Mean field fracture in disordered solids: Statistics of fluctuations. (January 2022)

• Record Type: Journal Article
• Authors: Borja da Rocha, Hudson; Truskinovsky, Lev
• Is Part Of: Journal of the mechanics and physics of solids. Volume 158(2022)
• Publication Date: 2022-01
• Subjects: Fracture -- Criticality -- Brittle to ductile -- Fluctuations; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2021.104646
• Languages: English
• ISSNs: 0022-5096

Abstract

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.