From infinitesimal to full contact between rough surfaces: Evolution of the contact area

• Evolution of the contact area with increasing pressure for different surface spectra.
• Effect of the spectral breadth (Nayak’s parameter) on the contact area evolution.
• Lower cutoff wavenumber controls the Gaussianity of the surface roughness.
• Formulae linking Hurst exponent, cutoff wavenumbers and Nayak’s parameter.

We carry out a statistically meaningful study on self-affine rough surfaces in elastic frictionless non-adhesive contact. We study the evolution of the true contact area under increasing squeezing pressure from zero up to full contact, which enables us to compare the numerical results both with asperity based models at light pressures and with Persson’s contact model for the entire range of pressures. A good agreement of numerical results with Persson’s model is obtained for the shape of the area-pressure curve especially near full contact, however, we obtain qualitatively different results for its derivative at light pressures. We investigate the effects of the longest and shortest wavelengths in surface spectrum, which control the surface Gaussianity and spectrum breadth (Nayak’s parameter). We revisit the influence of Nayak’s parameter, which is frequently assumed to play an important role in mechanics of rough contact.

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