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

• Published in: Journal of the mechanics and physics of solids Vol. 146; p. 104214
• Main Authors: Andresen, H., Fleury, R.M.N., Moore, M.R., Hills, D.A.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.01.2021; Elsevier BV
• Subjects: and bulk tension; Asymptotes; Asymptotic methods; Contact mechanics; Exact solutions; Half-plane theory; Mathematical analysis; moment; Partial slip; shear load; Slip; Steady state; Varying normal load; Partial slip; Asymptotes; Contact mechanics; Half-plane theory; shear load; Varying normal load; and bulk tension; moment
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2020.104214

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.