Precursors of catastrophe in the Bak-Tang-Wiesenfeld, Manna, and random-fiber-bundle models of failure

Pradhan, Srutarshi; Chakrabarti, Bikas K.

doi:10.1103/physreve.65.016113

Cited by 58 publications

(96 citation statements)

References 17 publications

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“…It has been found that under a slowly increasing external load macroscopic failure is preceded by a bursting activity due to the cascading nature of local breakings [3,4]. Since the bursts can be recorded experimentally by the acoustic emission technique, these precursors addressed the possibility of forecasting the imminent failure event [11][12][13][14]. The size distribution of bursts was proven to be a power law with an exponent which is universal for a broad class of disorder distributions [3,4].…”

mentioning

confidence: 99%

Universality class of fiber bundles with strong heterogeneities

Hidalgo¹,

Kovács²,

Pagonabarraga³

et al. 2008

Europhys. Lett.

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Abstract. -We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0 ≤ α ≤ 1 of fibers is unbreakable, while the remaining 1 − α fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components αc which separates two qualitatively different regimes of the system: below αc the burst size distribution is a power law with the usual exponent τ = 5/2, while above αc the exponent switches to a lower value τ = 9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena.

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mentioning

confidence: 99%

Universality class of fiber bundles with strong heterogeneities

Hidalgo¹,

Kovács²,

Pagonabarraga³

et al. 2008

Europhys. Lett.

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“…from equation (10). Hence the susceptibility diverges as the applied stress σ approaches the critical value σ c = 1 4 .…”

Section: Breaking Dynamics Of the Els Modelsmentioning

confidence: 99%

“…Therefore the relaxation time diverges following a power-law as σ → σ c from below 10,11 . One can also consider the breakdown susceptibility χ, defined as the change of U * (σ) due to an infinitesimal increment of the applied stress σ 10,11,12…”

Section: Breaking Dynamics Of the Els Modelsmentioning

confidence: 99%

“…The recent mean field estimate of the 'avalanches' in the ELS bundles 8,11 , gives a new power law 11 . The phase transition 7,8 and dynamic critical behavior of the fracture process in such bundles has been established through recursive formulation 9,10,11,12 of the failure dynamics. The exact solutions 10,11,12 of the recursion relations suggest universal values of the exponents involved.…”

Section: Introductionmentioning

confidence: 99%

“…The phase transition 7,8 and dynamic critical behavior of the fracture process in such bundles has been established through recursive formulation 9,10,11,12 of the failure dynamics. The exact solutions 10,11,12 of the recursion relations suggest universal values of the exponents involved. Attempt has also been made 13 to study the ELS ans LLS bundles from a single framework introducing a 'range of interaction' parameter which determines the load transfer rule.…”

Section: Introductionmentioning

confidence: 99%

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Failure Properties of Fiber Bundle Models

Pradhan

Chakrabarti

2003

Int. J. Mod. Phys. B

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We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load sharing model. The strength of the fibers are assumed to be distributed randomly within a finite interval. The democratic fiber bundles show a solvable phase transition at a critical stress (load per fiber). The dynamic critical behavior is obtained analytically near the critical point and the critical exponents are found to be universal. This model also shows elastic-plastic like nonlinear deformation behavior when the fiber strength distribution has a lower cutoff. We solve analytically the fatigue-failure in a democratic bundle, and the behavior qualitatively agrees with the experimental observations. The strength of the local load sharing bundles is obtained numerically and compared with the existing results. Finally we map the failure phenomena of fiber bundles in terms of magnetic model (Ising model) which may resolve the ambiguity of studying the failure properties of fiber bundles in higher dimensions.

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2015

The Fiber Bundle Model

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Precursors of catastrophe in the Bak-Tang-Wiesenfeld, Manna, and random-fiber-bundle models of failure

Cited by 58 publications

References 17 publications

Universality class of fiber bundles with strong heterogeneities

Universality class of fiber bundles with strong heterogeneities

Failure Properties of Fiber Bundle Models

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