Plane contact problem for a prestressed incompressible elastic layer clamped along the base

The problem of a rigid punch penetration into the upper face of a layer is considered in the case of a homogeneous field of initial stresses. The model of isotropic incompressible nonlinearly elastic material determined by the Mooney potential is used. The case of rigid clamping of the layer along its lower face is considered under the assumption that the additional stresses caused by the penetrating punch are small compared with the initial ones. This assumption allows one to linearize the problem of determining the additional stresses. This problem is then reduced to solving an integral equations of the first kind with a difference kernel which allows one to determine the pressure in the contact region. An asymptotic solution is constructed for large values of the parameter characterizing the relative thickness of the layer. Amodified Multhopp-Kalandiyamethod is also used to obtain a solution for a wider range of the parameter.