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

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IUTAM Symposium on Scaling in Solid Mechanics

Part of the book series: Iutam Bookseries ((IUTAMBOOK,volume 10))

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Civil Engineering Institute of Structural Mechanics, Brno University of Technology, Veveří 95, 602 00, Brno, Czech Republic

    Miroslav Vořechovský

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  1. Miroslav Vořechovský
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Editors and Affiliations

  1. School of Engineering, Cardiff University, Queen’s Bldg., The Parade, Cardiff CF24 3AA, UK

    F.M. Borodich (borodichfm@cardiff.ac.uk) (borodichfm@cardiff.ac.uk)

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Vořechovský, M. (2009). Statistical Length Scale in Weibull Strength Theory and Its Interaction with Other Scaling Lengths in Quasibrittle Failure. In: Borodich, F. (eds) IUTAM Symposium on Scaling in Solid Mechanics. Iutam Bookseries, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9033-2_20

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  • DOI: https://doi.org/10.1007/978-1-4020-9033-2_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9032-5

  • Online ISBN: 978-1-4020-9033-2

  • eBook Packages: EngineeringEngineering (R0)

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