Applied Mathematics and Mechanics >
Adhesion of stretched elastomers: a model based on Lennard-Jones potential
Received date: 2025-12-29
Revised date: 2026-03-04
Online published: 2026-05-06
Supported by
Project supported by the National Natural Science Foundation of China (No. 12321002) and the 111 Project of China (No. B21034)
Copyright
Pre-strain and pre-stress in soft materials have significant effects on their adhesive behavior, thereby influencing their functions and applications. Whereas prior theoretical studies on the adhesion of pre-strained elastomers predominantly rely on fracture mechanics frameworks based on the assumption of short-range forces, this study models surface interactions using the Lennard-Jones potential, thereby elucidating more intricate details of the adhesive behavior. The results of the proposed model are initially validated through finite element simulations and the analytical models in the literature. Subsequently, the effects of substrate pre-stretch on the adhesive behavior, including the pull-off force, JKR-Bradley transition, jump-in and jump-out instabilities, surface profile, and pressure distribution, are revealed by the proposed model. Based on the ‘semi-rigid’ theory (SRT), an analytical solution is derived to predict the displacement and central gap at the jump-in point. A modified Tabor parameter that incorporates the substrate pre-stretch effect is also proposed. The JKR-Bradley transition characterized by this modified parameter coincides with the unstretched case. This study offers new insights into understanding the adhesive behavior of pre-stretched elastomers.
Le DU , Jianmin LONG , Zhaohe DAI , Rui XIAO , Weiqiu CHEN . Adhesion of stretched elastomers: a model based on Lennard-Jones potential[J]. Applied Mathematics and Mechanics, 2026 , 47(5) : 1001 -1018 . DOI: 10.1007/s10483-026-3379-9
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