Stresses and Deformations in Elastic Layers Indented by a Conical Punch

Abstract

The numerical solutions to problems of the contact between an elastic layer in complete adhesion with a rigid foundation (bonded layer) or resting without friction on a rigid foundation (unbonded layer) and a frictionless rigid cone (conical punch) are presented. The present numerical scheme is a modification of that developed by the author for a smooth indenter profile. The modified analysis uses the Fejér method in order to eliminate completely the Gibbs phenomenon at the neighbourhood of the singularity. Calculations are performed to examine the effects of the layer thickness and/or the layer compressibility on the results. It was found that as the layer thickness was decreased then the contact pressure approaches a triangular form for unbonded layer and bonded layer with Poisson's ratio v < 0.5; for an incompressible layered surface (v = 0.5) the pressure gradient tends to zero at the contact ends. Moreover, the contact radius and the surface deformation depend not only on the layer thickness but are also influenced by the layer compressibility. The present method showed excellent agreement with the existing solutions when the layer becomes either a half-space or thin.