Failure of hierarchical distributions of fibre bundles. I

The failure properties of hierarchically organized bundles of fibers with equal load sharing are investigated using both computational and analytical methods. Results revealed an apparently universal asymptotic scaling law relating the stress threshold for failure to the size of the system. It was found that the bound identified by the weakest-link theory did not provide a realistic indication of the threshold for failure. It is shown that the threshold decreased so slowly as to be practically indistinguishable from a critical point. (I.S.)