Contact Properties and Adhesion of Incompressible Power-Law Gradient Media with High Gradients

We discuss contact stiffness and adhesion of flat-ended cylindrical indenters with a graded material the elastic coefficient of which is a power-function of the depth with an exponent 1 < k < 3. So far, only graded materials with k < 1 have been considered in the literature as the stiffness of the medium becomes zero when k is approaching 1. However, it is known that the case of incompressible media is an exception. We argue that in this case the final stiffness can be defined up to values of k < 3. The interval 1 < k < 3, which has not been considered earlier occurs to be of special interest, since for k > 1 the adhesive properties of contacts change qualitatively from "brittle" to very tough even in the case of a purely elastic material.