Filter Fasern
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Filter Fasern

Modelling of Microstructures: Fibresystems

Stochastic geometry models are fit to real structures based on geometric characteristics measured from 3D image data. Varying model parameters creates virtual fiber systems with different microstructures. Consequences on the macroscopic behavior can be studied by numerical simulations

Widely used stochastic models for fibrous structures are Boolean models of cylinders and Poisson processes of dilated lines. For both models, the orientation distribution of the cylinders can be chosen to match the one observed in the materials isotropic or anisotropic, e. g. with a preferred direction or directions isotropically distributed in a plane.

Dilatiertes Poissonsches Geradenfeld
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Dilatiertes Poissonsches Geradenfeld, Orientierungen in z-Richtung bevorzugt
Boolsches Modell trilobaler Zylinder
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Boolsches Modell trilobaler Zylinder, isotrop
Boolsches Modell trilobaler Zylinder
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Boolsches Modell trilobaler Zylinder, Orientierungen in x-y-Ebene bevorzugt

Modeling dense systems of non overlapping fibers with a controllable level of bending requires a different typ of model. The Altendorf-Jeulin model operates in two steps.

  1. First, a random walk with a multivariate von Mises-Fisher orientation distribution defines bent fibers.
  2. Second, a force-biased packing approach arranges them in a non overlapping configuration.

All parameters needed for the fitting of this model to a real microstructure can be estimated from 3D images. With a fiber length to fiber thickness ratio of up to 15, isotropic fiber systems with fiber volume fractions above 60 percent can be generated.

Z-Richtung bevorzugt
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Preferentially Z-direction
Isotropy
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Isotropy
Isotropy in the x-y plane
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Isotropy in the x-y plane

The stochastic model developed by Hellen Altendorf generates fiber systems with separate fibers. Since nonwovens, for example, often also contain fiber bundles, the Altendorf-Jeulin model is generalized to allow fiber-fiber interactions. Realizations of the model with fiber bundles can be seen in the figure below.

Z-Richtung bevorzugt
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Preferentially Z-direction
Isotropie
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Isotopy
Isotropie in der x-y-Ebene
© ITWM
Isotropy in the x-y plane

Publications

  • Easwaran, P.;Lehmann, M. J.; Wirjadi, O.; Prill, T. ; Didas, S.; Redenbach, C.:
    Automatic Fiber Thickness Measurement in SEM Images Validated Using Synthetic Data.
    Proceedings of FILTECH 2015.
    Filtech Exhibitions Germany: Cologne
  • Redenbach, C.; Schladitz, K.; Vecchio, I.; Wirjadi, O. :
    Image Analysis for Microstructures Based on Stochastic Models.
    GAMM-Mitteilungen. 37, (2), 281-305, (2014).
  • Altendorf H.; Jeulin D.: 
    Random-walk-based stochastic modeling of three-dimensional fiber systems.
    Phys. Rev. E 83, 041804, 2011.