Tribology Letters

, Volume 56, Issue 1, pp 171–183 | Cite as

The Contact of Elastic Regular Wavy Surfaces Revisited

  • Vladislav A. Yastrebov
  • Guillaume Anciaux
  • Jean-François Molinari
Original Paper


We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we discover previously overlooked transition regimes. These are seen in particular in the evolution with applied load of the contact area and perimeter, the mean pressure and the probability density of contact pressure. These transitions are correlated with the contact area shape, which is affected by long range elastic interactions. Our analysis has implications for general random rough surfaces, as similar local transitions occur continuously at detached areas or coalescing contact zones. We show that the probability density of null contact pressures is nonzero at full contact. This might suggest revisiting the conditions necessary for applying Persson’s model at partial contacts and guide the comparisons with numerical simulations. We also address the evaluation of the contact perimeter for discrete geometries and the applicability of Westergaard’s solution for three-dimensional geometries.


Wavy surface Elastic contact Contact area Contact perimeter Compactness of contact area Persson’s boundary condition Probability density of contact pressure 



We are grateful to James A. Greenwood and to anonymous reviewers for constructive comments. GA and JFM greatly acknowledge the financial support from the European Research Council (ERCstg UFO-240332).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Vladislav A. Yastrebov
    • 1
  • Guillaume Anciaux
    • 2
  • Jean-François Molinari
    • 2
  1. 1.MINES ParisTechPSL Research University, Centre des Matériaux, CNRS UMR 7633EvryFrance
  2. 2.Civil Engineering (LSMS, IIC-ENAC, IMX-STI)Ecole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland

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