Similarity considerations in adhesive contact problems

The classical ‘JKR’ solution for the force required to separate two elastic spheres is independent of the elastic moduli. We demonstrate that this remarkable simplification is a rigorous consequence of the quadratic character of the spherical profile and hence that it must also apply exactly to more general quadratic profiles such as the contact of two ellipsoids. The same feature is also responsible for the fact that Bradleyʹs ‘rigid sphere’ solution depends only on the interface energy and not on the detailed character of the adhesive force law.