Avalanche dynamics of fiber bundle models

Hidalgo, R. C.; Kun, Ferenc; Kovács, Kornél; Pagonabarraga, Ignacio

doi:10.1103/physreve.80.051108

Cited by 44 publications

(62 citation statements)

References 36 publications

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“…Note that the absence of a catastrophic avalanche means that even the last avalanche obeys the same statistics as all others. This behavior is in strong contrast to what is usually observed when the disorder is moderate: as the load increases the size of bursts spans a broader and broader range when approaching global failure so that the average event size rapidly increases towards failure [16,20,21].…”

Section: Crackling Noisecontrasting

confidence: 73%

“…This mechanism explains the absence of increasing bursting activity in figure 2 with increasing load. Note that a catastrophic avalanche occurs when ( ) σ > a 1 [20], which can only be obtained in our case for µ > 1. Hence, for any µ < 1 the system approaches failure in a stable way, all fibers breaking in finite avalanches.…”

Section: Crackling Noisementioning

confidence: 59%

“…In order to understand the absence of acceleration in the avalanche activity and the emergence of the low exponent of the size distribution it is instructive to calculate the average number a of fiber breakings triggered immediately by the failure of a single fiber at the strain ε [20,21]. Since the load σ ε = E dropped by the broken fiber is equally shared by all the intact fibers of number…”

Section: Crackling Noisementioning

confidence: 99%

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Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture

2015

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Abstract.We investigate the eect of the amount of disorder on the fracture process of heterogeneous materials in the framework of a fiber bundle model. The limit of high disorder is realized by introducing a power law distribution of fiber strength over an infinite range. We show that on decreasing the amount of disorder by controlling the exponent of the power law the system undergoes a transition from the quasi-brittle phase where fracture proceeds in bursts to the phase of perfectly brittle failure where the first fiber breaking triggers a catastrophic collapse. For equal load sharing in the quasi-brittle phase the fat tailed disorder distribution gives rise to a homogeneous fracture process where the sequence of breaking bursts does not show any acceleration as the load increases quasi-statically. The size of bursts is power law distributed with an exponent smaller than the usual mean field exponent of fiber bundles. We demonstrate by means of analytical and numerical calculations that the quasi-brittle to brittle transition is analogous to continuous phase transitions and determine the corresponding critical exponents. When the load sharing is localized to nearest neighbor intact fibers the overall characteristics of the failure process prove to be the same, however, with dierent critical exponents. We show that in the limit of the highest disorder considered the spatial structure of damage is identical with site percolation-however, approaching the critical point of perfect brittleness spatial correlations play an increasing role, which results in a dierent cluster structure of failed elements.

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Section: Crackling Noisecontrasting

confidence: 73%

Section: Crackling Noisementioning

confidence: 59%

Section: Crackling Noisementioning

confidence: 99%

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Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture

2015

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“…Figure 10 presents the exponent τ k obtained by fitting with Eq. (10). For the lowest rank the exponent has a high value τ k = 3.26 then it monotonically decreases and for the highest ranks it tends to the vicinity of τ k = 1.0.…”

Section: Approach To Failure Through Breaking Of Recordsmentioning

confidence: 87%

“…The ultimate challenge of the field is to find statistical signatures, which could be exploited to forecast the impending catastrophic failure [8]. For this purpose the analysis of synthetic time series of simulated fracture processes is indispensable since they allow a range of variables to be controlled and investigated independently, and allow representative sampling of underlying trends and statistical variability over a large number of trials [9,10].…”

Section: Introductionmentioning

confidence: 99%

Record-breaking events during the compressive failure of porous materials

et al. 2016

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An accurate understanding of the interplay between random and deterministic processes in generating extreme events is of critical importance in many fields, from forecasting extreme meteorological events to the catastrophic failure of materials and in the Earth. Here we investigate the statistics of record-breaking events in the time series of crackling noise generated by local rupture events during the compressive failure of porous materials. The events are generated by computer simulations of the uniaxial compression of cylindrical samples in a discrete element model of sedimentary rocks that closely resemble those of real experiments. The number of records grows initially as a decelerating power law of the number of events, followed by an acceleration immediately prior to failure. The distribution of the size and lifetime of records are power laws with relatively low exponents. We demonstrate the existence of a characteristic record rank k * , which separates the two regimes of the time evolution. Up to this rank deceleration occurs due to the effect of random disorder. Record breaking then accelerates towards macroscopic failure, when physical interactions leading to spatial and temporal correlations dominate the location and timing of local ruptures. The size distribution of records of different ranks has a universal form independent of the record rank. Subsequences of events that occur between consecutive records are characterized by a power-law size distribution, with an exponent which decreases as failure is approached. High-rank records are preceded by smaller events of increasing size and waiting time between consecutive events and they are followed by a relaxation process. As a reference, surrogate time series are generated by reshuffling the event times. The record statistics of the uncorrelated surrogates agrees very well with the corresponding predictions of independent identically distributed random variables, which confirms that temporal and spatial correlation in the crackling noise is responsible for the observed unique behavior. In principle the results could be used to improve forecasting of catastrophic failure events, if they can be observed reliably in real time.

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