The axisymmetric double contact problem for a frictionless elastic layer

The general axisymmetric double contact problem for an elastic layer pressed against a half space by an elastic stamp is considered. The problem is solved under the assumptions that the three materials have different elastic properties, the contact along the interfaces is frictionless and only compressive normal tractions can be transmitted across the interfaces, and, in the case of the elastic stamp, the local radius of curvature of the stamp is large compared to the stamp-layer contact radius. The problem is reduced to a system of singular integral equations in which the contact pressures are the unknown functions. The solution is obtained and extensive numerical results are given for three stamp geometries, namely, rigid and elastic spherical stamps, and a flat-ended rigid cylindrical stamp. The results show that in the case of a flat-ended rigid cylindrical stamp the radius b of the contact area between the layer and the subspace is independent of the magnitude P of the total transmitted load and in all other cases b will depend on P.