Universality class of fiber bundles with strong heterogeneities

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

doi:10.1209/0295-5075/81/54005

Cited by 29 publications

(46 citation statements)

References 23 publications

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“…For β = 1/(2 ln 10) Eqn. (17) yields ∆ c = ∞. Thus only the ξ = 3/2 power law is observed as any avalanche of finite size ∆ is less than the value of ∆ c at this particular value of β.…”

Section: Avalanche Size Distributionmentioning

confidence: 82%

“…Such cases of extremely heterogeneous disorder has not been very well studied in the literature of fiber bundle model. Another form of strong heterogeneity has been studied where a fraction of fibers are completely unbreakable and the breaking thresholds of the rest are drawn from some distribution [17,18]. In this paper we therefore address the problem of FBMs with highly heterogeneous power law distributed breaking thresholds of individual fibers.…”

Section: Introductionmentioning

confidence: 99%

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Fiber bundle model with highly disordered breaking thresholds

2015

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We present a study of the fiber bundle model using equal load sharing dynamics where the breaking thresholds of the fibers are drawn randomly from a power law distribution of the form p(b) ∼ b −1 in the range 10 −β to 10 β . Tuning the value of β continuously over a wide range, the critical behavior of the fiber bundle has been studied both analytically as well as numerically. Our results are: (i) The critical load σc(β, N ) for the bundle of size N approaches its asymptotic value σc(β) as σc(β, N ) = σc(β)+AN −1/ν(β) where σc(β) has been obtained analytically as σc(β) = 10 β /(2βe ln 10) for β ≥ βu = 1/(2 ln 10), and for β < βu the weakest fiber failure leads to the catastrophic breakdown of the entire fiber bundle, similar to brittle materials, leading to σc(β) = 10 −β ; (ii) the fraction of broken fibers right before the complete breakdown of the bundle has the form 1 − 1/(2β ln 10); (iii) the distribution D(∆) of the avalanches of size ∆ follows a power law D(∆) ∼ ∆ −ξ with ξ = 5/2 for ∆ ≫ ∆c(β) and ξ = 3/2 for ∆ ≪ ∆c(β), where the crossover avalanche size ∆c(β) = 2/(1−e10 −2β ) 2 .

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Section: Avalanche Size Distributionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Fiber bundle model with highly disordered breaking thresholds

2015

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“…Theoretical studies of crackling noise are usually based on stochastic fracture models such as fiber bundles [9,24,25] and the fuse model [2]. As a novel approach to the problem, in the present paper we investigated the properties of crackling noise emerging during the jerky propagation of a crack in three-point bending tests using a discrete element modeling technique.…”

Section: Discussionmentioning

confidence: 99%

Crackling noise in three-point bending of heterogeneous materials

Timár

Kun

2011

Phys. Rev. E

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We study the crackling noise emerging during single crack propagation in a specimen under three-point bending conditions. Computer simulations are carried out in the framework of a discrete element model where the specimen is discretized in terms of convex polygons and cohesive elements are represented by beams. Computer simulations revealed that fracture proceeds in bursts whose size and waiting-time distributions have a power-law functional form with an exponential cutoff. Controlling the degree of brittleness of the sample by the amount of disorder, we obtain a scaling form for the characteristic quantities of crackling noise of quasibrittle materials. Analyzing the spatial structure of damage we show that ahead of the crack tip a process zone is formed as a random sequence of broken and intact mesoscopic elements. We characterize the statistics of the shrinking and expanding steps of the process zone and determine the damage profile in the vicinity of the crack tip.

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“…Indeed the coarse-grained paradigm appears to be the more appropriate framework for the modeling of fibrosis considering the recent developments in the fibers of cytoskeleton [214][215][216]. …”

Section: Coarse-grained Modelingmentioning

confidence: 99%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Bianca

2016

Physics of Life Reviews

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Pathological fibrosis is the result of a failure in the wound healing process. The comprehension and the related modeling of the different mechanisms that trigger fibrosis is a challenge of many researchers that work in the field of medicine and biology. The modern scientific analysis of a phenomenon generally consists of three major approaches: theoretical, experimental, and computational. Different theoretical tools coming from mathematics and physics have been proposed for the modeling of the physiological and pathological fibrosis. However a complete framework is missing and the development of a general theory is required. This review aims at finding a unified approach in the modeling of fibrosis diseases that takes into account the different phenomena occurring at each level: molecular, cellular and tissue. Specifically by means of a critical analysis of the different models that have been proposed in the mathematical, computational and physical biology, from molecular to tissue scales, a multiscale approach is proposed, an approach that has been strongly recommended by top level biologists in the past decades.

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Universality class of fiber bundles with strong heterogeneities

Cited by 29 publications

References 23 publications

Fiber bundle model with highly disordered breaking thresholds

Fiber bundle model with highly disordered breaking thresholds

Crackling noise in three-point bending of heterogeneous materials

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

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