This calculator can be used to calculate the adhesion pressure and pull-off pressure between two ealstic rough surfaces (macroscopically flats). The calculator is based on a simplified theory developed by Professor Ciavarella, see details here. Also see the description below according to reference [1]. For more details, contact please Professor Ciavarella [email protected]

For a given separation  u , adhesive pressure  P  is calculated according to a folowing expression:

 P/P_{th} = 3/(8 \gamma) * q_0*h_{RMS}*E^*/P_{th}*exp(\frac{-u}{\gamma*h_{RMS}}) - 1/{2k}*(Erfc(\frac{u-dr}{\sqrt(2)h_{RMS}}) - Erfc(\frac{u}{sqrt(2)h_{RMS}})) .

Here,  \gamma=0.4 ,  k=2 ,  q_0 is the roll-off wavelength,  P_{th}=w/dr with  w being the work of adhesion and  dr atomic spacing.  h_{RMS}   is the comined RMS roughness and  1/{E^*} = (\frac{1-\nu_1^2}{E_1} + \frac{1-\nu_2^2}{E_2}) is the reduced Young’s modulus,  \nu_1, E_1, \nu_2, E_2 are the Poisson and Young’s moduli of the bodies. Pull-off pressure is calculated as the minimum adhesion pressure for all possible separations.

[1] A very simple estimate of adhesion of hard solids with rough surfaces based on a bearing area model, M. Ciavarella, Meccanica, DOI 10.1007/s11012-017-0701-6.