Inclusion of "interaction" in the Greenwood & Williamson contact theory

Recent direct implementation of asperity theories is reinterpreted here to formulate an improved version of the Greenwood and Williamson (GW) theory with the inclusion of interaction between asperities. This is achieved by treating the contact pressures as uniformly distributed over the apparent contact area and the resulting deformation as uniform. The correction is equivalent to an increase of the effective separation of the mean planes by a quantity proportional to the nominal pressure, resulting in a reduction of the “real” area of contact and of total load for a given separation. However, the area–load relationship is unchanged. The correction effectively depends on the ratio between the nominal pressure and the elastic modulus multiplied by the ratio between the size of the nominal contact area and standard deviation of the asperity heights. For contacts much larger than the size of roughness, uniform interaction effectswould be dominant at relatively modest pressures (particularly for soft materials). This also means that the effect of interaction is unlimited. However, the only significant change is in the prediction of gas-tightness, it is harder to seal a large area than a small one. The modification of the theory has a significant effect on stiffness and conductance. Indeed, a parallel is drawn between this correction and the “clustering” terms of resistance in the Holm–Greenwood formulae for a cluster of circular spots. Finally, numerical contact simulations using Weierstrass–Mandelbrot (WM) surfaces show a general agreement with the improved theory but also significant scatter for low load levels. Taking into account the effect of asperity interaction, the improved GWtheory is now able to predict the numerically obtained contact response for intermediate load levels.