Mean field fracture in disordered solids: Statistics of fluctuations

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

Automated summary

Power law distributed fluctuations are known to accompany terminal failure in disordered brittle solids, emerging universally from threshold-type nonlinearity, quenched disorder, and long-range interactions. Systems are expected to transition between brittle and quasi-brittle (ductile) responses, characterized by a power law distribution of avalanches in the former and predominantly Gaussian statistics of avalanches in the latter. The self-tuning of the system towards the boundary separating brittle and ductile regimes is indicated by robust criticality observed in cases like earthquakes and collapsing porous materials.