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An Incremental Contact Model for Hyperelastic Solids with Rough Surfaces

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Abstract

Hyperelastic materials like gels and rubbers have numerous applications in daily life and industrial production. However, most traditional contact models for rough solids do not include the hyperelastic deformation mechanism. This paper extends the linear-elastic incremental equivalent contact model to study the contact processes of hyperelastic rough solids. For any specific surface separation, the contact stiffness is determined by the total area and number of the contact patches, as well as the instantaneous tangent modulus. Analogous to buckle theory, we introduce the hyperelasticity of materials through employing the tangent modulus. By integrating the stiffness of contact spots, the normal contact force is then obtained. The load-area relation predicted by the present model exhibits consistency with finite element results even up to a contact area fraction of 90%. For hyperelastic solids with self-affine fractal rough surfaces, we investigate the effect of surface morphologies and material nonlinearity on contact behaviors. This research will be helpful for further studies on the lubrication, leakage, and wear of contact interfaces.

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Data Availability

All data included in this study are available upon request by contact with the corresponding author.

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Funding

This research was funded by the National Natural Science Foundation of China (Grant numbers 11525209).

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  1. Department of Engineering Mechanics, SVL and MMML, Xi’an Jiaotong University, Xi’an, 710049, China

    Chunyun Jiang & Xuanming Liang

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  1. Chunyun Jiang
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Contributions

CJ and XL contributed to the study’s conception and design. FEM simulations and analysis were performed by CJ. The first draft of the manuscript was written by CJ and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Xuanming Liang.

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Jiang, C., Liang, X. An Incremental Contact Model for Hyperelastic Solids with Rough Surfaces. Tribol Lett 72, 1 (2024). https://doi.org/10.1007/s11249-023-01800-w

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