Problems Involving a Receding Contact Between a Layer and a Half Space

Abstract

The work reconsiders the smooth receding contact between an elastic layer and a half space when the two bodies are pressed together. The analysis leads to a Fredholm integral equation of the second kind for an auxiliary function that is directly related to the contact pressure. An unexpected result is that the integral equation is homogeneous, and that finding the extent of contact can be viewed as an eigenvalue problem. The integral equation can be solved numerically to any required degree of accuracy, and the extent of contact and the contact pressure are computed for concentrated and uniformly distributed loads in both plane and axisymmetric problems. The present analysis confirms the results of Weitsman rather than Pu and Hussain over a wide range of mismatch in the elastic constants.