The accuracy of the geometric assumptions in the jkr (johnson–kendall–roberts) theory of adhesion

The accuracy of the geometric assumptions in the Johnson- Kendall-Roberts (JKR) theory of adhesion are examined in this work. In particular, the effect of surface curvature on the validity of the JKR theoryis analyzed by developing a perturbation solution to the problem of two cylinders in contact. The pressure distribution inside the contact zone as predicted by the JKR theory is shown to be accurate toorder ε2, where ε is the ratio of the contact width to the radius of the smaller cylinder. The relative normal approach of the cylinders is also given in a closed form. Based on these results, a correction to the normal approach is derived for the case of three-dimensional contact of hemispheres. The validity of these correction terms and of the JKR theory for hemispheres is investigated numericallyusing a non-linear finite element method capable of simulating large strains. The effect of thin lenses on the validity of the JKR theory is also examined using the FEM.