Print available parameterizations of second-order fiber orientation tensors (FOT)

[1]:

import vofotensors as vot

[2]:

print("Available parameterizations of second order fiber orientation tensors:\n")
vot.utils.print_nested(vot.fabric_tensors.N2s_parametric)

Available parameterizations of second order fiber orientation tensors:


####################
Group: planar
alpha1
Matrix([
[3*alpha1/4 + 1/2,                0, 0],
[               0, 1/2 - 3*alpha1/4, 0],
[               0,                0, 0]])

la1
Matrix([
[la1,       0, 0],
[  0, 1 - la1, 0],
[  0,       0, 0]])


####################
Group: transv_isotropic
alpha1
Matrix([
[alpha1 + 1/3,              0,              0],
[           0, 1/3 - alpha1/2,              0],
[           0,              0, 1/3 - alpha1/2]])

alpha2
Matrix([
[1/3 - alpha2/2,            0,              0],
[             0, alpha2 + 1/3,              0],
[             0,            0, 1/3 - alpha2/2]])

alpha3
Matrix([
[1/3 - alpha3/2,              0,            0],
[             0, 1/3 - alpha3/2,            0],
[             0,              0, alpha3 + 1/3]])

la1
Matrix([
[la1,           0,           0],
[  0, 1/2 - la1/2,           0],
[  0,           0, 1/2 - la1/2]])


####################
Group: orthotropic
la1_la2
Matrix([
[la1,   0,              0],
[  0, la2,              0],
[  0,   0, -la1 - la2 + 1]])

la1_la2_la3
Matrix([
[la1,   0,   0],
[  0, la2,   0],
[  0,   0, la3]])

alpha1_alpha3
Matrix([
[alpha1 - alpha3/2 + 1/3,                          0,                        0],
[                      0, -alpha1/2 - alpha3/2 + 1/3,                        0],
[                      0,                          0, -alpha1/2 + alpha3 + 1/3]])

alpha1_alpha2_alpha3
Matrix([
[alpha1 - alpha2/2 - alpha3/2 + 1/3,                                   0,                                   0],
[                                 0, -alpha1/2 + alpha2 - alpha3/2 + 1/3,                                   0],
[                                 0,                                   0, -alpha1/2 - alpha2/2 + alpha3 + 1/3]])