On the Sevostianov–Kachanov approximation for the incremental compliances of non-elliptical contacts

Abstract

The incremental normal contact compliance of an elastic body beneath a frictionless indenter of arbitrary smooth shape is considered under the assumption of a simply connected domain of contact. An approximate expression for the contact stress-intensity factor in conjunction with the Griffith–Irwin formula for the variation of the elastic energy under a small perturbation of the contact contour is used to estimate the contact compliance. It is shown that the Sevostianov–Kachanov variational approach allows to derive upper and lower bounds, whose arithmetic mean is found to possess high accuracy for contacts of regular polygonal form. A number of possible generalizations are briefly discussed.