Research Progress on Mathematical Model of Adhesive Contact Based on Interface Interaction

Adhesion is a phenomenon that a substance is attached to the surface of another substance, and adhesion force refers to the external force required to separate the two substances that have adhesion. Adhesion contact phenomenon plays a very important role and influence in various fields. At present, we are exploring the repair work of the aging surface of silicone rubber insulating materials. It is necessary to select appropriate repair materials coated on the surface of aging materials, so that degradation of performance caused by surface aging can be recovered. In order to study the adhesion behavior and force on the interface of interaction between materials, it is necessary to establish an appropriate theoretical model for the adhesion interface between materials. Based on the corresponding contact theory, the stability and durability of the interface between heterogeneous materials can be predicted and calculated by mathematical analysis. The method of applying mathematical models to analysis can not only theoretically calculate the value of material adhesion force and provide reference for experimental design, but also guide the selection of materials in the actual experiment according to the value range of material parameters in the mathematical model. At present, there are many kinds of mathematical models in the literature, and applicable theories of adhesion phenomena under different forces are not the same. In this paper, the common adhesion phenomena were divided into elastomer contact, rough surface adhesion, substrate surface stripping and other categories according to their different forms of force, and the theoretical models and applications used to analyze the above contact behaviors were summarized respectively. Then the basic principle and application development of modern simulation model based on computer simulation technology were described comprehensively. A general model for adhesion analysis between general objects was introduced. The purpose was to provide guidance and reference for research and modeling in the field of bonding contact. Firstly, the classical contact theories commonly used in elastomer contact were introduced, including Hertz contact, JKR model and DMT model. The differences between JKR model and DMT model were discussed according to Tabor number. This theory was the basis of modern contact mechanics and still had an important influence on contact science. Secondly, the numerical methods and theoretical models commonly used in the adhesion analysis of rough surfaces were briefly summarized, with emphasis on the improvement and extension of the GW model proposed by Greenwood and Williamson. Then the Kendall stripping model used in the process of substrate surface stripping was described comprehensively. As a basic theory in material stripping, this theoretical model played a guiding role in the subsequent research on the stripping process of various materials. Finally, molecular dynamics model (MD model) and finite element model (FEM) based on computer simulation technology were discussed. The popularization and application of these two computer simulation technologies played a great role in promoting the development of mathematical modeling. There are many kinds of existing adhesive contact mathematical modeling methods, such as micromechanical analysis, micro-statistics analysis, macro-energy conservation, finite element analysis and bond energy analysis at atomic scale, etc., but so far, there are differences between any of the modeling methods and the actual situation, one of the reasons is that the assumptions used by all kinds of modeling methods do not exist in the actual situation. In order to reduce this difference, a modeling method combining macroscopic and microscopic scales is a very important development direction of adhesive contact model, such as the combination of intermolecular forces and finite element method, and the combination of microscopic mechanical analysis and macroscopic energy transition. And another important development direction is the construction of general model. Among the many kinds of adhesion models in the current literature, a considerable number of them are highly targeted, that is, they are only applicable to special problems with specific geometric characteristics, which causes great difficulties for their promotion and application. With the progress of computer simulation technology, it is believed that the mathematical analysis method based on theoretical model will greatly promote the research progress in the field of adhesive contact. © 2024 Chongqing Wujiu Periodicals Press. All rights reserved.