Statistical failure cascades: from individual fibers to catastrophic breakdown
Model
--
Intact fibers
--
Last avalanche size
The fiber bundle model (Peirce 1926, Daniels 1945) is a paradigm for statistical fracture. Under equal load sharing, there is an exact critical point where the bundle fails catastrophically — a mean-field phase transition. Avalanche sizes follow a power law D(Δ) ~ Δ^(-5/2).