Contact problem of wearing elastic solid with thin coating (Q2759470)

A problem of contact between a rigid stamp and a half-space overlayed by a thin coating is considered. The stamp is moving along the surface thus producing wear of intensity proportional to the work of frictional forces (thermal effects are neglected). In the quasistatic formulation the problem is reduced to integration of biharmonic equation for the coating and static Lame equations under boundary conditions at interface and conditions of contact. A singular integral equation for the contact pressure is derived. For different values of parameters this equation models: (i) approximation of the Kirchhoff-Love plate theory; (ii) problem of wear of elastic half-plane, and (iii) the case of the Winkler elastic foundation. In the latter case a solution is sought in the form of a series in Chebyshev polynomials of the second kind. An infinite algebraic system for coefficients of series is derived. A numerical example is considered, plots of contact pressure are presented.