Self-Consistency Conditions in Static Three-Body Elastic Tangential Contact

The contact problem for an elastic third-body particle between two elastic half-spaces is considered. The contact is assumed to consist of three Hertzian contact spots. The normal and tangential contact problems are analyzed analytically considering partial slip in the contacts and the influence of third-body weight. Self-consistency conditions between global equilibrium and the contact solution are formulated to give criteria, under which circumstances static slip and stationary sliding are possible states for the third-body particle. The sliding case is solved in detail.