Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

Abstract

This paper studies a receding contact problem of a functionally graded layer laminate pressed against a functionally graded coated homogeneous half-plane substrate by a rigid flat indenter. The shear modulus of the functionally graded materials with a constant Poisson’s ratio is modeled by an exponential function which varies along the thickness direction. Both the governing equations and the boundary conditions of the receding contact problem are converted into a pair of singular integral equations using the Fourier integral transforms, which are numerically integrated by the Chebyshev–Gauss quadrature. The contact pressure and the contact size at both contact interfaces are eventually obtained iteratively, as developed from the steepest descent algorithm. Extensive parametric studies suggest that it is possible to regulate the contact pressure and contact size by constructing the top layer from a soft functionally graded material.