Contact problems for a wedge with rounded apex

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Description/Abstract

Elastic contact between a shallow elastic wedge, whose apex is blunted by a finite radius, and an elastically similar half-plane is studied. A closed-form contact law is found, and the interior stress field is then deduced using a Muskhelishvili's solution in series form, for frictionless and sliding conditions. This geometry removes one of the principal objections to classical solutions to the wedge indentation problem--the unrealistic infinite stress concentration implied by an atomically sharp apex--and in the latter part of the paper the strength of the contact is evaluated explicitly. Further, cases of partial slip associated with the application of tangential load less than needed to cause sliding are considered.