Asymptotic Methods

Abstract

The inequalities defining unilateral contact and frictional slip control the partition of the potential contact surface into regions of slip, stick or separation. The asymptotic elastic fields at the boundaries between these regions generally exhibit singularities, either in the stresses or in the stress gradients, and the properties of the corresponding singular fields often lead to results of some generality. For example, we can show that in any non-conformal frictionless elastic contact problem, the contact pressure must tend to zero with the square root of the distance from the edge of the contact region, provided that the contact surfaces are continuous up to and including the first derivative.