SCALE-INVARIANT DISORDER IN FRACTURE AND RELATED BREAKDOWN PHENOMENA

We introduce and discuss the concept of scale-invariant disorder in connection with breakdown and fracture models of disordered brittle materials. We show that in the case of quenched-disorder models where the local breaking thresholds are randomly sampled, only two numbers determine the scaling properties of the models. These numbers characterize the behavior of the distribution of thresholds close to zero and to infinity. We review briefly some results obtained in the literature and show how they fit into this framework. Finally, we address the case of an annealed disorder, and show via a mapping onto a quenched-disorder model, that our analysis is also valid there.