Contact mechanics for coated spheres that includes the transition from weak to strong adhesion

Recently published results for a rigid spherical indenter contacting a thin, linear elastic coating on a rigid planar substrate have been extended to include the case of two contacting spheres, where each sphere is rigid and coated with a thin, linear elastic material. This is done by using an appropriately chosen effective radius and coating modulus. The earlier work has also been extended to provide analytical results that span the transition between the previously derived Derjaguin–Müller–Toporov (DMT)-like (work of adhesion/coating-modulus ratio is small) and Johnson–Kendall–Roberts (JKR)-like (work of adhesion/coating-modulus ratio is large) limits.