Extension of the Two-Dimensional JKR Theory to the Case with a Large Contact Width

Abstract

Contact mechanics pioneered by Hertz [1] has been widely applied in many branches of engineering, particularly in studies of tribology and indentation. Since the 1970s, molecular interactions between contacting objects have also been incorporated into contact mechanics models. Johnson et al. [2] developed the JKR model of adhesive contact based on a balance between elastic and surface energies. On the other hand, Derjaguin et al. [3] proposed the DMT model in which the stress field remains in the Hertz profile within the contact region while intermolecular adhesion is assessed outside the contact area. A more general model (MD model) was developed by Maugis [4], who showed that the JKR and DMT models can in fact be unified within a Dugdale type of cohesive model of adhesive contact.