Statistical Length Scale in Weibull Strength Theory and Its Interaction with Other Scaling Lengths in Quasibrittle Failure

摘要

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.