem

In this paper, we study a dynamic contact problem with Clarke subdifferential boundary conditions. The material is assumed to be viscoplastic which has an implicit expression of the stress field in constitutive law. weak form model governed by evolutionary hemivariational inequality coupled integral equation. We fully discrete approximation scheme and bound errors. Under appropriate solution regularity assumptions, optimal-order error estimates can derived. Finally, numerical example also included support our theoretical analysis. Particularly, it gives evidence on theoretically predicted optimal convergence order.