Analysing the accuracy of asymptotic approximations in incomplete contact problems

TL;DR

This paper evaluates the accuracy of first-order asymptotic approximations for contact pressure in incomplete contact problems, analyzing errors across various geometries and extending to shear traction distributions under full stick conditions.

Contribution

It provides a detailed assessment of the errors in asymptotic contact pressure representations and introduces an asymptotic model for shear traction in full stick scenarios.

Findings

Maximum relative error identified across geometries

Asymptotic representation of shear traction under full stick

Quantitative error bounds for asymptotic approximations

Abstract

The error incurred in the representation of the contact pressure at the edges of incomplete contacts by first order asymptotes is treated, and the maximum value of the relative error found for a range of geometries, both symmetric and non-symmetric. Shear tractions are excited by both the application of a shear force and the application of bulk tension in one body. An asymptotic representation of the shear traction distribution under conditions of full stick is presented.