#6804. Mean field fracture in disordered solids: Statistics of fluctuations

December 2026publication date
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Journal’s subject area:
Mechanical Engineering;
Mechanics of Materials;
Condensed Matter Physics;
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Abstract:
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.
Keywords:
Brittle to ductile; Criticality; Fluctuations; Fracture

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