Nucleation versus percolation: Scaling criterion for failure in disordered solids

Biswas, Soumyajyoti; Roy, Subhadeep; Ray, Purusattam

doi:10.1103/physreve.91.050105

Cited by 35 publications

(66 citation statements)

References 25 publications

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“…affecting a total of R 2 fibers). Redistributions that affect a finite range are expected to be captured by this process, which is also the case for catastrophic failure [22]. The two extreme cases are the nearest neighbor (R = 1) and mean-field (R L, where L is the system size) interactions and we find a crossover length scale R c above which the system starts behaving like the mean-field limit.…”

Section: Modelmentioning

confidence: 56%

“…Several attempts have been made to interpolate between these two limits [18][19][20][21][22]. However, in the case of catastrophic failures, the stress at which the system just breaks (critical stress) becomes non-zero only when the range of interaction is sufficiently large, so that it suppresses any spatial stress concentration [22]. Hence, statistics that are qualitatively similar to experiments [23] are observed only in the mean-field limit.…”

Section: Introductionmentioning

confidence: 99%

“…The local (nearest neighbors, introduced in [17]) and mean-field (global load sharing [16]) limits are well studied but are rather idealized in view of the fact that any realistic stress concentration range in a solid is neither of these two extremes. Several attempts have been made to interpolate between these two limits [18][19][20][21][22]. However, in the case of catastrophic failures, the stress at which the system just breaks (critical stress) becomes non-zero only when the range of interaction is sufficiently large, so that it suppresses any spatial stress concentration [22].…”

Section: Introductionmentioning

confidence: 99%

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Interface propagation in fiber bundles: local, mean-field and intermediate range-dependent statistics

Biswas¹,

Goehring²

2016

New J. Phys.

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The fiber bundle model is essentially an array of elements that break when sufficient load is applied on them. With a local loading mechanism, this can serve as a model for a one-dimensional interface separating the broken and unbroken parts of a solid in mode-I fracture. The interface can propagate through the system depending on the loading rate and disorder present in the failure thresholds of the fibers. In the presence of a quasi-static drive, the intermittent dynamics of the interface mimic front propagation in disordered media. Such situations appear in diverse physical systems such as mode-I crack propagation, domain wall dynamics in magnets, charge density waves, contact lines in wetting etc. We study the effect of the range of interaction, i.e. the neighborhood of the interface affected following a local perturbation, on the statistics of the intermittent dynamics of the front. There exists a crossover from local to global behavior as the range of interaction grows and a continuously varying 'universality' in the intermediate range. This means that the interaction range is a relevant parameter of any resulting physics. This is particularly relevant in view of the fact that there is a scatter in the experimental observations of the exponents, in even idealized experiments on fracture fronts, and also a possibility in changing the interaction range in real samples.

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Section: Modelmentioning

confidence: 56%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interface propagation in fiber bundles: local, mean-field and intermediate range-dependent statistics

Biswas¹,

Goehring²

2016

New J. Phys.

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“…It is known that at the critical point, the relaxation time scales as τ ∼ N α , with α = 1/3 for b = 0 [25,29]. But for b > 0 the power law scaling seems to be lost, with τ becoming almost independent of N for b > 1 (see Fig.…”

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confidence: 97%

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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“…Both the number of clusters and the maximum cluster area stabilizes after some point as damage develops within the cohesive elements. Although the models are of different nature, an analysis using fiber bundle models showed that the statistics of successive broken fiber patches signal a similar nonmonotonic behavior [33].…”

Section: Damage Clustersmentioning

confidence: 99%

Damage cluster distributions in numerical concrete at the mesoscale

2017

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We investigate the size distribution of damage clusters in concrete under uniaxial tension loading conditions. Using the finite-element method, the concrete is modeled at the mesoscale by a random distribution of elastic spherical aggregates within an elastic mortar paste. The propagation and coalescence of damage zones are then simulated by means of dynamically inserted cohesive elements. Dynamic failure analysis shows that the size distribution of damage clusters follows a power law when a system-spanning cluster is first observed, with an exponent close to that of percolation theory. This is found for a range of selected mesostructural parameters, material defects, and applied strain rates. In all cases, the system-spanning cluster occurs prior to the onset of local decohesion, a regime of crack nucleation and propagation, and eventual material failure. The resulting fully damaged crack surfaces after failure are found to be only weakly correlated with the percolated damage region structures.

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Nucleation versus percolation: Scaling criterion for failure in disordered solids

Cited by 35 publications

References 25 publications

Interface propagation in fiber bundles: local, mean-field and intermediate range-dependent statistics

Interface propagation in fiber bundles: local, mean-field and intermediate range-dependent statistics

Maximizing the Strength of Fiber Bundles under Uniform Loading

Damage cluster distributions in numerical concrete at the mesoscale

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