Variational descriptions of wearing out solids and wear particles in contact mechanics

Experimental studies demonstrated the central role played by wear particles in sliding contacts. In this contribution, the classical variational formulation of contact problems is extended to wearing out solids by including the interfacial layer of wear debris between contacting bodies. Variational formulations are developed starting from strong forms of governing relations for the wearing solids and the layer. An implementation of a finite element representation of the contact problem is presented. The Lagrange multiplier method is applied to determine contact forces and to satisfy kinematic contact constraints. Discretized forms of the variational functionals lead to equations which can be useful in numerical analysis.