Numerical analysis of a viscoplastic contact problem with normal compliance, unilateral constraint, memory term and friction

In this paper, we consider a model which describes the quasistatic contact between a viscoplastic body and a foundation. The material’s behavior is modeled with a rate-type viscoplastic constitutive law with an internal state variable. The contact is modeled with normal compliance, unilateral constraint, memory term, and friction which is under a total slip-dependent version of Coulomb’s law. For the weak formulation of the problem, which is in the form of a system coupling two nonlinear integral equations with a history-dependent variational–hemivariational inequality, we introduce a fully discrete scheme and derive an error estimate. Under appropriate regularity assumptions, we obtain an optimal-order error estimate in finite element spaces. Finally, numerical results are reported to show the performance of the numerical method