A Contact Stress Problem for a Rigid Smooth Sphere in an Extended Elastic Solid

Abstract

A three-dimensional axisymmetric elasticity problem pertaining to the contact stresses between a smooth rigid sphere and an infinite elastic solid with a smooth spherical cavity of the same diameter has been considered. Uniaxial loading is applied to the solid at infinity, resulting in a separation along a portion of the boundary between the sphere and the solid. The problem has been considered as a mixed boundary-value problem of elasticity. The angle of contact and the stress distributions along the contact surface are determined by solving a set of dual-series equations associated with Legendre polynomials. Numerical results are presented.