On Elastic Line Contact

Abstract

Two-dimensional elastic half-space contact theory suffers from the defect that the surface displacement with respect to infinity becomes infinitely large when the total force carried by the half space is different from zero. Several authors removed this defect by altering the geometry so that the depth of the elastic body becomes finite. In the present paper another approach is chosen by considering contact areas which are many times as long as they are wide, but which still are small as compared with a characteristic dimension of the body which is approximated by the half space. As one of the examples, the Hertz problem is considered, and the asymptotic results are compared with the exact theory. It is found that errors of 10–15 percent are found when the contact ellipse is twice as long as wide, and errors of 2–3 percent are encountered when the ratio of the axes is five.