The Johnson–Kendall–Roberts (JKR) theory remains the most cited model of adhesive contact. It was demonstrated that the JKR theory can be substantially extended, allowing adhesive JKR-type contact problems to be solved through an explicit transformation of the corresponding nonadhesive Hertz-type load‒displacement curve. This framework enables the application of the extended JKR theory to nonclassical scenarios where analytical nonadhesive solutions are unavailable, and therefore, numerical methods can be employed. However, the transformation formulae involve the first and second derivatives of the load‒displacement curve, posing challenges when applied to discrete numerical data. This study presents a straightforward and effective numerical approach that converts a numerically obtained data series of load–displacement–contact radius for a nonadhesive contact problem into the corresponding JKR-type adhesive solution. While any appropriate numerical method can be used to generate these data, the finite element method (FEM) is employed here. The proposed approach is validated by comparing numerical results with established analytical solutions for adhesive contact problems involving an elastic half-space and a thin elastic layer bonded to a rigid substrate, as well as with experimental data. These comparisons demonstrate excellent agreement between the numerical and analytical solutions. It is argued that the proposed method offers significant potential for solving many important practical problems, e.g., adhesive contact analysis for coated or multilayered media.

Living organisms, such as geckos and insects, exhibit excellent climbing ability on various complex surfaces due to the hair-like hierarchical adhesive systems of their attachment devices. Over the past few decades, an increased understanding of the mechanisms of multiscale hierarchical adhesion systems and the continual improvement of theoretical modeling have promoted the rapid advancement in the design and application of biomimetic artificial adhesives. The modeling of biomimetic artificial adhesives has developed from simple structures to complex constructions with multilevel hierarchical properties. A review of advances in the development of these contact mechanics models is presented here. Adhesion and friction models considering multiscale hierarchical structural forms are discussed, with a focus on multiscale hierarchical models based on the development of the Cantor‒Borodich profiles. Finally, the most recent developments in studies of artificial setae with spatula-like ends, both axisymmetric and non-axisymmetric, are reviewed.

A detailed review of various fractal models used in tribology is presented. The analysis of the models is based on the use of the Cantor–Borodich (C_B) profile and its modifications. This profile and related models may be studied analytically and, therefore, they provide us with tools for rigorous analysis of fractal approaches to description of surface roughness and corresponding contact problems. In turn, this allows us to present a critical review of current fractal approaches to tribology. It will be demonstrated that fractal dimension alone cannot give a full description of surface roughness, however, some of these models may reflect the multilevel hierarchical structure of real surface roughness. This review helps to avoid the repetition of common erroneous statements about the use of fractal concepts in tribology.