Representation of incomplete contact problems by half-planes

TL;DR

This paper develops a method to accurately model partial-slip frictional contact problems using half-plane theory, leveraging finite element data to improve slip-zone size estimates beyond traditional finite element analysis.

Contribution

It introduces a novel approach combining finite element data with half-plane theory to better predict slip zones in contact problems.

Findings

Enhanced slip-zone size estimates compared to standard finite element analysis.

Method effectively incorporates traction ratio and strain data from simulations.

Provides more precise solutions satisfying frictional slip laws.

Abstract

Methods for finding the optimal choices of the applied remote loads -- the applied normal force, moment, shear force and remote bulk stresses -- needed to solve frictional contact problems in partial-slip using half-plane theory are derived by using data from contacts analysed by the finite element method. While the normal and shear forces and moment are readily found from equilibrium considerations, in order to determine the bulk stresses we must exploit details of the traction ratio and the direct strain within the contact, both of which are readily extracted from simulations. These contact loads enable the formulation of an equivalent half-plane problem for the contact, which can be used to determine much more precise estimates of the slip-zone sizes than are obtainable from direct use of frictional finite element analysis, as aggregated data from the finite element output is employed, and the half-plane analysis will add precision in terms of satisfaction of the laws of frictional slip and stick.