Mesoscopic description of the equal-load-sharing fiber bundle model

Hendrick, Martin; Pradhan, Srutarshi; Hansen, Alex

doi:10.1103/physreve.98.032117

Cited by 3 publications

(3 citation statements)

References 21 publications

(47 reference statements)

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“…Analytically known that in the mean-field limit this kind of hybrid phase transition happens, e.g. power law behavior of damage is obtained when approaching the critical load of global failure d c − d ∝ (σ c − σ ) 1/2 (see 47,48 ). This permits to have non-diverging cluster sizes at the LLS to ELS transition point, smaller than the typical distance of WS: ξ = 1/(2p) 1/2 (see 44 ).…”

Section: Discussionmentioning

confidence: 99%

Scaling laws of failure dynamics on complex networks

Pál,

Danku,

Batool

et al. 2023

Sci Rep

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The topology of the network of load transmitting connections plays an essential role in the cascading failure dynamics of complex systems driven by the redistribution of load after local breakdown events. In particular, as the network structure is gradually tuned from regular to completely random a transition occurs from the localized to mean field behavior of failure spreading. Based on finite size scaling in the fiber bundle model of failure phenomena, here we demonstrate that outside the localized regime, the load bearing capacity and damage tolerance on the macro-scale, and the statistics of clusters of failed nodes on the micro-scale obey scaling laws with exponents which depend on the topology of the load transmission network and on the degree of disorder of the strength of nodes. Most notably, we show that the spatial structure of damage governs the emergence of the localized to mean field transition: as the network gets gradually randomized failed clusters formed on locally regular patches merge through long range links generating a percolation like transition which reduces the load concentration on the network. The results may help to design network structures with an improved robustness against cascading failure.

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Section: Discussionmentioning

confidence: 99%

Scaling laws of failure dynamics on complex networks

Pál,

Danku,

Batool

et al. 2023

Sci Rep

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“…One such step was done in Ref. [45] by writing down a mesoscopic description of the ELS-FBM. By specifically, writing the time evolution of the order parameter n(σ) − n c η and the driving field (stress increase) as J σ c − σ, the dynamics is described by…”

Section: Some Related Work On the Dynamics Of Fbmmentioning

confidence: 99%

Cooperative Dynamics in the Fiber Bundle Model

2021

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We discuss the cooperative failure dynamics in the fiber bundle model where the individual elements or fibers are Hookean springs that have identical spring constants but different breaking strengths. When the bundle is stressed or strained, especially in the equal-load-sharing scheme, the load supported by the failed fiber gets shared equally by the rest of the surviving fibers. This mean-field-type statistical feature (absence of fluctuations) in the load-sharing mechanism helped major analytical developments in the study of breaking dynamics in the model and precise comparisons with simulation results. We intend to present a brief review on these developments.

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“…One such step was done in Ref. [43] by writing down a mesoscopic description of the ELS-FBM. specifically, writing the time evolution of the order parameter n(σ) − n c = η and the driving field (stress increase) as J = σ c − σ, the dynamics is described by…”

Section: Some Related Work On the Dynamics Of Fbmmentioning

confidence: 99%

Cooperative dynamics in the Fiber Bundle Model

Chakrabarti¹,

Biswas²,

Pradhan³

2020

Preprint

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We discuss the cooperative failure dynamics in the Fiber Bundle Model where the individual elements or fibers are Hookean springs, having identical spring constant but different breaking strengths. When the bundle is stressed or strained, especially in the equal-load-sharing scheme, the load supported by the failed fiber gets shared equally by the rest of the surviving fibers. This meanfield type statistical feature (absence of fluctuations) in the load-sharing mechanism helped major analytical developments in the study of breaking dynamics in the model and precise comparisons with simulation results. We intend to present a brief review on these developments.

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Mesoscopic description of the equal-load-sharing fiber bundle model

Cited by 3 publications

References 21 publications

Scaling laws of failure dynamics on complex networks

Scaling laws of failure dynamics on complex networks

Cooperative Dynamics in the Fiber Bundle Model

Cooperative dynamics in the Fiber Bundle Model

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