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Register a new userAvalanche dynamics in higher dimensional fiber bundle models
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We investigate how the dimensionality of the embedding space affects the microscopic crackling dynamics and the macroscopic response of heterogeneous materials. Using a fiber bundle model with localized load sharing computer simulations are performed from 1 to 8 dimensions slowly increasing the external load up to failure. Analyzing the constitutive curve, fracture strength and avalanche statistics of bundles we demonstrate that a gradual crossover emerges from the universality class of localized behavior to the mean field class of fracture as the embedding dimension increases. The evolution between the two universality classes is described by an exponential functional form. Simulations revealed that the average temporal profile of crackling avalanches evolves with the dimensionality of the system from a strongly asymmetric shape to a symmetric parabola characteristic for localized stresses and homogeneous stress fields, respectively.
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The present work deals with the behavior of fiber bundle model under heterogeneous loading condition. The model is explored both in the mean-field limit as well as with local stress concentration. In the mean field limit, the failure abruptness decreases with increasing order k of heterogeneous loading. In this limit, a brittle to quasi-brittle transition is observed at a particular strength of disorder which changes with k. On the other hand, the model is hardly affected by such heterogeneity in the limit where local stress concentration plays a crucial role. The continuous limit of the heterogeneous loading is also studied and discussed in this paper. Some of the important results related to fiber bundle model are reviewed and their responses to our new scheme of heterogeneous loading are studied in details. Our findings are universal with respect to the nature of the threshold distribution adopted to assign strength to an individual fiber.
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 $p(b)sim b^{-1}$ in the range $10^{-beta}$ to $10^{beta}$. Tuning the value of $beta$ 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 $sigma_c(beta,N)$ for the bundle of size $N$ approaches its asymptotic value $sigma_c(beta)$ as $sigma_c(beta,N) = sigma_c(beta)+AN^{-1/ u(beta)}$ where $sigma_c(beta)$ has been obtained analytically as $sigma_c(beta) = 10^beta/(2beta eln10)$ for $beta geq beta_u = 1/(2ln10)$, and for $beta<beta_u$ the weakest fiber failure leads to the catastrophic breakdown of the entire fiber bundle, similar to brittle materials, leading to $sigma_c(beta) = 10^{-beta}$; (ii) the fraction of broken fibers right before the complete breakdown of the bundle has the form $1-1/(2beta ln10)$; (iii) the distribution $D(Delta)$ of the avalanches of size $Delta$ follows a power law $D(Delta)sim Delta^{-xi}$ with $xi = 5/2$ for $Delta gg Delta_c(beta)$ and $xi = 3/2$ for $Delta ll Delta_c(beta)$, where the crossover avalanche size $Delta_c(beta) = 2/(1-e10^{-2beta})^2$.
We investigate the fracture of heterogeneous materials occurring under unloading from an initial load. Based on a fiber bundle model of time dependent fracture, we show that depending on the unloading rate the system has two phases: for rapid unloading the system suffers only partial failure and it has an infinite lifetime, while at slow unloading macroscopic failure occurs in a finite time. The transition between the two phases proved to be analogous to continuous phase transitions. Computer simulations revealed that during unloading the fracture proceeds in bursts of local breakings triggered by slowly accumulating damage. In both phases the time evolution starts with a relaxation of the bursting activity characterized by a universal power law decay of the burst rate. In the phase of finite lifetime the initial slowdown is followed by an acceleration towards macroscopic failure where the increasing rate of bursts obeys the (inverse) Omori law of earthquakes. We pointed out a strong correlation between the time where the event rate reaches a minimum value and of the lifetime of the system which allows for forecasting of the imminent catastrophic failure.
We have studied the dynamics of avalanching wet granular media in a rotating drum apparatus. Quantitative measurements of the flow velocity and the granular flux during avalanches allow us to characterize novel avalanche types unique to wet media. We also explore the details of viscoplastic flow (observed at the highest liquid contents) in which there are lasting contacts during flow, leading to coherence across the entire sample. This coherence leads to a velocity independent flow depth at high rotation rates and novel robust pattern formation in the granular surface.
A detailed characterization of avalanche dynamics of wet granular media in a rotating drum apparatus is presented. The results confirm the existence of the three wetness regimes observed previously: the granular, the correlated and the viscoplastic regime. These regimes show qualitatively different dynamic behaviors which are reflected in all the investigated quantities. We discuss the effect of interstitial liquid on the characteristic angles of the material and on the avalanche size distribution. These data also reveal logarithmic aging and allow us to map out the phase diagram of the dynamical behavior as a function of liquid content and flow rate. Via quantitative measurements of the flow velocity and the granular flux during avalanches, we characterize novel avalanche types unique to wet media. We also explore the details of viscoplastic flow (observed at the highest liquid contents) in which there are lasting contacts during flow, leading to coherence across the entire sample. This coherence leads to a velocity independent flow depth at high rotation rates and novel robust pattern formation in the granular surface.
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