On the almost-complete contact of elastic rough surfaces: The removal of tensile patches

The “almost-complete” contact of elastic rough surfaces is studied by the method introduced by Johnson of reducing the mean pressure below the value needed for full contact, and then removing the resulting patches of tensile stresses by superposition (Johnson et al., 1985). The procedure is examined for circular tensile patches using Sneddon’s (1946) equations, applied to a variety of (tensile) pressure distributions: Sneddon’s analysis is extended slightly to find the associated pressure distributions. It is found that the removal of circular patches of tensile stress does not alter the total load. The total out-of-contact area is always greater than the total area of tensile stress, but the increase depends on the behaviour of the pressures adjacent to the tensile region, and area increases of any amount from 14% upwards can be obtained with plausible pressure distributions: the hope that the increase will always be close to 50% is unwarranted.