Statistical Length Scale in Weibull Strength Theory and Its Interaction with Other Scaling Lengths in Quasibrittle Failure
The main result of the paper is the introduction of a statistical length scale into the Weibull theory. The classical Weibull strength theory is self-similar; a feature that can be illustrated by the fact that the strength dependence on structural size is a power law (a straight line in double logarithmic plot). Therefore, the theory predicts unlimited strength for extremely small structures. In the paper, we show that such behavior is a direct implication of the assumption that the structural elements have independent random strengths. We show that by introduction of statistical dependence in a form of spatial autocorrelation, the size dependent strength becomes bounded at the small size extreme. The local random strength is phenomenologically modeled as a random field with a certain autocorrelation function. In such model, the autocorrelation length plays a role of a statistical length scale. The theoretical part is followed by applications in fiber bundle models, chains of fiber bundle models and stochastic finite element method in the context of quasibrittle failure.
KeywordsAutocorrelation length strength random field chain of bundles extreme value theory extremes of random fields statistical length scale
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