Explicit transformation between non-adhesive and adhesive contact problems by means of the classical Johnson–Kendall–Roberts formalism

Abstract

The classic Johnson–Kendall–Roberts (JKR) contact theory was developed for frictionless adhesive contact between two isotropic elastic spheres. The advantage of the classical JKR formalism is the use of the principle of superposition of solutions to non-adhesive axisymmetric contact problems. In the recent years, the JKR formalism has been extended to other cases, including problems of contact between an arbitrary-shaped blunt axisymmetric indenter and a linear elastic half-space obeying rotational symmetry of its elastic properties. Here the most general form of the JKR formalism using the minimal number of a priori conditions is studied. The corresponding condition of energy balance is developed. For the axisymmetric case and a convex indenter, the condition is reduced to a set of expressions allowing explicit transformation of force–displacement curves from non-adhesive to corresponding adhesive cases. The implementation of the developed theory is demonstrated by presentation of a two-term asymptotic adhesive solution of the contact between a thin elastic layer and a rigid punch of arbitrary axisymmetric shape. Some aspects of numerical implementation of the theory by means of Finite-Element Method are also discussed. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

A Study on the Physical Properties of Banana Straw Based on the Discrete Element Method

“…In the actual situation, banana straw has certain viscosity characteristics after being crushed. Thus, certain surface energy was applied to the particles through the particle surface energy contact model to simulate the viscosity characteristics of crushed materials in the actual situation [20][21][22][23].…”

Adhesion and wear of diamond: formation of nanocracks and adhesive craters of torn out material

“…It was shown that the JKR formalism may be reinforced if one employs the properties of slopes of the force–displacement diagrams of non-adhesive indentation [29]. The reinforced JKR formalism may be applied to an enormous number of adhesive contact problems for various elastic structures [30,32]. In particular, it has been shown that in the JKR-type contact problems, the connections between the external force P, the approach of solids δ and the radius of the contact region can be written as P=PH−8πwE∗a31emand1emδ=δH−(2πwaE∗)1/2. …”

“…and O.N.G.) and presented in their preprint in 1994 [27], these results have never been published and developed further except for the development of the Johnson-Kendall-Roberts (JKR) theory [28] (see discussions of the JKR formalism in [29][30][31][32]). We see that the models introduced by the authors and the mechanism of abrasive wear mentioned above [27] have not been rediscovered by other researchers.…”