Multiscale electrical contact resistance in clustered contact distribution

For contact between rough surfaces of conductors in which a clustered contact spot distribution is dominant through a multiscale process, electrical contact resistance (ECR) is analysed using a smoothed version of Greenwood's model (Jang and Barber 2003 J. Appl. Phys. 94 7215), which is extended to estimate the statistical distribution of contact spots considering the size and the location simultaneously. The application of this statistical method to a contact spot distribution, generated by the finite element method using a fractal surface defined by the random midpoint displacement algorithm, identifies the effect of the clustered contact distribution on ECR, showing that including a finer scale in the fractal contact surface causes the predicted resistance to approach a finite limit. It is also confirmed that the results are close to that of Barber's analogy (Barber 2003 Proc. R. Soc. Lond. A 459 53) regarding incremental stiffness and conductance for elastic contact.