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A revisit of Jeffery’s equation – modeling fiber suspensions with Smoothed Particle Hydrodynamics (SPH)

Thursday (27.09.2018)
14:45 - 15:00 S1/01 - A2
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Simulating fiber suspensions is a challenging task and of special interest for discontinuous reinforced plastics, because their properties depend on fiber orientation and fiber length after processing. The first description of a single suspended rigid ellipsoidal body was proposed by Jeffery (1922) almost hundred years ago. Since then, two research communities established in this field: The first one models macroscopic flow of fiber suspensions based on phenomenological extensions to Jeffery’s equation and the second one considers the deformation of discrete flexible fibers for a given flow. However, most of them consider one-way coupling, i.e. the fluid only deforms fibers and not vice versa. The lack of fluid-fiber interaction is mainly caused by the difficulties arising with mesh-based approaches for deforming domains.

An alternative description of flexible fiber suspensions can be achieved by employing Smoothed Particle Hydrodynamics (SPH), which is a Lagrangian method highly suited for fluid-structure interactions. Therefore, the first approach to model fibers with SPH-particle bead chains by Yang et al. (2014) is extended in this work with surface traction and contact formulations. The implemented method is validated for quasi-rigid fibers against Jeffery’s equation, experimental observations and other numerical results. Then, multi-fiber suspensions are modelled and potential applications for the improvement of phenomenological models are demonstrated, which may help building a bridge from single fiber models to the commercially attractive macroscopic models.


Nils Meyer
Karlsruhe Institute of Technology (KIT)
Additional Authors:
  • Oleg Saburow
    Karlsruhe Institute of Technology (KIT)
  • Martin Hohberg
    Karlsruhe Institute of Technology (KIT)
  • Prof. Andrew Hrymak
    University of Western Ontario
  • Prof. Dr. Frank Henning
    Karlsruhe Institute of Technology (KIT)
  • Dr. Luise Kärger
    Karlsruhe Institute of Technology (KIT)


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