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We have employed a numerical procedure to analyze the adhesive contactbetween a soft elastic layer and a rough rigid substrate. The solution of theproblem is obtained by calculating the Green's function which links thepressure distribution to the normal displacements at the interface. The problemis then formulated in the form of a Fredholm integral equation of the firstkind with a logarithmic kernel, and the boundaries of the contact area arecalculated by requiring that the energy of the system is stationary. Themethodology has been employed to study the adhesive contact between an elasticsemi-infinite solid and a randomly rough rigid profile with a self-affinefractal geometry. We show that, even in presence of adhesion, the true contactarea still linearly depends on the applied load. The numerical results are thencritically compared with the prediction of an extended version of the Persson'scontact mechanics theory, able to handle anisotropic surfaces, as 1Dinterfaces. It is shown that, for any given load, Persson's theoryunderestimates the contact area of about 50% in comparison with our numericalcalculations. We find that this discrepancy is larger than what is found for 2Drough surfaces in case of adhesionless contact. We argue that this increaseddifference might be explained, at least partially, by considering thatPersson's theory is a mean field theory in spirit, so it should work better for2D rough surfaces rather than for 1D rough surfaces. We also observe, that thepredicted value of separation is in very good agreement with our numericalresults as well as the exponent of the power spectral density of the contactpressure distribution and of the elastic displacement of the solid. Therefore,we conclude that Persson's theory captures almost exactly the main qualitativebehavior of the rough contact phenomena.

Adhesive contact of rough surfaces: comparison between numerical calculations and analytical theories