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 (J KR) theory of adhesion are examined in this work. In particular, the effect of surface curvature on the validity of the JKR theory is analyzed by deve loping a perturbation solution to the problem of two cylinders in contact. The pressure distribution inside the contact zone as predicted by the JKR t heory is shown to be accurate to order epsilon(2), where epsilon is the rat io 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 correcti on terms and of the JKR theory for hemispheres is investigated numerically using a non-linear finite element method capable of simulating large strain s. The effect of thin lenses on the validity of the JKR theory is also exam ined using the FEM.