Fiber orientation models and closures
Project description
Fiberoripy
This python package provides basic functionality and tools for fiber orientations and closure models.
For example, the Jupyter Notebook
example/orientation/comparison_perfectshear.ipynb
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,
'Orientation behavior of fibers in concentrated suspensions',
Journal of Reinforced Plastic Composites 3, 98-119, 1984.
(https://doi.org/10.1177%2F073168448400300201) - 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.
(https://doi.org/10.1016/j.jnnfm.2010.04.001) - 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.
(https://doi.org/10.1122/1.4939098) - 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.
(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",
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.
(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, Hybrid:
Kyeong-Hee Han and Yong-Taek Im,
'Modified hybrid closure approximation for prediction of flow-induced fiber orientation',
Journal of Rheology 43, 569, 1999.
(https://doi.org/10.1122/1.551002) - IBOF:
Du Hwan Chung and Tai Hun Kwon,
'Invariant-based optimal fitting closure approximation for the numerical prediction of flow-induced fiber orientation',
Journal of Rheology 46(1), 169-194, 2002.
(https://doi.org/10.1122/1.1423312) - ORF, ORW, ORW3:
Joaquim S. Cintra and Charles L. Tucker III,
'Orthotropic closure approximations for flow-induced fiber orientation',
Journal of Rheology, 39(6), 1095-1122, 1995. (https://doi.org/10.1122/1.550630)\ Du Hwan Chung and Tai Hun Kwon,
'Improved model of orthotropic closure approximation for flow induced fiber orientation',
Polymer Composites, 22(5), 636-649, 2001.
(https://doi.org/10.1002/pc.10566) *SQC:
Tobias Karl, Davide Gatti, Bettina Frohnapfel and Thomas Böhlke,
'Asymptotic fiber orientation states of the quadratically closed Folgar--Tucker equation and a subsequent closure improvement',
Journal of Rheology 65(5) : 999-1022, 2021
(https://doi.org/10.1122/8.0000245) - SIC:
Tobias Karl, Matti Schneider and Thomas Böhlke,
'On fully symmetric implicit closure approximations for fiber orientation tensors',
Journal of Non-Newtonian Fluid Mechanics 318 : 105049, 2023.
(https://doi.org/10.1016/j.jnnfm.2023.105049)
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.
(http://doi.org/10.1017/S0022112071000259) - 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.
(http://doi.org/10.1115/1.4004831)
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