# -*- coding: utf-8 -*-
"""Compute equivalent aspect ratios."""
import numpy as np
[docs]def get_cox_aspect_ratio(aspect_ratio):
"""Compute an equivalent aspect ratio according to Cox.
Parameters
----------
aspect_ratio : float
Aspect ratio of a cylindrical fiber.
Returns
-------
float
Equivalent aspect ratio for an ellipsoid.
References
----------
.. [1] Cox, R.G.
'The motion of long slender bodies in a viscous fluid Part 2. Shear flow.',
J. Fluid Mech. 1971, 45, 625-657.
https://doi.org/10.1017/S0022112071000259
"""
return 1.24 * aspect_ratio / np.sqrt(np.log(aspect_ratio))
[docs]def get_zhang_aspect_ratio(aspect_ratio):
"""Compute an equivalent aspect ratio according to Zhang.
Parameters
----------
aspect_ratio : float
Aspect ratio of a cylindrical fiber.
Returns
-------
float
Equivalent aspect ratio for an ellipsoid.
References
----------
.. [1] 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.
https://doi.org/10.1115/1.4004831
"""
return (
0.000035 * aspect_ratio**3
- 0.00467 * aspect_ratio**2
+ 0.764 * aspect_ratio
+ 0.404
)