Investigation of the solution for discontinuous contact problem between a functionally graded (FG) layer and homogeneous half-space

In this study, the discontinuous contact problem between a functionally graded (FG) layer, which is loaded symmetrically with point load P through a rigid block, and a homogeneous half-space was solved using the theory of elasticity and integral transform techniques. The shear modulus and density of the layer addressed in the problem vary with an exponential function along with its height. The half-space is homogeneous, and no binder exists on the contact surface containing the FG layer. In the solution, the body force of the FG layer was considered, whereas that of the homogeneous half-space was neglected. The Poisson’s ratios of both the FG layer and homogeneous half-space were assumed to remain constant. Additionally, all the surfaces addressed in the problem were assumed to be frictionless. Using the theory of elasticity and integral transform techniques, the discontinuous contact problem was reduced to two integral equations, wherein the contact stress under the rigid block and the slope of the separation, which occurred at the interface of the FG layer and homogeneous half-space, are unknown. These integral equations were solved numerically for the flat condition of the rigid block profile using the Gauss–Chebyshev integration formula. Consequently, the stress distributions, start–end points of the separation region, and separation displacements between the FG layer and homogeneous half-space were obtained for various dimensionless quantities.