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On the Contact Area of Nominally Flat Hertzian Contacts

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In a recent paper, Pastewka and Robbins (Appl Phys Lett 108:221–601, 2016) state an analytical expression for the real contact area of a Hertzian tip with small-scale roughness. We confirm that their formula predicts real contact areas quite well—with less than 10 % error. Nonetheless, the complementary contact area does not show the proper scaling to the continuum results at large loads. This shortcoming is fixed in the present work by abandoning a mean-field approximation made in the original work. Analytical results can even be made essentially perfect with a relation giving the accurate dependence of contract area on pressure for contacts between solids with nominally flat surfaces.

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The author gratefully acknowledges computing time on JUQUEEN at the Jülich Supercomputing Centre and the Deutsche Forschungsgemeinschaft for support through Grant Mu 1694/5-1.

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Correspondence to Martin H. Müser.

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Müser, M.H. On the Contact Area of Nominally Flat Hertzian Contacts. Tribol Lett 64, 14 (2016). https://doi.org/10.1007/s11249-016-0750-3

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  • Contact mechanics
  • Surface roughness
  • Analysis and models
  • Molecular dynamics