Elastic Contact Stiffness and Contact Resistance for Fractal Profiles

A recent theorem due to Barber shows an analogy between conductance and incremental stiffness of a contact, implying bounds on conductance based on peak-to-peak roughness. This shows that even a fractal roughness, with bounded amplitude, has a finite conductance. The analogy also permits a simple interpretation of classical results of rough contact models based on independent asperities such as Greenwood-Williamson and developments. For example, in the GW model with exponential distribution of asperity heights, the conductance is found simply proportional to load, and inversely proportional to a roughness amplitude parameter which does not depend greatly on resolution, contrary to parameters of slopes and curvatures. However, for the Gaussian distribution or for more refined models also considering varying curvature of asperities (such as Bush Gibson and Thomas), there is dependence on sampling interval and the conductance grows unbounded. An alternative choice of asperity definition (Aramaki-Majumdar-Bhushan) is suggested, which builds on the geometrical intersection of the rough surface, with the consequence of a finite contact area, and converging load-separation and load-conductance relationship. A discussion follows, also based on numerical results.