Contact problem of two layers, one funtionally graded layer, loaded via rigid circular block and resting on a pasternak foundation

In this study, frictionless receding contact problem of two elastic layers which one is functionally graded material (FGM) resting on a Pasternak foundation is considered. The external load is applied to the homogeneous elastic layer by means of a circular rigid block and the functionally graded layer rests on a Pasternak foundation. The effect of gravity forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. Displacement and stress expressions for the layers are obtained using the theory of elasticity and integral transformation technique. By applying the boundary conditions for the problem, reduced to two integral equations in which the contact stresses and contact lengths are unknown. The system of integral equations is numerically solved by making use of appropriate Gauss Chebyshev integration formulas. The equilibrium conditions are satisfied in the solution and the contact stresses and contact distances related to the problem are obtained for various dimensionless quantities.