A New Fudge Factor for Persson's Theory of Purely Normal Elastic Rough Surface Contact

After more than two decades of development, Persson's theory has become one of the dominantly used theoretical tools to analyze the interaction between a nominally flat rough surface and a rigid flat. The original theory (Persson in J. Chem. Phys. 115(8):3840-3861, 2001) tends to overestimate and underestimate the relative contact area and strain energy, respectively, for linear elastic purely normal contact. Several fudge factors, obtained empirically based on numerical solutions, have been used to amend the strain energy associated with each wavenumber, resulting in scale history-dependent formulations for the relative contact area and probability density function (PDF) of contact pressure, which significantly complicate the solution process. We provide a new fudge factor that results in simple formulations of the relative contact area and PDF of contact pressure, which only relies on the present scale. Compared with the relative contact area and PDF of contact pressure solved by Green's Function Molecular Dynamics (GFMD), Persson's theory using the new fudge factor shows similar accuracy to other variants. Among all variants of Persson's theory, the use of the new hybrid formulation of strain energy results in the best agreement with GFMD. Using the new fudge factor, various interfacial properties (e.g., the average interfacial gap) can be derived with a simple form, and solved more quickly, with acceptable accuracy.