Smooth Asymmetric Indentation of a Finite Elastic Layer

Abstract

Standard methods of indentation analysis use a beam theory solution to obtain an overall load-displacement relationship and then a Hertzian contact solution to calculate local stresses under the indenter. However, these techniques are only applicable in a fairly limited class of problems: previous modeling efforts have shown that the stress distribution in the region of contact will differ significantly from a Hertzian one when the contact length exceeds the thickness of the beam. In such cases, point contact can no longer be assumed and Hertzian relations are not valid. The indentation model developed herein is an improvement over current GLOBAL/LOCAL approaches in that it uses an elasticity solution to establish the load-displacement relationship at the contact site. The solution technique is applied to two end conditions: (1) simple supports, and (2) fixed ends. Superposition of appropriate elasticity expressions results in systems of Fredholm integral equations of the second kind that are solved numerically. Maximum contact stresses are obtained and compared with the predictions of the previous GLOBAL/LOCAL model. The validity of the solutions presented is assessed by comparing the results obtained to the predictions of modified beam theory solutions.