Frictional slip of a rigid punch on an elastic half-plane

If a rigid punch is perfectly bonded to an elastic half-plane, the stress state possesses a well-known oscillating singularity. Because the shear and normal stresses are out of phase with each other, the application of a frictional slip model is expected to result in a slip zone at each of the corners. A solution exists in the literature if the punch is subjected to a normal load. It was shown that the extent of the slip zone is an eigenvalue which depends upon Poisson's ratio and the coefficient of friction, but is independent of the magnitude of the applied load. In this investigation, the extent of the slip zone as well as the slip displacement is determined from the perfect bond solution. The analysis is valid if the length of the slip zone is small compared with the punch width. However, the results are shown to be in excellent agreement with the solution in the literature even when the total length of the slip zones is equal to half of the punch width. A solution is then obtained for combined normal and tangential loading. This work, and its extensions, is expected to be applicable in the study of the mechanics of fretting.