On the compression of a rigid disc by finitely deformed elastic halfspaces

Abstract

The paper examines the problem of a flat rigid circular disc that is compressed between two finitely deformed incompressible elastic halfspace regions with smooth surfaces. This problem yields a unilateral contact problem where the zone of separation needs to be determined. The analysis of the unilateral contact problem is reduced to the solution of a set of triple integral equations associated with the internal indentation of a penny-shaped crack and the internal tensile pressurization of an annular crack. The solutions to these problems can be obtained in an approximate series form in terms of the non-dimensional parameter involving the radius of the rigid disc to the radius of the separation zone. The extent of the separation zone is determined from the vanishing of the contact stress at the point of separation. Specific solutions are developed for the case where the initial finite deformation is for halfspace regions with a strain energy function of the Mooney-Rivlin form.