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Fiber orientation models and closures

Project description

LICENSE Documentation Status PyPI version Black DOI Binder


This python package provides basic functionality and tools for fiber orientations and closure models.

For example, the Jupyter Notebook


should reproduce Figure 2 in Favaloro, A.J., Tucker III, C.L., Composites Part A, 126 (2019):


Orientation models

Following models have been implemented:

  • Jeffery:
    G.B. Jeffery,
    'The motion of ellipsoidal particles immersed in a viscous fluid',
    Proceedings of the Royal Society A, 1922.
  • Folgar-Tucker:
    F. Folgar, C.L. Tucker,
    'Orientation behavior of fibers in concentrated suspensions',
    Journal of Reinforced Plastic Composites 3, 98-119, 1984.
  • FTMS:
    A. Latz, U. Strautins, D. Niedziela,
    'Comparative numerical study of two concentrated fiber suspension models',
    Journal of Non-Newtonian Fluid Mechanics 165, 764-781, 2010.
  • iARD(-RPR):
    H.C. Tseng, R.Y. Chang, C.H. Hsu,
    'An objective tensor to predict anisotropic fiber orientation in concentrated susp ensions',
    Journal of Rheology 60, 215, 2016.
  • pARD(-RPR):
    H.C. Tseng, R.Y. Chang, C.H. Hsu,
    'The use of principal spatial tensor to predict anisotropic fiber orientation in concentrated fiber suspensions',
    Journal of Rheology 62, 313, 2017.
  • MRD:
    A. Bakharev, H. Yu, R. Speight and J. Wang,
    “Using New Anisotropic Rotational Diffusion Model To Improve Prediction Of Short Fibers in Thermoplastic Injection Molding",
    ANTEC, Orlando, 2018.
  • RSC:
    J. Wang, J.F. O'Gara, and C.L. Tucker,
    'An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence',
    Journal of Rheology 52, 1179, 2008.
  • ARD-RSC:
    J. H. Phelps, C. L. Tucker,
    'An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics',
    Journal of Non-Newtonian Fluid Mechanics 156, 165-176, 2009.


  • Linear
  • Quadratic
  • IBOF
  • Sampling from directions
  • ORF
  • ORW
  • ORW3

Approximations for equivalent aspect ratios

  • Cox:
    R.G. Cox,
    'The motion of long slender bodies in a viscous fluid. Part 2. Shear flow.',
    J. Fluid Mech. 1971, 45, 625–657.
  • Zhang:
    D. Zhang, D.E. Smith, D.A. Jack, S. Montgomery-Smith,
    'Numerical Evaluation of Single Fiber Motion for Short-Fiber-Reinforced Composite Materials Processing',
    J. Manuf. Sci. Eng. 2011, 133, 51002.

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