Mean field fracture in disordered solids: statistics of fluctuations

Abstract

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 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.

24 pages, 15 figures

References in corpus (10)

• Power-law distributions in empirical data
• Statistical Models of Fracture
• Stability of adhesion clusters under constant force
• Impact of receptor-ligand distance on adhesion cluster stability
• Analysis of power-law exponents by maximum-likelihood maps
• Geometry and the onset of rigidity in a disordered network
• Rigidity percolation control of the brittle-ductile transition in disordered networks
• Rigidity-Controlled Crossover: From Spinodal to Critical Failure
• Slip avalanches in a fiber bundle model
• Damage spreading in quasi-brittle disordered solids: II. What the statistics of precursors teach us about compressive failure

Cited by in corpus (2)

• Thermal effects on fracture and brittle-to-ductile transition
• Damage spreading in quasi-brittle disordered solids: II. What the statistics of precursors teach us about compressive failure