scholarly journals Cooperative Dynamics in the Fiber Bundle Model

2021 ◽  
Vol 8 ◽  
Author(s):  
Bikas K. Chakrabarti ◽  
Soumyajyoti Biswas ◽  
Srutarshi Pradhan
Keyword(s):  
Fiber Bundle ◽  
Mean Field ◽  
Load Sharing ◽  
Statistical Feature ◽  
Sharing Scheme ◽  
Fiber Bundle Model ◽  
Cooperative Dynamics ◽  
Simulation Results ◽  
The Individual ◽  
Spring Constants

We discuss the cooperative failure dynamics in the fiber bundle model where the individual elements or fibers are Hookean springs that have identical spring constants 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.

scholarly journals Local load-sharing fiber bundle model in higher dimensions

2015 ◽  
Vol 92 (2) ◽  
Author(s):  
Santanu Sinha ◽  
Jonas T. Kjellstadli ◽  
Alex Hansen
Keyword(s):  
Fiber Bundle ◽  
Load Sharing ◽  
Higher Dimensions ◽  
Local Load ◽  
Fiber Bundle Model

scholarly journals FIBERS ON A GRAPH WITH LOCAL LOAD SHARING

2007 ◽  
Vol 18 (06) ◽  
pp. 919-926 ◽  
Author(s):  
UMA DIVAKARAN ◽  
AMIT DUTTA
Keyword(s):  
Critical Behavior ◽  
Mean Field ◽  
Finite Size ◽  
Load Sharing ◽  
Local Load ◽  
Finite Size Scaling ◽  
Scaling Method ◽  
Avalanche Size ◽  
Fiber Bundle Model ◽  
The Mean

We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical behavior of the model numerically using a finite size scaling method and the mean field critical behavior is established. The avalanche size distribution is also found to exhibit a mean field nature in the asymptotic limit.

scholarly journals Criterion for Imminent Failure During Loading—Discrete Element Method Analysis

2021 ◽  
Vol 9 ◽  
Author(s):  
Wojciech Dȩbski ◽  
Srutarshi Pradhan ◽  
Alex Hansen
Keyword(s):  
Discrete Element Method ◽  
Elastic Energy ◽  
Fiber Bundle ◽  
Load Sharing ◽  
Discrete Element ◽  
Rate Of Change ◽  
Change Rate ◽  
Fiber Bundle Model ◽  
Method Analysis ◽  
Element Method

It has recently been reported that the equal load sharing fiber bundle model predicts the rate of change of the elastic energy stored in the bundle reaches its maximum before catastrophic failure occurs, making it a possible predictor for imminent collapse. The equal load sharing fiber bundle model does not contain central mechanisms that often play an important role in failure processes, such as localization. Thus, there is an obvious question whether a similar phenomenon is observed in more realistic systems. We address this question using the discrete element method to simulate breaking of a thin tissue subjected to a stretching load. Our simulations confirm that for a class of virtual materials which respond to stretching with a well-pronounced peak in force, its derivative and elastic energy we always observe an existence of the maximum of the elastic energy change rate prior to maximum loading force. Moreover, we find that the amount of energy released at failure is related to the maximum of the elastic energy absorption rate.

scholarly journals Mesoscopic description of the equal-load-sharing fiber bundle model

2018 ◽  
Vol 98 (3) ◽  
Author(s):  
Martin Hendrick ◽  
Srutarshi Pradhan ◽  
Alex Hansen
Keyword(s):  
Fiber Bundle ◽  
Load Sharing ◽  
Fiber Bundle Model

Temporal and Spatial Evolution of Bursts in a Fiber Bundle Model of Creep Rupture

2013 ◽  
Vol 592-593 ◽  
pp. 773-776
Author(s):  
Zsuzsa Danku ◽  
Ferenc Kun
Keyword(s):  
Fiber Bundle ◽  
Failure Modes ◽  
Load Sharing ◽  
Model Material ◽  
Creep Rupture ◽  
Fracture Mechanisms ◽  
Temporal Shape ◽  
Fiber Bundle Model ◽  
Micro Level ◽  
Macroscopic Failure

We present a theoretical study of the creep rupture of heterogeneous materials based on a fiber bundle model which provides a direct connection between the microscopic fracture mechanisms and the macroscopic time evolution. In the model, material elements fail either due to immediate breaking or undergo a damage accumulating ageing process. We found that on the micro-level the competition of the two failure modes gives rise to bursts of breakings with power law distributed size and waiting time between events. We demonstrate that approaching macroscopic failure the system accelerates which can be fully described as a non-homogeneous Poissonian process for long range load sharing, however, when localization occurs breaking events get clustered. Bursts are composed of sub-avalanches which lead to a non-trivial temporal shape comparable to measurements. The pulse shape proved to be sensitive to the range of load sharing.

Scaling law in avalanche breaking of composite materials

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ahmed Hader ◽  
Hicham Sbiaai ◽  
Mohammed Tanasehte ◽  
Layla Amallah ◽  
Yahia Boughaleb
Keyword(s):  
Composite Materials ◽  
External Load ◽  
Fiber Bundle ◽  
Applied Load ◽  
Scaling Law ◽  
Load Sharing ◽  
Local Load ◽  
Vicsek Model ◽  
Content Type ◽  
Fiber Bundle Model

PurposeThe fibers are loaded by the cosine component of the external load, when a fiber fails, and due to the local load-sharing nature, its force is shared by surviving neighboring fibers. The results show that the system presents a greater resistance and toughness toward the applied load compared to the classical one.Design/methodology/approachIn this paper, the authors adopt the dynamics of a local load-sharing fiber bundle model in two dimensions under an external load to study scaling law in failure process of composite materials with randomly oriented fibers. The model is based on the fiber bundle model where the fibers are randomly oriented. The system is different to the classical one where the fibers are arranged in parallel with the applied load direction.FindingsThe evolution time of the fraction of broken fiber is described by an exponential law with two characteristic times. The latter decrease linearly and exponentially respectively with both applied load and temperature.Originality/valueScaling behavior of the broken fiber numbers with the size system shows that the system exhibits a scaling law of Family–Vicsek model with universal exponents.

scholarly journals Size Distribution of Emitted Energies in Local Load Sharing Fiber Bundles

2021 ◽  
Vol 9 ◽  
Author(s):  
Subhadeep Roy ◽  
Soumyajyoti Biswas
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Linear Relation ◽  
Fiber Bundle ◽  
Average Energy ◽  
Load Sharing ◽  
Local Load ◽  
Fiber Bundles ◽  
Avalanche Size ◽  
Fiber Bundle Model

We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size (s) and the corresponding average energy burst (〈E〉) in this version of the model have a non-linear relation (〈E〉 ~ sγ). Numerical results indicate that γ ≈ 2.5 universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of −(γ + 1).

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