A variational formulation of the wear contact problems for coated bodies

Abstract

Plane wear contact problems for an elastic half-plane with thin coating and a rigid punch are considered. A local (differential) setting of the wear contact problem assumes that actual contact areas are unknown in advance, may be multiple (discrete), and may change through wear. The thin coating is modelled by a Winkler-type layer. An additional normal displacement of a substrate surface is proportional to a local pressure. A variational approach to the problem is used. The variational formulation in the form of a system of an evolutionary variational inequality and an ordinary differential equation of first order is obtained. An explicit Euler scheme is used for the time discretization. A spatial discretization of the problems is made using spaces of integrated fundamental solutions. The boundary element method is applied to construct such spaces, whose elements satisfy homogeneous equilibrium equations and compatibility conditions.