An approximate solution for the contact area and elastic compliance of a smooth punch of arbitrary shape

Abstract

An approximate solution is developed for the contact area and the load-penetiation relation for frictionless indentation of the elastic half-space by a punch of arbitrary profile. The method makes use of a previous result to the effect that the contact area in this problem is that which maximizes the total indenting force. An estimate of this force is obtained by applying the reciprocal theorem to the solution for indentation by a flat punch of the same plan-form, for which an approximate solution has recently been developed by Fabrikant. The method is illustrated using an example, the results of which are compared with a direct numerical solution using Hartnett's algorithm.