The Love Equation for the Normal Loading of a Rigid Cone on an Elastic Half-Space and a Recent Modification: A Review

Abstract

This review confirms that the Love equation which connects the load on a rigid cone loaded normally on an elastic half-space, and its penetration into the half space, has been verified by several theoreticians. Furthermore, the predictions of the Love equation have been experimentally validated. It is argued here that a modification of the Love equation made about 20 years ago is incompatible with several theoretical treatments as well as with the expression for radial surface particle displacement outside the contact. Moreover, it is also shown that normal loading behaviour of a rigid cone on an elastic half-space cannot be likened to that of the normal loading behaviour of a rigid three-sided or a four-sided pyramid. Lastly, corrections are made to some important expressions given in a well cited paper by Sneddon (1965).

In situ photograph of the surface profile when a 90° included angle tungsten carbide cone is loaded on a block of PDMS (1:10). The surface profile, shown below, is well fitted by eq. (3). (Adapted from Ref. 13). (Reprinted by permission of Taylor & Francis Ltd, http://www.tandfonline.com)