About some singularities of contact interaction of a stamp and an elastic layer in presence of friction forces in the contact area

Abstract

Two plane contact problems about interaction of a stamp with a flat foundation and an elastic layer in presence of the Coulomb friction forces in the contact area are investigated by the asymptotic method of large $\lambda$. The lower bound of the layer is either fixed, or there are no normal displacements and tangential stresses, while normal and tangential forces act on the stamp; the stamp-layer system is under the conditions of limit equilibrium, and the stamp does not turn during deformation of the layer.

The results obtained describe the action of geometric and mechanical parameters of the problems on the form of a deformed surface of the layer outside the contact area; the diagram of contact stresses and their moment has been drawn up taking into account friction forces in the contact area.