fiberoripy 1.0.2

Fiber orientation models and closures

Fiberoripy

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

For example,

example/orientation/comparison_perfectshear.py

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. (https://doi.org/10.1098/rspa.1922.0078)
• Folgar-Tucker: F. Folgar, C.L. Tucker III, 'Orientation behavior of fibers in concentrated suspensions', Journal of Reinforced Plastic Composites 3, 98-119, 1984. (https://doi.org/10.1177%2F073168448400300201)
• Maier-Saupe: 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. (https://doi.org/10.1016/j.jnnfm.2010.04.001)
• iARD(-RPR): Tseng, Huan-Chang; Chang, Rong-Yeu; Hsu, Chia-Hsiang, 'An objective tensor to predict anisotropic fiber orientation in concentrated susp ensions',Journal of Rheology 60, 215, 2016. (https://doi.org/10.1122/1.4939098)
• pARD(-RPR): Tseng, Huan-Chang; Chang, Rong-Yeu; Hsu, Chia-Hsiang, 'The use of principal spatial tensor to predict anisotropic fiber orientation in concentrated fiber suspensions', Journal of Rheology 62, 313, 2017. (https://doi.org/10.1122/1.4998520)
• 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," in ANTEC, Orlando, 2018.
• RSC: Jin Wang, John F. O'Gara, and Charles L. Tucker, 'An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence', Journal of Rheology 52, 1179, 2008. (https://doi.org/10.1122/1.2946437)
• 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.(https://doi.org/10.1016/j.jnnfm.2008.08.002)

Closures

• Linear
• Quadratic
• IBOF
• Sampling from directions

Approximations for equivalent aspect ratios

• Cox: Cox, R.G. The motion of long slender bodies in a viscous fluid. Part 2. Shear flow. J. Fluid Mech. 1971, 45, 625–657.(http://doi.org/10.1017/S0022112071000259)
• Zhang: Zhang, D.; Smith, D.E.; Jack, D.A.; Montgomery-Smith, S. Numerical Evaluation of Single Fiber Motion for Short-Fiber-Reinforced Composite Materials Processing. J. Manuf. Sci. Eng. 2011, 133, 51002.(http://doi.org/10.1115/1.4004831)
• Goldsmith-Mason: Forgacs, O.; Mason, S. Particle motions in sheared suspensions. J. Colloid Sci. 1959, 14, 457–472.(http://doi.org/10.1016/0095-8522(59)90012-1)