Elastic contact of random surfaces with fractal and Hurst effects

Yaswanth Sai Jetti, Martin Ostoja-Starzewski

Research output: Contribution to journalArticlepeer-review


Most of the recent research on random surface contact mechanics has been on self-affine surfaces. In such models, the fractal dimension (which represents the 'roughness') and the Hurst parameter (which represents the 'spatial memory') are linearly dependent. In this study, we investigate the non-adhesive, frictionless contact between elastic solids with non-self-affine manifolds. In particular, we use Cauchy and Dagum covariance functions, which can decouple the fractal and Hurst effects, to describe the height distribution of the random surfaces. A numerical model based on the Boussinesq point load fundamental solutions is employed along with the discrete convolution FFT method to perform the contact analysis. We investigate the true contact area evolution under increasing load for surfaces with a wide range of fractal and Hurst parameters. It is observed that the contact area evolution at light loads is almost independent of the Hurst parameter and non-monotonically dependent on the fractal dimension. By contrast, previous studies predicted the contact evolution to be weakly dependent on the Hurst parameter and the fractal dimension. The curvature of the plots of the slope of the contact area evolution is found to depend on the fractal dimension, contrary to previous studies, which predicted either convexity or concavity.

Original languageEnglish (US)
Article number20220384
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2268
StatePublished - Dec 21 2022


  • fractal dimension
  • Hurst effect
  • rough surfaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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