Indentation of an elastic half-space reinforced with a functionally graded interlayer by a conical punch

An elastic half-space with a two-layered coating is considered. The upper layer is homogeneous while the lower layer is assumed to be made of a functionally graded material. Elastic moduli of the interlayer vary with depth according to arbitrary differentiable functions. The half-space is indented by a rigid conical punch. Approximated analytical expressions for the contact stresses are obtained using the bilateral asymptotic method. Expressions for the subsurface stresses and displacements are obtained in the form of some quadratures. Numerical results illustrating difference between the stress distributions for one- and two-layered coatings are presented