Size Distribution of Emitted Energies in Local Load Sharing Fiber Bundles

Roy, Subhadeep; Biswas, Soumyajyoti

doi:10.3389/fphy.2021.643602

Cited by 7 publications

(12 citation statements)

References 33 publications

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“…We observe that when γ is low, E increases with s linearly. A recent article [13] has already discussed such correlation between avalanche size and emitted energy in the mean-field limit of the model, which we obtain here by keeping a high range (hence low γ) of load redistribution. On the other hand, when γ is high, the plot of s vs. E shows a scatter with a relatively lower correlation between the two quantities.…”

Section: Relation Between S and Esupporting

confidence: 62%

“…The fact that 〈E〉 is not linear with s for high γ is also reflected by the scattered behavior of E with s. For this nonlinear part, the variation of s and 〈E〉 is 〈E〉~s β , with an exponent, which is dependent on γ, β ≡ β(γ). For large values of γ, β = 2.5, which was also seen in [13] for the LLS scheme, i.e., γ → ∞. We will again come back to this linear and nonlinear relationship between s and 〈E〉 while discussing the distributions of avalanche sizes and emitted energies.…”

Section: Frontiers Inmentioning

confidence: 51%

“…While the average values of energy bursts (〈E〉) and avalanche sizes or damage (〈s〉) are known in those systems, in this work, we focus on how does the individual correspondence between the avalanche size and energy of a particular event vary with localization of load redistribution in the context of the fiber bundle model in one and two dimensions. It was noted earlier [13] that in the extreme limit of the nearest neighbor load sharing, those avalanches of large sizes can have small energy release and vice versa. In terms of the size distribution functions, the avalanche size distribution is exponential, but the energy distribution is a power law.…”

Section: Introductionmentioning

confidence: 94%

“…• Throughout the entire range of γ, the energy distribution is a power law (Q(E)~E −τ E ), while the avalanche size distribution is a power law (P(s)~s −τs ) for γ < γ c and exponential for γ > γ c . • It is possible to show that τ E = β(γ) + 1 [13], assuming the aforementioned nonlinear relation between s and 〈E〉 and P(s) to be an exponential distribution. We see here that this scaling form is in fact generally valid for γ > γ c (see Figure 5).…”

Section: Study Of the Distributions P(s) And Q(e)mentioning

confidence: 99%

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Correlation Between Avalanches and Emitted Energies During Fracture With a Variable Stress Release Range

2022

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We observe the failure process of a fiber bundle model with a variable stress release range, γ, and higher the value of γ, lower the stress release range. By tuning γ from low to high, it is possible to go from the mean-field (MF) limit of the model to the local load-sharing (LLS) limit where local stress concentration plays a crucial role. In the MF limit, individual avalanches (number of fibers breaking in going from one stable state to the next, s) and the corresponding energies E emitted during those avalanches have one-to-one linear correlation. This results in the same size distributions for both avalanches (P(s)) and energy bursts (Q(E)): a scale-free distribution with a universal exponent value of −5/2. With increasing γ, the model enters the LLS limit beyond some γc. In this limit, due to the presence of local stress concentrations around a damaged region, such correlation C(γ) between s and E decreases, i.e., a smaller avalanche can emit a large amount of energy or a large avalanche may emit a small amount of energy. The nature of the decrease in the correlation between s and E depends highly on the dimension of the bundle. In this work, we study the decrease in the correlation between avalanche size and the corresponding energy bursts with an increase in the load redistribution localization in the fiber bundle model in one and two dimensions. Additionally, we note that the energy size distribution remains scale-free for all values of γ, whereas the avalanche size distribution becomes exponential for γ > γc.

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Section: Relation Between S and Esupporting

confidence: 62%

Section: Frontiers Inmentioning

confidence: 51%

Section: Introductionmentioning

confidence: 94%

Section: Study Of the Distributions P(s) And Q(e)mentioning

confidence: 99%

See 2 more Smart Citations

Correlation Between Avalanches and Emitted Energies During Fracture With a Variable Stress Release Range

2022

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“…The simplicity of the fiber bundle model allows us to include extra parameters like stress release range compared to the random fuse network model and study its effect as well on the spatial correlation as the model evolves. The precursor events (such as scale-free size distribution of rupture events prior to global failure and scale free distribution of emitted energies during such avalanches), previously seen in the statistical models [7,58], would imply that a nucleation-like failure would not be achievable even in the large system size limit. Such precursor events are observed experimentally [59] as well for which the extreme disorder is not necessarily the physical condition.…”

Section: Discussionmentioning

confidence: 99%

From Nucleation to Percolation: The Effect of System Size when Disorder and Stress Localization Compete

Roy

2021

Front. Phys.

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A phase diagram for a one-dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding the dynamics of the model: strength of disorder and range of stress relaxation. When the range of stress relaxation is very low, the stress concentration plays a prominent role and the failure process is nucleating where a single crack propagates from a particular nucleus with a very high spatial correlation unless the disorder strength is high. On the other hand, a high range of stress relaxation represents the mean-field limit of the model where the failure events are random in space. At an intermediate disorder strength and stress release range, when these two parameters compete, the failure process shows avalanches and precursor activities. As the size of the bundle is increased, it favors a nucleating failure. In the thermodynamic limit, we only observe a nucleating failure unless either the disorder strength is extremely high or the stress release range is high enough so that the model is in the mean-field limit. A complex phase diagram on the plane of disorder strength, stress release range, and system size is presented showing different failure modes - 1) nucleation 2) avalanche, and 3) percolation, depending on the spatial correlation observed during the failure process.

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Seismic events miss important kinematically governed grain scale mechanisms during shear failure of porous rock

et al. 2022

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Catastrophic failure in brittle, porous materials initiates when smaller-scale fractures localise along an emergent fault zone in a transition from stable crack growth to dynamic rupture. Due to the rapid nature of this critical transition, the precise micro-mechanisms involved are poorly understood and difficult to image directly. Here, we observe these micro-mechanisms directly by controlling the microcracking rate to slow down the transition in a unique rock deformation experiment that combines acoustic monitoring (sound) with contemporaneous in-situ x-ray imaging (vision) of the microstructure. We find seismic amplitude is not always correlated with local imaged strain; large local strain often occurs with small acoustic emissions, and vice versa. Local strain is predominantly aseismic, explained in part by grain/crack rotation along an emergent shear zone, and the shear fracture energy calculated from local dilation and shear strain on the fault is half of that inferred from the bulk deformation.

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Size Distribution of Emitted Energies in Local Load Sharing Fiber Bundles

Cited by 7 publications

References 33 publications

Correlation Between Avalanches and Emitted Energies During Fracture With a Variable Stress Release Range

Correlation Between Avalanches and Emitted Energies During Fracture With a Variable Stress Release Range

From Nucleation to Percolation: The Effect of System Size when Disorder and Stress Localization Compete

Seismic events miss important kinematically governed grain scale mechanisms during shear failure of porous rock

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