Failure of hierarchical distributions of fibre bundles. I

Abstract

We consider by computational and analytic means the failure properties of hierarchically organized bundles of fibres with equal load sharing, a problem that may be treated exactly by renormalization methods. We show, independent of the specific failure properties of an individual fibre, that the threshold for failure of a fibre bundle obeys a universal scaling law with respect to the size of the bundle. Moreover, this scaling law is preserved for any hierarchical organization of fibre bundles.