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Analytical and Numerical Models for Tangential Stiffness of Rough Elastic Contacts

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Abstract

The paper considers elastic contact of rough surfaces and develops a simple analytical expression for the stiffness of the contact under tangential loading, which predicts that the contact stiffness is proportional to normal load and independent of Young’s Modulus. The predictions of this model are compared to a full numerical analysis of a rough elastic contact of finite size. The two approaches are found to be in good agreement at low loads, when the asperity spacing is large, but the numerical approach predicts much lower stiffnesses at medium and high loads. It is shown that the overall stiffness cannot exceed that of the equivalent smooth contact, and a simple means of modifying the analytical approach is proposed and validated.

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Notes

  1. The fact that the theorem provides results for Poisson’s ratio equal to zero implies that the tangential and normal stiffness computed using this technique are identical (see Eq. (30)). We have implemented the tangential stiffness calculations to perform explicit comparisons between the analytical and the numerical results.

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Acknowledgments

The authors would like to acknowledge the financial support of the Engineering and Physical Sciences Research Council under grant numbers EP/E058337/1 and EP/E057985/1. The authors are grateful to Professor J.R. Barber for suggesting the unit cell approach presented in Sect. 2.2.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London, SW7 2AZ, UK

    S. Medina & D. Dini

  2. Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, UK

    D. Nowell

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  1. S. Medina
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  2. D. Nowell
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  3. D. Dini
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Correspondence to D. Dini.

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Medina, S., Nowell, D. & Dini, D. Analytical and Numerical Models for Tangential Stiffness of Rough Elastic Contacts. Tribol Lett 49, 103–115 (2013). https://doi.org/10.1007/s11249-012-0049-y

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