Mean field fracture in disordered solids: Statistics of fluctuations

Power law distributed fluctuations are known to accompany \emph{terminal} failure in disordered brittle solids. The associated intermittent scale-free behavior is of interest from the fundamental point view as it emerges universally an intricate interplay threshold-type nonlinearity, quenched disorder, and long-range interactions. We use simplest mean-field description such systems show that they can be expected undergo a transition between quasi-brittle (ductile) responses. While former characterized by power distribution avalanches, latter, statistics avalanches predominantly Gaussian. realization particular regime depends on variance disorder effective rigidity represented combination elastic moduli. argue robust criticality, cases earthquakes collapsing porous materials, indicates self-tuning system towards boundary separating ductile regimes.