The implementation of the Johnson–Kendall–Roberts formalism on the basis of numerically simulated contact problems

Abstract 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.