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Mahesh, S.; Phoenix, S. Leigh; Beyerlein, Irene J.

doi:10.1023/a:1015729607223

Cited by 70 publications

(42 citation statements)

References 45 publications

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“…For large values of a 0 we see a narrowing of the distribution (in fact, ∆σ c /σ c goes to zero with a 0 increasing) and the distribution is well approximated in the central part by a Gaussian shape. This is interesting, since the Gaussian distribution is also obtained in global load sharing fiber bundles [18] and in chains-of-fiber-bundle models with local load sharing and heterogeneous fiber strengths [50]. However, even for the largest a 0 = 48 the tails are broader than in the Gaussian case.…”

Section: Strength Of Materials With Flawsmentioning

confidence: 84%

Size effects in statistical fracture

Alava

Nukala

Zapperi

2009

J. Phys. D: Appl. Phys.

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We review statistical theories and numerical methods employed to consider the sample size dependence of the failure strength distribution of disordered materials. We first overview the analytical predictions of extreme value statistics and fiber bundle models and discuss their limitations. Next, we review energetic and geometric approaches to fracture size effects for specimens with a flaw. Finally, we overview the numerical simulations of lattice models and compare with theoretical models.

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Section: Strength Of Materials With Flawsmentioning

confidence: 84%

Size effects in statistical fracture

Alava

Nukala

Zapperi

2009

J. Phys. D: Appl. Phys.

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“…The brittle-to-tough transition was observed in simulated bundle failures of Hedgepeth load sharing bundles by Mahesh et al [6,7]. They found that as ρ decreased below about a value of about 2, deviations from the weakest-link scaling given by Eq.…”

Section: Introduction I1 Backgroundmentioning

confidence: 87%

“…More distant fibres carry the remaining 1 ⁄3 load dropped by the broken fibre. While realistic, the determination of stress concentration on intact fibres using the Hedgepeth [4] or Hedgepeth and Van Dyke [5] models is computationally tedious for model composites with more than a few thousand fibre breaks [6,7].…”

Section: Introduction I1 Backgroundmentioning

confidence: 99%

Strength distribution of planar local load-sharing bundles

Habeeb

Mahesh

2015

Phys. Rev. E

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Monte Carlo simulations and probabilistic modeling are employed to understand the strength distribution of a planar bundle of local load-sharing fibers. The fibers are distributed randomly within a unit square according to a Poisson process, and the fiber strengths are Weibull distributed with exponent ρ. Monte Carlo failure simulations of bundles comprised of up to 10(5) fibers suggests that the bundle strength distribution obeys weakest-link scaling for all ρ. Also, a probabilistic model of the weakest-link event is proposed. This model introduces a failure event at a size scale between that of the fiber and that of the bundle, whose failure statistics follows that of equal load-sharing bundles. The weakest-link event is modelled as the growth of a tight cluster of these equal load-sharing bundles. The size of the equal load-sharing bundles increases with decreasing ρ. The simulated bundle strength distributions and those predicted by the model are compared, and excellent agreement is obtained.

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“…This model was introduced [7], indeed, to estimate the strength of cotton in textile engineering. Since then, it has been extensively studied in the context of distribution of failure strength and failure time of disordered materials under tensile loading or twist by viewing fibers as elements of the disordered solids having a finite failure threshold (or even a finite lifetime dependent of loading) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] (see [23] for a review).Conventionally, the fiber bundle model is viewed as a set of parallel fibers, having failure thresholds randomly drawn from a distribution (say, uniform in [0 : 1]), clamped between two horizontal plates. When the bottom plate is loaded, some of the weak fibers break, and their load is redistributed among the surviving fibers, which may in turn break or survive depending on their failure thresholds.…”

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confidence: 99%

Maximizing the Strength of Fiber Bundles under Uniform Loading

Biswas

Sen

2015

Phys. Rev. Lett.

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The collective strength of a system of fibers, each having a failure threshold drawn randomly from a distribution, indicates the maximum load carrying capacity of different disordered systems ranging from disordered solids, power-grid networks, to traffic in a parallel system of roads. In many of the cases where the redistribution of load following a local failure can be controlled, it is a natural requirement to find the most efficient redistribution scheme, i.e., following which system can carry the maximum load. We address the question here and find that the answer depends on the mode of loading. We analytically find the maximum strength and corresponding redistribution schemes for sudden and quasi static loading. The associated phase transition from partial to total failure by increasing the load has been studied. The universality class is found to be dependent on the redistribution mechanism.The response of an ensemble of elements having random failure thresholds plays a crucial role in the breakdown properties of heterogeneous systems [1]. Such systems can be, for example, disordered solids under stress, power-grid networks carrying currents, roads carrying car traffic, or redundant computer circuitry etc. The failure properties of these systems are strongly dependent upon the load redistribution mechanism following a local breakdown. While in some cases (e.g. solids under stress) such mechanisms are properties inherent to the system, in many other cases (e.g. power-grids [2], traffic controls [3]) it is a matter of design that can be optimized so as to achieve the most robust configuration (see e.g. [4]). Such robustness properties of networks connecting elements with varying failure thresholds under targeted or random attacks have received substantial attention [5,6].In this Letter, we address the question of maximizing the strength of a disordered system by finding the most effective redistribution scheme analytically using the fiber bundle model as a generic example. This model was introduced [7], indeed, to estimate the strength of cotton in textile engineering. Since then, it has been extensively studied in the context of distribution of failure strength and failure time of disordered materials under tensile loading or twist by viewing fibers as elements of the disordered solids having a finite failure threshold (or even a finite lifetime dependent of loading) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] (see [23] for a review).Conventionally, the fiber bundle model is viewed as a set of parallel fibers, having failure thresholds randomly drawn from a distribution (say, uniform in [0 : 1]), clamped between two horizontal plates. When the bottom plate is loaded, some of the weak fibers break, and their load is redistributed among the surviving fibers, which may in turn break or survive depending on their failure thresholds. The load transfer rule, generally a function of distance from the broken fiber, plays a vital role (see e.g., [24,25]). While substantial attention has been concentra...

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Cited by 70 publications

References 45 publications

Size effects in statistical fracture

Size effects in statistical fracture

Strength distribution of planar local load-sharing bundles

Maximizing the Strength of Fiber Bundles under Uniform Loading

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