Contact between an elastic half-plane and a partly separated stamp (Q579050)

Problems for an elastic half-plane in contact with a stamp (or stamps) partly with full coupling, partly in contact with slippage, are considered. The problems reduce to the combined Dirichlet-Riemann boundary value problem and can, in general, be solved in quadratures. Solutions of homogeneous problems are given in terms of elementary functions. All combinations of the geometrical, force and other parameters at which contact with slippage occurs in a single region are shown, formulas showing the extent of the zones of smooth adhesion of the separated layers of the contacting bodies are given, and stress intensity coefficients are found for the cracks where separation into layers occurs and at the stamp edges.