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Srutarshi Pradhan

Publications and source records attributed to Srutarshi Pradhan.

At least 19 recordsLinked to original sources
arXiv2020

Cooperative dynamics in the Fiber Bundle Model

We discuss the cooperative failure dynamics in the Fiber Bundle Model where the individual elements or fibers are Hookean springs, having identical spring constant but different breaking strengths. When the bundle is stressed or strained, especially in the equal-load-sharing scheme, the load supported by the failed fiber gets shared equally by the rest of the surviving fibers. This mean-field type statistical feature (absence of fluctuations) in the load-sharing mechanism helped major analytical developments in the study of breaking dynamics in the model and precise comparisons with simulation results. We intend to present a brief review on these developments.

cond-mat.stat-mech↗
arXiv2019

Can Local Stress Enhancement Induce Stability in Fracture Processes? Part II: The Shielding Effect

We use the local load sharing fiber bundle model to demonstrate a shielding effect where strong fibers protect weaker ones. This effect exists due to the local stress enhancement around broken fibers in the local load sharing model, and it is therefore not present in the equal load sharing model. The shielding effect is prominent only after the initial disorder-driven part of the fracture process has finished, and if the fiber bundle has not reached catastrophic failure by this point, then the shielding increases the critical damage of the system, compared to equal load sharing. In this sense, the local stress enhancement may make the fracture process more stable, but at the cost of reduced critical force.

cond-mat.dis-nn↗
arXiv2019

Can Local Stress Enhancement Induce Stability in Fracture Processes? Part I: Apparent Stability

By comparing the evolution of the local and equal load sharing fiber bundle models, we point out the paradoxical result that stresses seem to make the local load sharing model stable when the equal load sharing model is not. We explain this behavior by demonstrating that it is only an apparent stability in the local load sharing model, which originates from a statistical effect due to sample averaging. Even though we use the fiber bundle model to demonstrate the apparent stability, we argue that it is a more general feature of fracture processes.

cond-mat.dis-nn↗
arXiv2019

Variation of elastic energy shows reliable signal of upcoming catastrophic failure

We consider the Equal-Load-Sharing Fiber Bundle Model as a model for composite materials under stress and derive elastic energy and damage energy as a function of strain. With gradual increase of stress (or strain) the bundle approaches a catastrophic failure point where the elastic energy is always larger than the damage energy. We observe that elastic energy has a maximum that appears after the catastrophic failure point is passed, i.e., in the unstable phase of the system. However, the slope of elastic energy vs. strain curve has a maximum which always appears before the catastrophic failure point and therefore this can be used as a reliable signal of upcoming catastrophic failure. We study this behavior analytically for power-law type and Weibull type distributions of fiber thresholds and compare the results with numerical simulations on a single bundle with large number of fibers.

cond-mat.stat-mech↗
arXiv2018

Mesoscopic Description of the Equal Load Sharing Fiber Bundle Model

One aim of the equal load sharing fiber bundle model is to describe the critical behavior of failure events. One way of accomplishing this, is through a discrete recursive dynamics. We introduce a continuous mesoscopic equation catching the critical behavior found through recursive dynamics. It allows us to link the model with the unifying framework of absorbing phase transitions traditionally used in the study of non-equilibrium phase transitions. Moreover, it highlights the analogy between equal load sharing and spinodal nucleation. Consequently, this work is a first step towards the quest of a field theory for fiber bundle models.

cond-mat.stat-mech↗
arXiv2018

A Renormalization Group Procedure for Fiber Bundle Models

We introduce two versions of a renormalization group scheme for the equal load sharing fiber bundle model. The renormalization group is based on formulating the fiber bundle model in the language of damage mechanics. A central concept is the work performed on the fiber bundle to produce a given damage. The renormalization group conserves this work. In the first version of the renormalization group, we take advantage of ordering the strength of the individual fibers. This procedure, which is the simpler one, gives EXACT results -but cannot be generalized to other fiber bundle models such as the local load sharing one. The second renormalization group scheme based on the physical location of the individual fibers may be generalized to other fiber bundle models.

