Analytical solution to contact problem on spherical indenter penetration into soft elastic layer

An efficient method for constructing an approximate analytical solution to the contact problem of the penetration of a spherical indenter into the soft elastic layer lying on a rigid elastic foundation is proposed. The method permits to obtain the problem solution effective for the full range of the problem characteristic geometrical and physical parameter values. Some cases when Young’s moduli of the layer and the substrate differ more than a hundredfold are analyzed. The obtained contact stresses for different values of the foundation stiffness are compared with the formerly known results for the nondeformable foundation case. It is shown that when the elastic properties of the layer and the substrate differ a hundredfold, maximum difference between these results is less than 3%. The relationship between the pressing force and the radius of the sphere is determined. The question is put owing to the control problem of the thin coatings elastic properties.