Receding contact problem for two-layer functionally graded media indented by a rigid punch

The present paper examines the plane strain receding frictionless contact problem of two functionally graded layers indented by a rigid cylindrical punch and with mismatched material properties at the interface. The shear moduli of the layers are assumed to vary in exponential form along the thickness direction and the Poisson’s ratios are taken as constant. With use of the Fourier integral transform, the governing equations are reduced to a system of two singular integral equations, in which the unknowns are the contact pressure and the contact widths. These integral equations are solved numerically using Gauss–Chebychev integration formulas. The main objective of this paper is to study the effect of the material inhomogeneity parameters and interface material property mismatch on the contact pressure and the size of the contact regions.