cond-mat.soft↗
arXiv2016

A simple Discrete-Element-Model of Brazilian Test

We present a statistical model which is able to capture some interesting features exhibited in the Brazilian test. The model is based on breakable elements which break when the force experienced by the elements exceed their own load capacity. In this model when an element breaks, the capacity of the neighboring elements are decreased by a certain amount assuming weakening effect around the defected zone. We numerically investigate the stress-strain behavior, the strength of the system, how it scales with the system size and also it's fluctuation for both uniformly and weibull distributed breaking threshold of the elements in the system. We find that the strength of the system approaches it's asymptotic value $σ_c=1/6$ and $σ_c=5/18$ for uniformly and Weibull distributed breaking threshold of the elements respectively. We have also shown the damage profile right at the point when the stress-strain curve reaches at it's maximum and then it is compared with our experimental observations.

cond-mat.soft↗
arXiv2015

Strength of Fractured Rocks

In this report we present a study on the strength of rocks which are partially fractured from before. We have considered a two dimensional case of a rock in the form of a lattice structure. The fiber bundle model is used for modelling the $2-D$ rock. Each lattice site is considered to be a fiber which has a breaking threshold. Fractures in this system will be of the form a cluster of sites and the length is defined as the number of sites belonging to a single cluster. We introduce fractures in the system initially and apply load until the rock breaks. The breaking of a rock is characterized by a horizontal fracture which connects the left side of the lattice to the right side. The length distribution and the strength of such systems have been measured.

cond-mat.dis-nn↗
arXiv2013

Noise induced rupture process: Phase boundary and scaling of waiting time distribution

A bundle of fibers has been considered here as a model for composite materials, where breaking of the fibers occur due to a combined influence of applied load (stress) and external noise. Through numerical simulation and a mean-field calculation we show that there exists a robust phase boundary between continuous (no waiting time) and intermittent fracturing regimes. In the intermittent regime, throughout the entire rupture process avalanches of different sizes are produced and there is a waiting time between two consecutive avalanches. The statistics of waiting times follows a Gamma distribution and the avalanche distribution shows power law scaling, similar to what have been observed in case of earthquake events and bursts in fracture experiments. We propose a prediction scheme that can tell when the system is expected to reach the continuous fracturing point from the intermittent phase.

cond-mat.stat-mech↗
arXiv2010

Can we predict the failure point of a loaded composite material?

As a model of composite material, the fiber bundle model has been chosen -where a bundle of fibers is subjected to external load and fibers have distributed thresholds. For different loading conditions, such a system shows few precursors which indicate that the complete failure is imminent. When external load is increased quasi-statically - \textit{bursts} (number of failing fibers) of different sizes are produced. The burst statistics shows a robust crossover behavior near the failure point, around which the average burst size seems to diverge. If the load is increased by discrete steps, susceptibility and relaxation time diverge as failure point is approached. When the bundle is overloaded (external load is more than critical load) the rate of breaking shows a minimum at half way to the collapse point. The pattern and statistics of energy emission bursts show characteristic difference for below-critical and over-critical load levels.

cond-mat.mtrl-sci↗
arXiv2010

Prediction of the collapse point of overloaded materials by monitoring energy emissions

A bundle of many fibers with stochastically distributed breaking thresholds is considered as a model of composite materials. The fibers are assumed to share the load equally, and to obey Hookean elasticity up to the breaking point. The bundle is slightly overloaded, which leads to complete failure. We study the properties of emission bursts in which an amount of energy $E$ is released. The analysis shows that the size of the energy bursts has a minimum when the system is half-way from the collapse point.

