Analytical Solution for an Elastic Sphere Indenting a Layered Half-Space

The contact problem for the elastic sphere indenting a layered half-space is considered. Analytical methods for solving this problem have been developed on the basis of the 3-D fundamental solution of a half space with a single coating layer under a normal concentrated force on the surface. The normal pressure distribution within the contact zone is assumed as Hertzian type. The solutions are constructed using superposition principle in the form of infinite series. Through comparing with the numerical results of FEM,it can be verified that the exact solutions have a rapid convergence rate and the stresses and displacements are mainly determined by the first term,which is corresponding to the solution of homogeneous half-space under Hertzian loading. The contact radius can be predicted applying the method.