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On the Validity of the Method of Reduction of Dimensionality: Area of Contact, Average Interfacial Separation and Contact Stiffness

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Abstract

It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one-dimensional (1D) elastic foundation model. Using this 1D mapping, we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness K and compare it with the result of an analytic study. We attribute the failure of the elastic foundation model to the incorrect treatment of the long-range elastic coupling between the asperity contact regions.

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Notes

  1. In a recent paper Popov states: “In Ref. [10] the size of the system was accidentally chosen in such a way that the area-force dependence was correct up to relative large contact. This result, however, cannot be generalized.”.

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Acknowledgments

We thank Giuseppe Carbone, Martin Müser and Mark Robbins for useful discussions. L.P. acknowledges funding from the European Commission (Marie-Curie IOF-272619).

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Authors and Affiliations

  1. Peter Grünberg Institut-1, FZ-Jülich, 52425, Jülich, Germany

    I. A. Lyashenko & Bo N. J. Persson

  2. Sumy State University, Rimskii-Korsakov Str. 2, 40007, Sumy, Ukraine

    I. A. Lyashenko

  3. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, 21218, USA

    Lars Pastewka

  4. MikoTribologie Centrum μTC, Fraunhofer-Institut für Werkstoffmechanik IWM, 79108, Freiburg, Germany

    Lars Pastewka

Authors
  1. I. A. Lyashenko
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  2. Lars Pastewka
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  3. Bo N. J. Persson
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Correspondence to Bo N. J. Persson.

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Lyashenko, I.A., Pastewka, L. & Persson, B.N.J. On the Validity of the Method of Reduction of Dimensionality: Area of Contact, Average Interfacial Separation and Contact Stiffness. Tribol Lett 52, 223–229 (2013). https://doi.org/10.1007/s11249-013-0208-9

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  • DOI: https://doi.org/10.1007/s11249-013-0208-9

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