Multiscale Modeling of Two Dimensional Rough Surface Contacts


A hybrid simulation method is used to study non-adhesive contact between two-dimensional self-affine rough surfaces. We find strong scale dependence as the contact dimensions decrease to the atomic scale. Both purely elastic and plastic materials are considered, and show different trends with system size. In all cases the contact area rises linearly with applied load, but the slope is substantially different from continuum predictions. We also examine the effect of commensurability between contacting surfaces. Contact area and frictional forces can be very different for commensurate and incommensurate surfaces, particularly for plastic materials.

This is a preview of subscription content, access via your institution.


  1. 1.

    J. A. Greenwood and J. B. P. Williamson, Proc. Roy. Soc. A295, 300(1966).

    Google Scholar 

  2. 2.

    A. W. Bush, R. D. Gibson and T. R. Thomas, Wear 35, 87 (1975).

    Article  Google Scholar 

  3. 3.

    K. L. Johnson, Contact Mechanics, (Cambridge, Cambridge, 1985), p. 90.

    Google Scholar 

  4. 4.

    B. N. J. Persson, Phys. Rev. Lett. 87, 116101 (2001).

    CAS  Article  Google Scholar 

  5. 5.

    B. Luan and M. O. Robbins, submitted (2004).

  6. 6.

    S. Hyun, L. Pei, J.-F. Molinari, and M. O. Robbins, Phy. Rev. E. 70, 26117 (2004).

    CAS  Article  Google Scholar 

  7. 7.

    T. J. R. Hughes and T. Belytschko, Journal of Applied Mechanics 50, 1033 (1983).

    Article  Google Scholar 

  8. 8.

    R. F. Voss, (Springer-Verlag, Berlin, 1985) pp. 805.

  9. 9.

    B. Luan, S. Hyun, N. Bernstein and M. O. Robbins, unpublished.

  10. 10.

    M. H. Müser, L. Wenning and M. O. Robbins Phys. Rev. Lett 86, 1295 (2001).

    Article  Google Scholar 

Download references


We thank J. F. Molinari and J. A. Harrison for helpful discussions. This material is based upon work supported by the National Science Foundation under Grant No.CMS-0103408.

Author information



Corresponding author

Correspondence to Binquan Luan.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Luan, B., Hyun, S., Robbins, M.O. et al. Multiscale Modeling of Two Dimensional Rough Surface Contacts. MRS Online Proceedings Library 841, R7.4 (2004).

Download citation