BURST AVALANCHES IN SOLVABLE MODELS OF FIBROUS MATERIALS

We review limiting models for fracture in bundles of fibers, with stat istically distributed thresholds for breakdown of individual fibers. D uring the breakdown process, avalanches consisting of simultaneous rup ture of several fibers occur, and the distribution D(Delta) of the mag nitude Delta of such avalanches is the central characteristic in our a nalysis. For a bundle of parallel fibers two limiting models of load s haring are studied and contrasted: the global model, in which the load carried by a bursting fiber is equally distributed among the survivin g members; and the local model, in which the nearest surviving neighbo rs take up the load. For the global model we investigate in particular the conditions on the threshold distribution which would lead to anom alous behavior, i.e., deviations from the asymptotics D(Delta) similar to Delta(-5/2), known to be the generic behavior. For the local model no universal power-law asymptotics exists, but we show for a particul ar threshold distribution how the avalanche distribution can neverthel ess be explicitly calculated in the large-bundle limit.