Deformation and adhesion of elastic bodies in contact

Abstract

The elastic deformation and adhesion of two convex bodies that interact via surface forces of finite range are calculated self-consistently. Hertz theory is compared to the result of an exponential repulsion, and it is found to be valid in the limit of short-ranged forces and high loads. A Lennard-Jones law is used to examine the classical theories of adhesion, which relate the surface energy to the pull-off force, and their regime of validity is explored. Explicit expressions are given for the displacement prior to contact, and for the jump instabilities due to elastic deformation, which occur for compliant bodies with rapidly changing surface forces. The loading-unloading cycle is shown to be hysteretic for large adhesions, and this is correlated with the onset of jumps. In these cases the pull-off force is demonstrated to depend upon the history of the sample, and it increases with increasing maximum applied loads.