Bounds on the electrical resistance between contacting elastic rough bodies

A method is developed for placing bounds on the electrical contact conductance between contacting elastic bodies with rough surfaces. An analogy is ­ rst established between contact conductance and the incremental sti¬ness in the mechanical contact problem. Results from contact mechanics and the reciprocal theorem are then used to bracket the mechanical load{displacement curve between those for two related smooth contact problems. This enable bounds to be placed on the incremental sti¬ness and hence on the electrical conductance for the rough contact problem. The method is illustrated by two simple examples, but its greatest potential probably lies in establishing the maximum e¬ect of neglected microscales of roughness in a solution of the contact problem for bodies with multiscale or fractal roughness.