Fracture model with variable range of interaction

Hidalgo, R. C.; Moreno, Yamir; Kun, Ferenc; Herrmann, Hans J.

doi:10.1103/physreve.65.046148

Cited by 136 publications

(194 citation statements)

References 41 publications

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“…The load transfer in the RFM is long-ranged and is thus possible that RFM and FBM display universal behavior [36]. An intermediate case is provided by FBM with long-range (power law) load transfer [37]: the difference with the RFM lies in the anisotropic current transfer function [36].…”

Section: Introductionmentioning

confidence: 99%

Crack roughness and avalanche precursors in the random fuse model

2005

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We analyze the scaling of the crack roughness and of avalanche precursors in the two dimensional random fuse model by numerical simulations, employing large system sizes and extensive sample averaging. We find that the crack roughness exhibits anomalous scaling, as recently observed in experiments. The roughness exponents (ζ, ζ loc ) and the global width distributions are found to be universal with respect to the lattice geometry. Failure is preceded by avalanche precursors whose distribution follows a power law up to a cutoff size. While the characteristic avalanche size scales as s0 ∼ L D , with a universal fractal dimension D, the distribution exponent τ differs slightly for triangular and diamond lattices and, in both cases, it is larger than the mean-field (fiber bundle) value τ = 5/2.

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Section: Introductionmentioning

confidence: 99%

Crack roughness and avalanche precursors in the random fuse model

2005

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“…A third model, intermediate between ELS and LLS, has also been considered in the following way. In this model the released stress is distributed non-uniformly and the share amount received by an intact fiber depends inversely to some power of the distance of separation from the broken fiber [13]. A number of other processes have been studied in the framework of fiber bundle models.…”

Section: Introductionmentioning

confidence: 99%

Fiber bundle model with highly disordered breaking thresholds

2015

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We present a study of the fiber bundle model using equal load sharing dynamics where the breaking thresholds of the fibers are drawn randomly from a power law distribution of the form p(b) ∼ b −1 in the range 10 −β to 10 β . Tuning the value of β continuously over a wide range, the critical behavior of the fiber bundle has been studied both analytically as well as numerically. Our results are: (i) The critical load σc(β, N ) for the bundle of size N approaches its asymptotic value σc(β) as σc(β, N ) = σc(β)+AN −1/ν(β) where σc(β) has been obtained analytically as σc(β) = 10 β /(2βe ln 10) for β ≥ βu = 1/(2 ln 10), and for β < βu the weakest fiber failure leads to the catastrophic breakdown of the entire fiber bundle, similar to brittle materials, leading to σc(β) = 10 −β ; (ii) the fraction of broken fibers right before the complete breakdown of the bundle has the form 1 − 1/(2β ln 10); (iii) the distribution D(∆) of the avalanches of size ∆ follows a power law D(∆) ∼ ∆ −ξ with ξ = 5/2 for ∆ ≫ ∆c(β) and ξ = 3/2 for ∆ ≪ ∆c(β), where the crossover avalanche size ∆c(β) = 2/(1−e10 −2β ) 2 .

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“…Certainly, our model represents a strong simplification of reality. Model improvements may include introducing local load-sharing rules (e.g., [2,26]) and using a more complex model for the load rheology instead of the Maxwell model (e.g., power-law creep [13,38]). Moreover, with a model capable of reproducing a more complex three-dimensional geometry (e.g., discrete element model DEM (e.g., [39,40]) the effect of the complex structure of the ice matrix could be studied.…”

Section: Discussionmentioning

confidence: 99%

“…with the shape factor k = 1.1 (e.g., [26]). We used the Weibull distribution because it is commonly used for statistical fracture models.…”

Section: Theoretical Considerations Of Fbm Model With Healingmentioning

confidence: 99%

Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

et al. 2018

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Snow is a heterogeneous material with strain-and/or load-rate-dependent strength. In particular, a transition from ductile-to-brittle failure behavior with increasing load rate is observed. The rate-dependent behavior can partly be explained with the existence of a unique healing mechanism in snow that stems from its high homologous temperature (temperature close to melting point). As soon as broken elements in the ice matrix get in contact, they start sintering and the structure may regain strength. Moreover, the ice matrix is subjected to viscous deformation, inducing a relaxation of local load concentrations and, therefore, further counteracting the damage process. Ideal tools for studying the failure process of heterogeneous materials are the fiber-bundle models (FBMs), which allow investigating the effects of basic microstructural characteristics on the general macroscopic failure behavior. We present an FBM with two concurrent time-dependent healing mechanisms: sintering of broken fibers and relaxation of load inhomogeneities. Sintering compensates damage by creating additional intact, load-supporting fibers which lead to an increase of the bundle strength. However, the character of the failure is not changed by sintering alone. With combined sintering and load relaxation, load is distributed from old stronger fibers to new fibers that carry fewer load. So as we additionally incorporated load redistribution to the FBM, the failure occurred suddenly without decrease of the order parameter-describing the amount of damage in the bundle-and without divergence of the fiber failure rate. Moreover, the b value, i.e., the power-law exponent of frequency-magnitude statistics of fibers breaking in load redistribution steps, at failure converged to b ≈ 2, a value higher than that of a classical FBM without healing (b = 3 2 ). These results indicate that healing, as the combined effect of sintering and load relaxation, changes the type of the phase transition at failure. This change of the phase transition is important for quantifying or predicting the failure (e.g., by monitoring acoustic emissions) of snow or other materials for which healing plays an important role.

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Fracture model with variable range of interaction

Cited by 136 publications

References 41 publications

Crack roughness and avalanche precursors in the random fuse model

Crack roughness and avalanche precursors in the random fuse model

Fiber bundle model with highly disordered breaking thresholds

Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

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