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The breakdown of continuum models for mechanical contacts

Nature volume 435, pages 929–932 (2005)Cite this article

Abstract

Forces acting within the area of atomic contact between surfaces play a central role in friction and adhesion. Such forces are traditionally calculated using continuum contact mechanics1, which is known to break down as the contact radius approaches atomic dimensions. Yet contact mechanics is being applied at ever smaller lengths, driven by interest in shrinking devices to nanometre scales2,3, creating nanostructured materials with optimized mechanical properties3,4, and understanding the molecular origins of macroscopic friction and adhesion5,6. Here we use molecular simulations to test the limits of contact mechanics under ideal conditions. Our findings indicate that atomic discreteness within the bulk of the solids does not have a significant effect, but that the atomic-scale surface roughness that is always produced by discrete atoms leads to dramatic deviations from continuum theory. Contact areas and stresses may be changed by a factor of two, whereas friction and lateral contact stiffness change by an order of magnitude. These variations are likely to affect continuum predictions for many macroscopic rough surfaces, where studies7,8 show that the total contact area is broken up into many separate regions with very small mean radius.

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Figure 1: Cylindrical surfaces with different atomic-scale roughness.
Figure 2: Variation of normal displacement, contact radius and friction with normal load.
Figure 3: Local pressure distributions for cylinders with different atomic-scale roughness.
Figure 4: Geometry and stress for spherical tips with and without adhesion.

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Acknowledgements

We thank R. W. Carpick, J. N. Israelachvili, P. M. McGuiggan and M. H. Müser for useful discussions. This material is based upon work supported by the National Science Foundation.

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Authors and Affiliations

  1. Department of Physics & Astronomy, Johns Hopkins University, 3400 N. Charles Streeet, Baltimore, 21218, Maryland, USA

    Binquan Luan & Mark O. Robbins

  2. Astronomy, Johns Hopkins University, 3400 N. Charles Streeet, Baltimore

    Binquan Luan & Mark O. Robbins

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  1. Binquan Luan
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  2. Mark O. Robbins
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Correspondence to Mark O. Robbins.

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Supplementary information

Supplementary Notes

Supplementary Methods describing simulation potentials and Supplementary Figure S1 showing comparison of results for rigid and flexible tips. (PDF 127 kb)

Supplementary Figure S2

Variation of normal displacement, contact radius, friction and lateral stiffness with normal load for non-adhesive spherical tips. (PDF 113 kb)

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Luan, B., Robbins, M. The breakdown of continuum models for mechanical contacts. Nature 435, 929–932 (2005). https://doi.org/10.1038/nature03700

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