Frictional Contact Mechanics for a Functionally Graded Porous Materials

Abstract

Abstract This paper investigates the plane sliding contact problem of a functionally graded (FG) porous layer pressed by a rigid flat punch analytically. According to the actual behavior of the contact, the friction effect between the punch and the FG porous layer is considered. It is assumed that it is completely bonded to the rigid base from the lower surface of the porous layer. With the help of the Fourier transform, the governing equations were reduced to ordinary differential equations, and the expressions for the general stress displacement and the change in the volume fraction of the pores were derived. Using the problem's boundary conditions, the contact problem is reduced to a Cauchy-type singular integral equation of the second kind where the contact stress and the contact widths under the punch are unknown. The Gauss-Jacobi integration formula is utilized for the numerical solution of the singular integral equation. Numerical results for contact and in-plane stresses under the rigid punch are presented for various parameters as graphs.