Numerical analysis of a contact problem between two elastic–viscoplastic bodies with hardening and nonmatching meshes

Abstract

We consider a quasistatic frictionless contact problem between two elastic–viscoplastic bodies with strain hardening. The latter is modeled as an internal state variable which verifies an ordinary differential equation. We present a variational formulation of the problem and state an existence and uniqueness result. Then, we study a fully discrete approximation for the two-dimensional case using a nonconforming finite element method, based on the mortar projection operator for the approximation of the spatial variables, and the backward Euler's discretization for the time derivatives. The existence of a unique solution for this scheme is given and error estimates are derived. Finally, four numerical examples are presented.