Extensions of Fibre Bundle Models

Kun, Ferenc; Raischel, Frank; Hidalgo, R. C.; Herrmann, Hans J.

doi:10.1007/3-540-35375-5_3

Cited by 57 publications

(67 citation statements)

References 67 publications

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“…In the framework of discrete models either randomness is introduced for the strength of cohesive elements or random dilution is applied on a regular lattice, where the amount of disorder is controlled by the width of the strength distribution [10][11][12][13][14] and by the degree of dilution [2,15] respectively. In these investigations the fiber bundle model (FBM) is a very useful tool since it captures the relevant aspects of fracture processes but it is still simple enough to obtain analytical solutions and to design ecient simulation techniques [16,17]. In the present paper we use fiber bundle modeling to investigate the limiting case of high disorder for the fracture process of heterogeneous materials.…”

Section: J Stat Mech (2016) 073211mentioning

confidence: 99%

Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture

2015

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Abstract.We investigate the eect of the amount of disorder on the fracture process of heterogeneous materials in the framework of a fiber bundle model. The limit of high disorder is realized by introducing a power law distribution of fiber strength over an infinite range. We show that on decreasing the amount of disorder by controlling the exponent of the power law the system undergoes a transition from the quasi-brittle phase where fracture proceeds in bursts to the phase of perfectly brittle failure where the first fiber breaking triggers a catastrophic collapse. For equal load sharing in the quasi-brittle phase the fat tailed disorder distribution gives rise to a homogeneous fracture process where the sequence of breaking bursts does not show any acceleration as the load increases quasi-statically. The size of bursts is power law distributed with an exponent smaller than the usual mean field exponent of fiber bundles. We demonstrate by means of analytical and numerical calculations that the quasi-brittle to brittle transition is analogous to continuous phase transitions and determine the corresponding critical exponents. When the load sharing is localized to nearest neighbor intact fibers the overall characteristics of the failure process prove to be the same, however, with dierent critical exponents. We show that in the limit of the highest disorder considered the spatial structure of damage is identical with site percolation-however, approaching the critical point of perfect brittleness spatial correlations play an increasing role, which results in a dierent cluster structure of failed elements.

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Section: J Stat Mech (2016) 073211mentioning

confidence: 99%

Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture

2015

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“…The arrays of nanopillars are encountered in many areas of nanotechnology and reveal the potential applicability as components for the fabrication of electro-mechanical sense devices. To analyse failure in such arrays, we adapt the Fibre Bundle Model (FBM) which is a fundamental statistical approach for studying failure phenomena of heterogeneous materials [6][7][8]. The essential component of the FBM is the range and form of interaction of elements (fibres).…”

Section: Introductionmentioning

confidence: 99%

Analysis of damage processes in nanopillar arrays with hierarchical load transfer

Derda

2016

J. Appl. Math. Comput. Mech.

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Abstract. A computational model for the damage analysis in the axially loaded nanopillar arrays was developed on the basis of the Fibre Bundle Model and hierarchical load sharing protocol. The nanopillars are characterised by random strength-thresholds drawn according to the nanoscale Weibull statistics. We study the influence of the coordination number and the number of hierarchy levels on the system strength, size of the catastrophic avalanche and probability of breakdown.

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“…On the other hand, in the case of the local load sharing rule, the stress is equally redistributed to the nearest intact neighbours of the broken one. Other rules and mixtures of them are also proposed [7].…”

Section: Introductionmentioning

confidence: 99%

Stochastic local load redistribution in the fibre bundle model of nanopillar arrays

Derda

2015

J. Appl. Math. Comput. Mech.

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Abstract. We study the breakdown of the nanopillar arrays subjected to axial loading. The pillar-strength-thresholds are drawn from a given probability distribution. Pillars are located in the nodes of the supporting regular lattice. In this work we introduce stochastic local load sharing -after pillar breakdown each of its nearest intact neighbours obtains a random fraction of the failing load. Two types of loading procedure are employed, namely quasi-static and finite force. We analyse critical loads, catastrophic avalanches as well as probabilities of cascade and breakdown.

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Extensions of Fibre Bundle Models

Cited by 57 publications

References 67 publications

Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture

Fractal frontiers of bursts and cracks in a fiber bundle model of creep rupture

Analysis of damage processes in nanopillar arrays with hierarchical load transfer

Stochastic local load redistribution in the fibre bundle model of nanopillar arrays

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