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 stochastic model developed by Hellen Altendorf 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. Simulated systems with a fiber volume fraction up to 57.3% are obtained.

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

Z-Richtung bevorzugt
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Preferentially Z-direction

Isotropie
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Isotopy

Isotropie in der x-y-Ebene
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Isotropy in the x-y plane