Biomedical subjects

Srutarshi Pradhan

Publications and source records attributed to Srutarshi Pradhan.

7 recordsLinked to original sources

PubMed2006

Crossover behavior in failure avalanches.

Composite materials, with statistically distributed thresholds for breakdown of individual elements, are considered. During the failure process of such materials under external stress (load or voltage), avalanches consisting of simultaneous rupture of several elements occur, with a distribution D(Delta) of the magnitude Delta of such avalanches. The distribution is typically a power law D(Delta) proportional to Delta (-xi). For the systems we study here, a crossover behavior is seen between two power laws, with a small exponent xi in the vicinity of complete breakdown and a larger exponent xi for failures away from the breakdown point. We demonstrate this analytically for bundles of many fibers where the load is uniformly distributed among the surviving fibers. In this case xi=3/2 near the breakdown point and xi=5/2 away from it. The latter is known to be the generic behavior. This crossover is a signal of imminent catastrophic failure of the material. Near the breakdown point, avalanche statistics show nontrivial finite size scaling. We observe similar crossover behavior in a network of electric fuses, and find xi=2 near the catastrophic failure and xi=3 away from it. For this fuse model power dissipation avalanches show a similar crossover near breakdown.

Journal Article↗

PubMed2005

Crossover behavior in burst avalanches: signature of imminent failure.

The statistics of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded only near the point at which the system fails catastrophically, one finds that the power law has an exponent which is different from that one finds if the recording of events starts away from the vicinity of catastrophic failure. We demonstrate this analytically for bundles of many fibers, with statistically distributed breakdown thresholds for the individual fibers and where the load is uniformly distributed among the surviving fibers. In this case the distribution D(Delta) of the avalanches (Delta) follows the power law Delta-xi with xi=3/2 near catastrophic failure and xi=5/2 away from it. We also study numerically square networks of electrical fuses and find xi=2.0 near catastrophic failure and xi=3.0 away from it. We propose that this crossover in xi may be used as a signal of imminent failure.

Journal Article↗

PubMed2005

Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution.

The presence of lower cutoff in fiber threshold distribution may affect the failure properties of a bundle of fibers subjected to external load. We investigate this possibility--both in an equal load sharing (ELS) model and in a local load sharing (LLS) one using analytic as well as numerical methods. In the ELS model, the critical strength gets modified and, beyond a certain lower cutoff level, the whole bundle fails instantly (brittle failure) after the first fiber ruptures. Although the dynamic exponents for the order parameter, susceptibility, and relaxation time remain unchanged, the avalanche size distribution shows a gradual deviation from the mean field power law. A similar "instant failure" situation occurs in the LLS model at a lower cutoff level, which reduces to that of the equivalent ELS model at higher (high enough) dimensions. Also, the system size variation of the bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.

Journal Article↗

PubMed2005

Crossover behavior in a mixed-mode fiber bundle model.

We introduce a mixed-mode load sharing scheme in a fiber bundle model. This model reduces exactly to equal-load-sharing (ELS) and local-load-sharing (LLS) models at the two extreme limits of a single-load-sharing parameter. We identify two distinct regimes: (a) the mean-field regime where the ELS mode dominates and (b) the short-range regime dominated by the LLS mode. The crossover behavior is explored through a numerical study of the strength variation, the avalanche statistics, susceptibility and relaxation time variations, the correlations among the broken fibers, and their cluster analysis. Analyzing the moments of the cluster size distributions we locate the crossover point of these regimes. We thus conclude that even in one dimension, the fiber bundle model shows crossover behavior from mean-field to short-range interactions.

Journal Article↗

PubMed2003

Failure due to fatigue in fiber bundles and solids.

We consider first a homogeneous fiber bundle model where all the fibers have got the same stress threshold (sigma(c)) beyond which all fail simultaneously in absence of noise. At finite noise, the bundle acquires a fatigue behavior due to the noise-induced failure probability at any stress sigma. We solve this dynamics of failure analytically and show that the average failure time tau of the bundle decreases exponentially as sigma-->sigma(c) from below and tau=0 for sigma>or=sigma(c). We also determine the avalanche size distribution during such failure and find a power law decay. We compare this fatigue behavior with that obtained phenomenologically for the nucleation of the Griffith cracks. Next we study numerically the fatigue behavior of random fiber bundles having simple distributions of individual fiber strengths, at stress sigma less than the bundle's strength sigma(c); (beyond which it fails instantly). The average failure time tau is again seen to decrease exponentially as sigma-->sigma(c); from below and the avalanche size distribution shows similar power law decay. These results are also in broad agreement with experimental observations on fatigue in solids. We believe, these observations regarding the failure time are useful for quantum breakdown phenomena in disordered systems.

Journal Article↗

PubMed2003

Phase transition in fiber bundle models with recursive dynamics.

We study the phase transition in a class of fiber bundle models in which the fiber strengths are distributed randomly within a finite interval and global load sharing is assumed. The dynamics is expressed as recursion relations for the redistribution of the applied stress and the evolution of the surviving fraction of fibers. We show that an irreversible phase transition of second-order occurs, from a phase of partial failure to a phase of total failure, when the initial applied stress just exceeds a critical value. The phase transition is characterized by static and dynamic critical properties. We calculate exactly the critical value of the initial stress for three models of this kind, each with a different distribution of fiber strengths. We derive exact expressions for the order parameter, the susceptibility to changes in the initial applied stress, and the critical relaxation of the surviving fraction of fibers for all the three models. The static and dynamic critical exponents obtained from these expressions are found to be universal.

Journal Article↗

PubMed2001

Precursors of catastrophe in the Bak-Tang-Wiesenfeld, Manna, and random-fiber-bundle models of failure.

We have studied precursors of the global failure in some self-organized critical models of sandpile [in Bak-Tang-Wiesenfeld (BTW) and Manna models] and in the random-fiber-bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed number of sand grains (heights) to any central site of the stable pile, the local dynamics starts and continues for an average relaxation time tau and an average number of topplings Delta spread over a radial distance xi. We find that these quantities all depend on the average height h(av) of the pile and they all diverge as h(av) approaches the critical height h(c) from below: Delta approximately (h(c)-h(av))(-delta), tau approximately (h(c)-h(av))(-gamma), and xi approximately (h(c)-h(av))(-nu). Numerically, we find delta approximately 2.0, gamma approximately 1.2, and nu approximately 1.0 for both BTW and Manna model in two dimensions. In the strained RFB model, we find that the breakdown susceptibility chi (giving the differential increment of the number of broken fibers due to increase in external load) and the relaxation time tau, both diverge as the applied load or stress sigma approaches the network failure threshold sigma(c) from below: chi approximately (sigma(c)-sigma)(-1/2) and tau approximately (sigma(c)-sigma)(-1/2). These self-organized dynamical models of failure, therefore, show some definite precursors with robust power laws long before the failure point. Such well-characterized precursors should help predicting the global failure point of the systems in advance.

Journal Article↗