Contact of the Stamp with an Elastic Half-Plane. Comparative Analysis of Models Accounting for Friction Between Them

A solution to the contact problem for a rigid stamp with a flat base indented into an elastic half-plane with friction. The friction is described by different models. Two of the models assume adhesion between the half-plane and the stamp in the central part of the contact zone and sliding at its edges. In one of the models it is assumed that in sliding zones there are tangential stresses proportional to the contact pressure, and in the other model these stresses are considered constant. In the third model, it is assumed that within the entire contact zone the tangential stresses are proportional to the contact pressure, but with a coefficient that varies linearly with the coordinate. Given the same input data, a numerical analysis of the problem was carried out using the three indicated models. The graphs of the numerical data allow for a comparative analysis of the results obtained for three friction models is presented.