Explicit and asymptotic solutions for frictional incomplete half-plane contacts subject to general oscillatory loading in the steady-state

TL;DR

This paper develops an asymptotic method to analyze the steady-state stick-slip behavior of incomplete contacts under oscillatory loads, extending analytical solutions to complex loading scenarios involving varying moments and bulk tension.

Contribution

It introduces an asymptotic formulation that approximates slip zone sizes and provides solutions beyond traditional analytical limits for incomplete contact problems.

Findings

Asymptotic approach accurately predicts slip zones during cyclic loading.

Method extends analytical solutions to cases with large varying moments and bulk tension.

Comparison with explicit solutions validates the asymptotic formulation.

Abstract

This contribution presents an asymptotic formulation for the stick-slip behaviour of incomplete contacts under oscillatory variation of normal load, moment, shear load and differential bulk tension. The asymptotic description allows us not only to approximate the size of the slip zones during the steady-state of a cyclic problem without knowledge of the geometry or contact law, but provides a solution when all known analytical solutions for incomplete contacts reach their limitations, that is, in the presence of a varying moment and a differential bulk tension large enough to reverse the direction of slip at one end of the contact. An insightful comparison between the mathematically explicit analytical solution and the asymptotic approach is drawn using the example geometry of a shallow wedge.