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Sci Rep. 2017 Jul 31;7(1):6900. doi: 10.1038/s41598-017-07234-4.

Load-separation curves for the contact of self-affine rough surfaces.

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Hamburg University of Technology, Department of Mechanical Engineering, Am Schwarzenberg-Campus 1, 21073, Hamburg, Germany.
Imperial College London, Exhibition Road, London, SW7 2AZ, UK.
Politecnico di BARI. Department of Mechanics, Mathematics and Management, V Gentile 182, 70126, Bari, Italy.


There are two main approximate theories in the contact of rough solids: Greenwood-Williamson asperity theories (GW) and Persson theories. Neither of them has been fully assessed so far with respect to load-separation curves. Focusing on the most important case of low fractal dimension (D f  = 2.2) with extensive numerical studies we find that: (i) Persson's theory describes well the regime of intermediate pressures/contact area, but requires significant corrective factors: the latter depend also on upper wavevector cutoff of the roughness; hence, (ii) Persson's theory does not predict the correct functional dependence on magnification; (iii) asperity theories in the discrete version even neglecting interaction effects are more appropriate in the range of relatively large separations, also to take into consideration of the large scatter in actual realization of the surface.

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