Weakest-Link Scaling and Extreme Events in Finite-Sized Systems

Hristopulos, Dionissios T.; Petrakis, Manolis P.; Kaniadakis, Giorgio

doi:10.3390/e17031103

Cited by 14 publications

(14 citation statements)

References 37 publications

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“…( 2) and yet are expressed in closed-form. The κ-Weibull distribution is an example of this and it has a tail that decays like a power-law in contrast with the usual Weibull distribution's exponentially decaying tail (Hristopulos et al 2015). The κ-Weibull distribution lies beyond the scope of the present investigation because its foundation in a strict flaw-size concept is not evident like with the ordinary Weibull distribution.…”

Section: Resultsmentioning

confidence: 90%

“…The weakest-link scaling premise is expressed in Eq. (1) for a system consisting of N links where R i,l i (x) refers to the survival function of the i-th link with support in l i while the system as a whole has support in l N (Hristopulos et al 2015).…”

Section: Introductionmentioning

confidence: 99%

“…As expressed in Eq. ( 2), such a system has a self-similarity property which implies that except for a size scaling, the probability distribution for the survival of a system composed of any cluster of subsystems has the same functional form as the single-link survival function (Hristopulos et al 2015).…”

Section: Introductionmentioning

confidence: 99%

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Failure modelling of glass plates in biaxial loading: using flaw-size based weakest-link systems

Kinsella

Serrano

2021

Glass Struct Eng

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Experimental strength tests are performed on two series of nominally equal plate specimens of annealed soda-lime glass subjected to either ring-on-ring or ball-on-ring bending. The Weibull effective area which represents a fictitious surface area exposed to uniform tension is calculated using closed-form solutions. Finite-size weakest-link systems are implemented numerically in a computationally intensive procedure for random sampling of plates extracted from a virtual jumbo pane whose surface area contains a set of stochastic Griffith flaws. A non-linear finite element analysis is conducted to compute the bending stresses. The glass surface condition is represented in different flaw-size concepts that depend on a truncated exponentially decaying flaw-size distribution. Stress corrosion effects are modelled by implementation of subcritical crack growth. The effective ball contacting radius is determined in a numerical computation. The results show that surface size effects in glass are not only a matter of strength-scaling, as also the shape of the distribution changes. While the lowest strength value, as per the major in-plane principal stress at the recorded fracture origin, in the respective data sets is very similar, the strongest specimen observed in ball-on-ring testing is over 70% stronger than the correspondingly strongest specimen observed in ring-on-ring bending. The Shift function is used to make visual comparisons of the difference in quantiles in the observed data sets. Use of an ordinary Weibull distribution leads to non-conservative strength predictions on smaller effective areas, and to too low strength predictions than are viable for glass design on larger areas. The numerical implementation of finite-size weakest-link systems can produce better predictions for the strength-scaling compared to a Weibull distribution, in particular when the flaw-size concept is modified to include a doubly stochastic flaw-size distribution or a random noise added to each subdivided region of the discretized surface area. The simulated ball-on-ring fracture origins exhibit greater spread from the centre point than otherwise observed in laboratory tests. It is indicated that the chosen representation of surface condition may not be accurate enough for the modelling of all fracture origins in the ball-on-ring setup even though acceptable results are obtained with the ring-on-ring model. There is a need for more insight into the surface condition of glass which can be conducive to the development of flaw-size based weakest-link modelling.

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Section: Resultsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

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Failure modelling of glass plates in biaxial loading: using flaw-size based weakest-link systems

Kinsella

Serrano

2021

Glass Struct Eng

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“…Cases fell rapidly first in adults and then in children even though all schools remained fully open at the time." However, we have seen before that "By the end of that lockdown (2 December 2020), B.1.1.7 was widespread throughout the UK" [6]. In any case, let us note that, in the time series proposed above, the peak was reached when England entered the third lockdown from 5 January 2021.…”

Section: Some Recent Literaturementioning

confidence: 83%

“…In [6], we can find discussed and defined the κ-Weibull. In the formalism of the given reference: arXiv:2111.03636 (4) In (4), x is the random variable.…”

Section: Methods -Weibull and κ-Weibull Pdfmentioning

confidence: 99%