Contact interaction of two elastic half spaces with circular groove

Abstract

We present the method of functions of intercontact gaps extended to axially symmetric contact problems for two half spaces one of which contains a circular surface groove. This approach is based on the construction of integral representations for the displacements and stresses in each body of the contact couple via the functions defined in an unknown (but bounded) region of the contact interface. In the analyzed case of frictionless contact of the half spaces, the integral representations contain a single unknown function, namely, the height of the gap. As examples, the analytic solutions are obtained for some shapes of the initial groove. Thus, for some shapes of the groove, the normal contact stresses exhibit peaks at the point corresponding to the edge of the initial defect. The indicated feature of the distribution of stresses is discussed.