cond-mat.mtrl-sci↗
arXiv2009

Failure Processes in Elastic Fiber Bundles

The fiber bundle model describes a collection of elastic fibers under load. the fibers fail successively and for each failure, the load distribution among the surviving fibers change. Even though very simple, the model captures the essentials of failure processes in a large number of materials and settings. We present here a review of fiber bundle model with different load redistribution mechanism from the point of view of statistics and statistical physics rather than materials science, with a focus on concepts such as criticality, universality and fluctuations. We discuss the fiber bundle model as a tool for understanding phenomena such as creep, and fatigue, how it is used to describe the behavior of fiber reinforced composites as well as modelling e.g. network failure, traffic jams and earthquake dynamics.

cond-mat.stat-mech↗
arXiv2009

Breaking rate minimum predicts the collapse point of over-loaded materials

As a model of composite materials, we choose a bundle of fibers with stochastically distributed breaking thresholds for the individual fibers. the fibers are assumed to share the load equally and to obey Hookean elasticity right up to the breaking point. We study the evolution of the fiber breaking rate at a constant load in excess of the critical load. The analysis shows that the breaking rate reaches a minimum when the system is half-way from its complete collapse.

cond-mat.mtrl-sci↗
arXiv2008

Energy bursts in fiber bundle models of composite materials

As a model of composite materials, a bundle of many fibers with stochastically distributed breaking thresholds for the individual fibers is considered. The bundle is loaded until complete failure to capture the failure scenario of composite materials under external load. The fibers are assumed to share the load equally, and to obey Hookean elasticity right up to the breaking point. We determine the distribution of bursts in which an amount of energy $E$ is released. The energy distribution follows asymptotically a universal power law $E^{-5/2}$, for any statistical distribution of fiber strengths. A similar power law dependence is found in some experimental acoustic emission studies of loaded composite materials.

cond-mat.stat-mech↗
arXiv2007

Relaxation dynamics in strained fiber bundles

Under an applied external load the global load-sharing fiber bundle model, with individual fiber strength thresholds sampled randomly from a probability distribution, will relax to an equilibrium state, or to complete bundle breakdown. The relaxation can be viewed as taking place in a sequence of steps. In the first step all fibers weaker than the applied stress fail. As the total load is redistributed on the surviving fibers, a group of secondary fiber failures occur, etc. For a bundle with a finite number of fibers the process stops after a finite number of steps, $t$. By simulation and theoretical estimates, it is determined how $t$ depends upon the stress, the initial load per fiber, both for subcritical and supercritical stress. The two-sided critical divergence is characterized by an exponent -1/2, independent of the probability distribution of the fiber thresholds.

cond-mat.stat-mech↗
arXiv2007

Burst statistics as a criterion for imminent failure

The distribution of the magnitudes of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded close to the point at which the system fails catastrophically, we find that the power law has an exponent which differs from the one characterizing the size distribution of all avalanches. We demonstrate this analytically for bundles of many fibers with statistically distributed breakdown thresholds for the individual fibers. In this case the magnitude distribution $D(Δ)$ for the avalanche size $Δ$ follows a power law $Δ^{-ξ}$ with $ξ=3/2$ near complete failure, and $ξ=5/2$ elsewhere. We also study a network of electric fuses, and find numerically an exponent 2.0 near breakdown, and 3.0 elsewhere. We propose that this crossover in the size distribution may be used as a signal for imminent system failure.

cond-mat.mtrl-sci↗
arXiv2007

Failure avalanches in fiber bundles for discrete load increase

The statistics of burst avalanche sizes $n$ during failure processes in a fiber bundle follows a power law, $D(n)\sim n^{-ξ}$, for large avalanches. The exponent $ξ$ depends upon how the avalanches are provoked. While it is known that when the load on the bundle is increased in a continuous manner, the exponent takes the value $ξ=5/2$, we show that when the external load is increased in discrete and not too small steps, the exponent value $ξ=3$ is relevant. Our analytic treatment applies to bundles with a general probability distribution of the breakdown thresholds for the individual fibers. The pre-asymptotic size distribution of avalanches is also considered.

cond-mat.stat-mech↗