Effect of roughness on the adhesive tractions between contacting bodies

A method is proposed for estimating the effect of broad spectrum surface roughness on the adhesion between elastic bodies. At each length scale, the effect of fine scale roughness is modelled by a modified traction law whilst an added coarse scale increment is described by a probability distribution of mean gap as modified by elastic deformation. Instabilities occur for relatively smooth surfaces whose linear dimensions are sufficiently large to support long wavelength perturbations. The method is validated by comparison with direct numerical calculations, in the range where this is practicable. It is then applied to power-law spectra with various values of height variance and lower wavenumber cutoff. The results show that the effect of roughness is dominated by the height variance m0, but at lower wavenumber elastic deformation reduces the dependence on m0, except near the unstable range.