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Analytical solutions to the shear-induced anisotropic area reduction in frictional elastomer contact

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Abstract

Shear-induced contact area reduction is a common phenomenon across scales. The corresponding contact morphology controls almost all the macroscopic features of the interface, including adhesion, wear, viscoelastic properties, stiffness, and even electric resistance. It is a long-standing challenge to predict the contact morphology of nonlinear soft elastomer contact since there has been no available analytical solution. The work presented in this paper aims to fill the blank. Here, we first establish a new framework for contact morphology, which involves two evolution equations of the contact boundary. The framework decouples nonlinear contact kinematics and contact forces to formulate the corresponding initial-value problem in a modular approach. Based on this, we present analytical solutions to the shear-induced anisotropic area reduction in elastomer contact by using the method of undetermined coefficient and Boussinesq type models. We theoretically demonstrate that the shear-induced normal deformation (originated from Poynting’s effect), but not tangential deformation, governs the anisotropic area reduction. Also, the power laws of the reduction parameters for both contact area and size are provided. The results show quantitative agreement with recent simulations and experiments. Our approaches to the contact morphology of frictional contact involving soft materials may shed some light on the theoretical modeling of large deformation contact mechanics.

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Authors and Affiliations

  1. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Mingzhu Xu, Mengru Zhang, Weiting Chen & Ya-Pu Zhao

  2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100190, China

    Mingzhu Xu, Mengru Zhang, Weiting Chen & Ya-Pu Zhao

Authors
  1. Mingzhu Xu
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  2. Mengru Zhang
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  3. Weiting Chen
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Correspondence to Weiting Chen or Ya-Pu Zhao.

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Conflict of interest The authors declare that they have no conflict of interest.

Additional information

This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB0620101, and XDB0620103), the National Natural Science Foundation of China (Grant Nos. 12241205, and 12032019), and the National Key Research and Development Program of China (Grant No. 2022YFA1203200). The authors are grateful to Professor Quanzi Yuan and Associate Professor Xianfu Huang for their valuable discussions, insightful suggestions, and financial support.

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Xu, M., Zhang, M., Chen, W. et al. Analytical solutions to the shear-induced anisotropic area reduction in frictional elastomer contact. Sci. China Phys. Mech. Astron. 68, 284611 (2025). https://doi.org/10.1007/s11433-025-2680-4

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