Strongly different adhesion reduction for 1D or 2D random fractal roughness

Abstract Afferrante Violano & Dini ("How does roughness kill adhesion?" J Mech Phys Solids 2023 105465) have recently studied by a finite element-based model how roughness kills adhesion in 1D self-affine fractal profiles. Their results confirm that for low fractal dimension (D<1.5), adhesion is influenced by long wavelength roughness only, but with high fractal dimensions, adhesion is found to be more sensitive to the magnification (the broadness of the power spectrum). The seem to conclude that this is in agreement with Persson-Tosatti's criterion, and not with Ciavarella's BAM criterion. However, by comparing their results with the Persson-Tosatti criterion (which we show is identical in 1D or 2D for a typical power law PSD if written in terms of rms roughness and magnification), we find that adhesion persists in their 1D case for rms roughness one or more orders of magnitude higher than expected for 2D isotropic roughness, showing both criteria are not really appropriate to 1D roughness. This suggests the mechanism of load amplification along contact lines and the associated elastic instabilities, excited by the pure 1D roughness, is at play. Finally, we show that unfortunately their dependences on magnification is not really conclusive to the debate of the Persson-Tosatti vs the Ciavarella's BAM criteria, because both can show a sensible dependence on magnification in appropriate range, for all fractal dimensions.