Tribology Letters

, Volume 52, Issue 2, pp 223–229 | Cite as

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

  • I. A. Lyashenko
  • Lars Pastewka
  • Bo N. J. Persson
Original Paper


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.


Contact mechanics Contact area Contact stiffness Randomly rough surfaces Method of reduction of dimensionality 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • I. A. Lyashenko
    • 1
    • 2
  • Lars Pastewka
    • 3
    • 4
  • Bo N. J. Persson
    • 1
  1. 1.Peter Grünberg Institut-1FZ-JülichJülichGermany
  2. 2.Sumy State UniversitySumyUkraine
  3. 3.Department of Physics and AstronomyJohns Hopkins UniversityBaltimoreUSA
  4. 4.MikoTribologie Centrum μTCFraunhofer-Institut für Werkstoffmechanik IWMFreiburgGermany

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