Numerical solution of the dynamic contact problem of elasto-plastic bodies

A plane dynamic problem of solid mechanics is considered. Basic relations for elastic and elasto-plastic materials are given. A finite element method for numerical solution of the problem is described, various time discretization schemes are presented. The dynamic contact problem formulation is given, a version of the Schwarz iterative method is proposed for its solution. The results of numerical solution for three test contact problems are shown: the problem of collision of two elastic rods and the problems of contact between two pipes in elastic and elastoplastic formulations (for the cross section). The convergence of the used Schwarz method is demonstrated on an example of calculation on refining grids.