Mechanics of multilayered or functionally graded material pressed onto an imperfect rigid base with a circular opening by localized surface loading

Abstract

Loaded materials constrained by imperfect boundary can be found in many engineering scenarios, including blanking process, contact pressure sensor and soil/rock foundation subjected to underground mining. This paper examines the surface loading problem of a multilayered or functionally graded material (FGM) resting on an imperfect rigid smooth base weakened by a circular opening. The surface loading is axisymmetric and coaxial with the circular opening. This mixed boundary value problem is analogous to a Mode-I penny-shaped crack in multilayered elastic medium. With the aid of the GKS-based method for N-layered elasticity, the problem is formulated as a system of dual integral equations and then reduced to a Fredholm integral equation of the second kind. Solutions of the SIF, COD and full elastic field are expressed in terms of the solution of the integral equation. Numerical results obtained from the present solutions are compared with the those from finite element method. Using the new solutions, numerical studies are also conducted for four examples, including a homogenous layer, a multilayered material, a material with FGM coating and an asphalt pavement structure with FGM properties. These numerical results demonstrate that (1) a small size of surface loading can result in high SIF value at the crack tip; (2) placing the hard layer as the top surface is most effective for reducing ground settlement; (3) the gradation in Poisson’s ratio can have non-negligible effect on the SIF for thin FGM coating; (4) effect of the circular opening to the ground settlement can be significant if its radius is comparable to the total thickness of the upper layers.