2017/12/27 by M. Ciavarella, Ciavarella, M.
Engineering · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #FOS: Physical sciences #Force Microscopy Techniques and Applications #Mechanical stress and fatigue analysis #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft
paper · pdf · doi:10.48550/arxiv.1712.09640
13 pages, 5 figures
arxiv created 2017/12/27 · openalex publication_date 2017/12/27 · arxiv updated 2017/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 proposed by the first author which necessitates only of adhesionless solutions, and an approximate adhesionless solution given in the literature. We find that depending on a single governing parameter of the problem, theta=DeltaR/(2 pi w R E*) where E* is the plane strain elastic modulus of the material couple, w the surface energy, DeltaR the clearance and R the radius of the sphere, the system shows the classical bistable 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" strongly enough and 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.