On the distribution and moments of the strength of a bundle of filaments

Suh, Myung‐Won; Bhattacharyya, B. B.; Grandage, A.

doi:10.1017/s0021900200110654

Cited by 17 publications

(9 citation statements)

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“…The dynamics of the model discussed in the present work is to some extent based on the Fibre-Bundle Model (FBM), a simple but revealing approach to the study of failure originally introduced by Peirce [4] to explore the properties of textiles and subsequently extensively explored [5,30,31,32,33,34,35]. The FBM consists of a bundle of N harmonic fibres loaded in parallel by a slowly increasing external load F .…”

Section: Model Details and Featuresmentioning

confidence: 99%

A random neighbour model for yielding

2010

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Abstract.We introduce a model for yielding, inspired by fracture models and the failure of a sheared granular medium in which the applied shear is resisted by self-organized force chains. The force chains in the granular medium (GM) are considered as a bundle of fibres of finite strength amongst which stress is randomly redistributed after any other fibre breaks under excessive load. The model provides an exponential distribution of the internal stress and a log-normal shaped distribution of failure stress, in agreement with experimental observations. The model displays critical behaviour which approaches mean field as the number of random neighbours k becomes large and also displays a failure strength which remains finite in the limit of infinite size. From comparison with different models it is argued that this is an effect of uncorrelation. All these macroscopic properties appear statistically stable with respect to the choice of the chains' initial strength distribution. The investigated model is relevant for all systems in which some generic external load or pressure is borne by a number of units, independent of one another except when failure of a unit causes load transfer to some random choice of neighbouring units.

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Section: Model Details and Featuresmentioning

confidence: 99%

A random neighbour model for yielding

2010

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“…Further properties of the distribution of the bundle strength have been discussed by Suh et al (1970), Sen (1973aSen ( , 1973b, Phoenix and Taylor (1973), and Sornette (1989). Moreover, this simple model has been generalized in several ways during the last years, by invoking nonlinear elastic properties (Phoenix and Taylor, 1973), and by connecting bundles of parallel fibers in series (Smith and Phoenix, 1981;Sornette and Redner, 1989).…”

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confidence: 99%

The Distribution of Simultaneous Fiber Failures in Fiber Bundles

Hemmer¹,

Hansen

1992

Journal of Applied Mechanics

236

214

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A bundle of many parallel fibers, with stochastically distributed thresholds for individual fibers, is loaded until complete failure. Equal load sharing is assumed. During the breakdown process, bursts of several fibers breaking simultaneously at a given load occur. We determine the expected number of such bursts before complete failure, as well as the frequency of bursts in which A fibers break simultaneously. This distribution follows asymptotically a universal power-law A~5 /2 , for any statistical distribution of the individual fiber strengths. Downloaded From: http://appliedmechanics.asmedigitalcollection.asme.org/ on 05/25/2015 Terms of Use: http://asme.org/terms Journal of Applied Mechanics DECEMBER 1992, Vol. 59 / 913 Downloaded From: http://appliedmechanics.asmedigitalcollection.asme.org/ on 05/25/2015 Terms of Use: http://asme.org/terms

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“…To adequately model the stress evolution of the force chains within the medium, perhaps the simplest non-trivial scheme is to consider a bundle of one-dimensional uniform fibers supporting a longitudinal stress. The first such Fiber-Bundle Model (FBM) was introduced [28] and extensively investigated [29,30] for describing the fracture of textiles. It consists of a bundle of N fibers loaded in parallel, whose individual strength to failure is randomly extracted from some preselected distribution p(σ).…”

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Shear Stress Fluctuations in the Granular Liquid and Solid Phases

et al. 2005

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We report on experimentally observed shear stress fluctuations in both granular solid and fluid states, showing that they are non-Gaussian at low shear rates, reflecting the predominance of correlated structures (force chains) in the solidlike phase, which also exhibit finite rigidity to shear. Peaks in the rigidity and the stress distribution's skewness indicate that a change to the force-bearing mechanism occurs at the transition to fluid behavior, which, it is shown, can be predicted from the behavior of the stress at lower shear rates. In the fluid state stress is Gaussian distributed, suggesting that the central limit theorem holds. The fiber bundle model with random load sharing effectively reproduces the stress distribution at the yield point and also exhibits the exponential stress distribution anticipated from extant work on stress propagation in granular materials.

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On the distribution and moments of the strength of a bundle of filaments

Cited by 17 publications

References 1 publication

A random neighbour model for yielding

A random neighbour model for yielding

The Distribution of Simultaneous Fiber Failures in Fiber Bundles

Shear Stress Fluctuations in the Granular Liquid and Solid Phases

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