Acta Mechanica

, Volume 229, Issue 7, pp 2835–2842 | Cite as

A JKR solution for a ball-in-socket contact geometry as a bi-stable adhesive system

  • M. Ciavarella
Original Paper


In the present note, we start by observing that in the classical JKR theory of adhesion, using the usual Hertzian approximations, the pull-off load grows unbounded when the clearance goes to zero in a conformal “ball-in-socket” geometry. To consider the case of the conforming geometry, we use a recent rigorous general extension of the original JKR energetic derivation, which requires only adhesionless solutions, and an approximate adhesionless solution given in the literature. We find that depending on a single governing parameter of the problem, \(\theta =\Delta R/\left( 2\pi wR/E^{*}\right) \) where \(E^{*}\) is the plane strain elastic modulus of the material couple, w the surface energy, \(\Delta R\) the clearance and R the radius of the sphere, the system shows the classical bi-stable behaviour for a single sinusoid or a dimpled surface: pull-off is approximately that of the JKR theory for \(\theta >0.82\) only if the system is not “pushed” strong enough, otherwise a “strong adhesion” regime is found. Below this value, \(\theta <0.82\), a strong spontaneous adhesion regime is found similar to “full contact”. From the strong regime, pull-off will require a separate investigation depending on the actual system at hand.


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© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Politecnico di BARI, Department of Mechanical EngineeringCenter of Excellence in Computational MechanicsBariItaly

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