Analytical Aspects of Cumulative Superposition Procedure for Elastic Indentation Problems

Abstract

Indentation problems for an elastic half-space may possess similarity solutions when the local shape of the contacting body is expressed by a homogeneous function. In this situation, the desired solution for curved punches can be obtained by the integration, namely, 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, the advantage of this procedure is explored from analytical and numerical points of view. Although the theoretical basis is laid down for frictionless indentation of an elastic half-space by a rigid punch, the method is 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 sections, 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. The use of the boundary element method for the reduced flatpunch problem is shown to be effective and promising for more complicated three-dimensional indentation problems.