Adhesive contact between a rigid sticky sphere and an elastic half space

The adhesive contact between a solid sphere and an elastic half space has been treated by Johnson, Kendall, and Roberts (JKR) for zero interfacial friction (slip boundary condition). The result is the famous JKR theory, which is now widely used. However, in the real situation, the interfacial friction may not be negligible especially when the contact is adhesive. A solution corresponding to the infinite interfacial friction (stick boundary condition) is derived in this paper. The results show that the effect of interfacial friction depends on the Poisson ratio of the elastic half space. For an incompressible half space, the two solutions are identical. These two solutions can be thought of as the lower and upper bonds for the general case of finite interfacial friction.