Adhesive contact of elastic spheres revisited: numerical models and scaling

Abstract

For the purpose of determining the relevant scaling, the fundamental and widely applicable problem of adhesive contact between elastic solids is revisited. A comprehensive and accurate finite-element modelling is undertaken. A local contact law, consistent with the current level of modelling, is used. The analysis of the results yields the following conclusions. For a broad range of physically reasonable contact laws, and for low values of the Tabor parameter, a simple modification of adhesive range entering in the Tabor parameter allows for one-parameter scaling of the problem. For high values of the modified Tabor parameter, the problem requires description in terms of two non-dimensional parameters, one of which represents the magnitude of the contact surface stretch. The contact surface stretch correction is significant for a wide range of problems with spheres smaller than the threshold size, which, for a broad range of materials, is 300 nm to 100 μm, depending on the adhesive energy and elastic compressibility.