Analytical Aspects of Cumulative Superposition Procedure for Elastic Indentation Problems.

Abstract

Indentation problems for an elastic half-space admit similarity analysis when the local shape of the contacting body can be expressed by a homogeneous function. In this situation, the solution for curved punches can be obtained by the cumulative superposition of the solution to a single auxiliary problem which amounts to indentation by a flat-ended punch. This procedure avoids treating the moving and unknown contact boundary explicitly, so that the contact region can be determined in an accurate manner. In this study, advantages of this procedure are explored from analytical and numerical points of view. Although the theoretical basis is first described for frictionless indentation of an elastic half-space by a rigid punch, the method is subsequently shown to be applicable to the contact between two elastic bodies and for more general frictional behavior. To demonstrate the use of this superposition principle, the three-dimensional indentation by a punch with elliptic cross-section, as well as the plane-strain indentation by an asymmetric punch are solved by this method. Numerical accuracy of the present procedure is verified employing some examples of plane-strain problems, together with its effectiveness in combination with the application of the boundary element analysis for the reduced flat-punch problem.