On the frictional receding contact problem of functionally graded orthotropic–isotropic layered systems

In this study, the receding contact problem for a layered system composed of an upper orthotropic layer and a lower isotropic layer—both functionally graded—is investigated within the framework of linear elasticity theory. An advanced contact interaction is considered between the load-transmitting rigid punch and the orthotropic functionally graded layer. The weight of the layers is neglected, whereas frictional effects at the contact interfaces are included. The elastic stiffness constants of both the orthotropic and isotropic functionally graded layers are assumed to vary exponentially through the thickness, while Poisson’s ratios remain constant. By applying the Fourier transform and enforcing the boundary conditions, a system of singular integral equations of the second kind is derived and subsequently solved numerically using the Gauss–Jacobi integration method. Finite element solutions are obtained to validate the study. The influence of key parameters—such as the friction coefficient, inhomogeneity parameters, indentation load, punch radius, and material properties—on the contact widths and contact stress distributions is examined. The results provide insight into the mechanical behavior of functionally graded layered structures under frictional receding contact conditions.