A Unified Treatment of Axisymmetric Adhesive Contact on a Power Law Graded Elastic Half Space

Abstract

In the present paper, axisymmetric frictionless adhesive contact between a rigid punch and a powerlaw graded elastic halfspace is analytically investigated with use of Betti's reciprocity theorem and the generalized Abel transformation, a set of general closedform solutions are derived to the Hertzian contact and Johnson–Kendall–Roberts (JKR)type adhesive contact problems for an arbitrary punch profile within a circular contact region. These solutions provide analytical expressions of the surface stress, deformation fields, and equilibrium relations among the applied load, indentation depth, and contact radius. Based on these results, we then examine the combined effects of material inhomogeneities and punch surface morphologies on the adhesion behaviors of the considered contact system. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials and the Gibson soil as special cases and, therefore, can also serve as the benchmarks for checking the validity of the numerical solution methods.