Solution to contact problem between an elastic body and a rigid base covered with a layer of deformable material

A contact problem for an elastic body with a base covered with a deformable layer is studied. The layer is rigid-elastic, i.e., it begins to deform when the yield strength is reached and exerts the normal pressure on the body, which depends on the penetration of the body into the layer. For the rigid base, the Signorini condition is used. The existence of a solution to the problem is proved using weak Schauder's fixed-point theorem. The results of numerical simulation using the finite element method are presented.