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Representation of incomplete contact problems by half-planes

Andresen, H.; Hills, D.A.; Moore, M.R.


H. Andresen

D.A. Hills


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.


Andresen, H., Hills, D., & Moore, M. (2021). Representation of incomplete contact problems by half-planes. European Journal of Mechanics - A/Solids, 85,

Journal Article Type Article
Acceptance Date Sep 27, 2020
Online Publication Date Oct 12, 2020
Publication Date 2021-01
Deposit Date Nov 17, 2021
Publicly Available Date Nov 18, 2021
Journal European Journal of Mechanics - A/Solids
Print ISSN 0997-7538
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 85
Article Number 104138
Keywords Contact mechanics; Half-plane theory; Incomplete contacts; Prototype analysis; Partial slip
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