Article2024

Statistical Scaling in Localization-Induced Failures

10 citations0/0 files storedApplied Mechanics Reviews

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Probabilistic and Robust Engineering Design Fatigue and fracture mechanics Structural Integrity and Reliability Analysis

Abstract

Abstract The investigation of statistical scaling in localization-induced failures dates back to da Vinci's speculation on the length effect on rope strength in 1500 s. The early mathematical description of statistical scaling emerged with the birth of the extreme value statistics. The most commonly known mathematical model for statistical scaling is the Weibull size effect, which is a direct consequence of the infinite weakest-link model. However, abundant experimental observations on various localization-induced failures have shown that the Weibull size effect is inadequate. Over the last two decades, two mathematical models were developed to describe the statistical size effect in localization-induced failures. One is the finite weakest-link model, in which the random structural resistance is expressed as the minimum of a set of independent discrete random variables. The other is the level excursion model, a continuum description of the finite weakest-link model, in which the structural failure probability is calculated as the probability of the upcrossing of a random field over a barrier. This paper reviews the mathematical formulation of these two models and their applications to various engineering problems including the strength distributions of quasi-brittle structures, failure statistics of micro-electromechanical systems (MEMS) devices, breakdown statistics of high– k gate dielectrics, and probability distribution of buckling pressure of spherical shells containing random geometric imperfections. In addition, the implications of statistical scaling for the stochastic finite element simulations and the reliability-based structural design are discussed. In particular, the recent development of the size-dependent safety factors is reviewed.

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References

1998Simulation of Stationary Non-Gaussian Translation Processes 2000Uncertain buckling: its past, present and future 1994Non-linear buckling of a column with initial imperfection via stochastic and non-stochastic convex models 1969Buckling under axial compression of long cylindrical shells with random axisymmetric imperfections 1962STATISTICAL METHODS IN THE NONLINEAR THEORY OF ELASTIC SHELLS 2014Size effect on reliability indices and safety factors of quasibrittle structures 2022Stochastic analysis of geometrically imperfect thin cylindrical shells using topology-aware uncertainty models 2024Uncovering the dual role of dimensionless radius in buckling of spherical shells with random geometric imperfections

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