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Stochastic mechanical degradation of multi-cracked fiber bundles with elastic and viscous interactions

  • Fabio Manca
  • Stefano Giordano
  • Pier Luca Palla
  • Fabrizio Cleri
Regular Article

Abstract

The mechanics of fiber bundles has been largely investigated in order to understand their complex failure modes. Under a mechanical load, the fibers fail progressively while the load is redistributed among the unbroken fibers. The classical fiber bundle model captures the most important features of this rupture process. On the other hand, the homogenization techniques are able to evaluate the stiffness degradation of bulk solids with a given population of cracks. However, these approaches are inadequate to determine the effective response of a degraded bundle where breaks are induced by non-mechanical actions. Here, we propose a method to analyze the behavior of a fiber bundle, undergoing a random distribution of breaks, by considering the intrinsic response of the fibers and the visco-elastic interactions among them. We obtain analytical solutions for simple configurations, while the most general cases are studied by Monte Carlo simulations. We find that the degradation of the effective bundle stiffness can be described by two scaling regimes: a first exponential regime for a low density of breaks, followed by a power-law regime at increasingly higher break density. For both regimes, we find analytical effective expressions described by specific scaling exponents.

Graphical abstract

Keywords

Living systems: Biological Matter 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Fabio Manca
    • 1
    • 2
  • Stefano Giordano
    • 1
    • 2
  • Pier Luca Palla
    • 1
    • 3
  • Fabrizio Cleri
    • 1
    • 3
  1. 1.Institute of ElectronicsMicroelectronics and Nanotechnology (IEMN UMR CNRS 8520)Villeneuve d’AscqFrance
  2. 2.Joint International Laboratory LIA LEMAC/LICSECLille, ComUE Lille Nord de FranceVilleneuve d’AscqFrance
  3. 3.University of Lille IVilleneuve d’AscqFrance

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