PlanarFibers
Example Notebooks
Get points witin admissible parameter space
[1]:
import planarfibers
import pandas as pd
pd.set_option('display.max_columns', 100)
pd.set_option('display.width', 1000)
[2]:
df = planarfibers.discretization.get_points_on_slices(
radii=["0", "1/2", "9/10"],
la1s=["1/2", "4/6", "5/6", "1"],
numeric=False,
)
[3]:
print(df)
la1 radius_factor beta r d_1 d_8
v00-upper-0 1/2 9/10 pi/2 9/80 69/560 0
v00-upper-1 2/3 9/10 pi/2 1/10 61/630 0
v00-upper-2 5/6 9/10 pi/2 1/16 89/5040 0
v00-mid-0 1/2 0 0 0 3/280 0
v00-mid-1 2/3 0 0 0 -1/315 0
v00-mid-2 5/6 0 0 0 -113/2520 0
v00-lower-0 1/2 9/10 -pi/2 9/80 -57/560 0
v00-lower-1 2/3 9/10 -pi/2 1/10 -13/126 0
v00-lower-2 5/6 9/10 -pi/2 1/16 -541/5040 0
v00-mid-3 1 0 0 0 -4/35 0
vshc-central-la1-0 1/2 0 0 0 3/280 0
vshc-m90-0-la1-0 1/2 1/2 -pi/2 1/16 -29/560 0
vshc-m90-1-la1-0 1/2 9/10 -pi/2 9/80 -57/560 0
vshc-m45-0-la1-0 1/2 1/2 -pi/4 1/16 3/280 - sqrt(2)/32 sqrt(2)/32
vshc-m45-1-la1-0 1/2 9/10 -pi/4 9/80 3/280 - 9*sqrt(2)/160 9*sqrt(2)/160
vshc-0-0-la1-0 1/2 1/2 0 1/16 3/280 1/16
vshc-0-1-la1-0 1/2 9/10 0 9/80 3/280 9/80
vshc-45-0-la1-0 1/2 1/2 pi/4 1/16 3/280 + sqrt(2)/32 sqrt(2)/32
vshc-45-1-la1-0 1/2 9/10 pi/4 9/80 3/280 + 9*sqrt(2)/160 9*sqrt(2)/160
vshc-90-0-la1-0 1/2 1/2 pi/2 1/16 41/560 0
vshc-90-1-la1-0 1/2 9/10 pi/2 9/80 69/560 0
vshc-central-la1-1 2/3 0 0 0 -1/315 0
vshc-m90-0-la1-1 2/3 1/2 -pi/2 1/18 -37/630 0
vshc-m90-1-la1-1 2/3 9/10 -pi/2 1/10 -13/126 0
vshc-m45-0-la1-1 2/3 1/2 -pi/4 1/18 -sqrt(2)/36 - 1/315 sqrt(2)/36
vshc-m45-1-la1-1 2/3 9/10 -pi/4 1/10 -sqrt(2)/20 - 1/315 sqrt(2)/20
vshc-0-0-la1-1 2/3 1/2 0 1/18 -1/315 1/18
vshc-0-1-la1-1 2/3 9/10 0 1/10 -1/315 1/10
vshc-45-0-la1-1 2/3 1/2 pi/4 1/18 -1/315 + sqrt(2)/36 sqrt(2)/36
vshc-45-1-la1-1 2/3 9/10 pi/4 1/10 -1/315 + sqrt(2)/20 sqrt(2)/20
vshc-90-0-la1-1 2/3 1/2 pi/2 1/18 11/210 0
vshc-90-1-la1-1 2/3 9/10 pi/2 1/10 61/630 0
vshc-central-la1-2 5/6 0 0 0 -113/2520 0
vshc-m90-0-la1-2 5/6 1/2 -pi/2 5/144 -401/5040 0
vshc-m90-1-la1-2 5/6 9/10 -pi/2 1/16 -541/5040 0
vshc-m45-0-la1-2 5/6 1/2 -pi/4 5/144 -113/2520 - 5*sqrt(2)/288 5*sqrt(2)/288
vshc-m45-1-la1-2 5/6 9/10 -pi/4 1/16 -113/2520 - sqrt(2)/32 sqrt(2)/32
vshc-0-0-la1-2 5/6 1/2 0 5/144 -113/2520 5/144
vshc-0-1-la1-2 5/6 9/10 0 1/16 -113/2520 1/16
vshc-45-0-la1-2 5/6 1/2 pi/4 5/144 -113/2520 + 5*sqrt(2)/288 5*sqrt(2)/288
vshc-45-1-la1-2 5/6 9/10 pi/4 1/16 -113/2520 + sqrt(2)/32 sqrt(2)/32
vshc-90-0-la1-2 5/6 1/2 pi/2 5/144 -17/1680 0
vshc-90-1-la1-2 5/6 9/10 pi/2 1/16 89/5040 0
Homogenize for representative N4 in slices of parameter space
[1]:
import planarfibers
import matplotlib.pyplot as plt
import pandas as pd
import vofotensors
from vofotensors.abc import la1, d1, d8
import sympy as sp
import numpy as np
[2]:
pd.set_option("display.max_columns", 100)
pd.set_option("display.width", 1000)
[3]:
# User input
SCALE_HOMOGENEOUS = False
key_quantity = "E_modulus"
homogenization_function = planarfibers.approximation.calc_MTOA
la1_values = ["3 / 6", "4 / 6", "5 / 6"]
[4]:
# Get points on views
df = planarfibers.discretization.get_points_on_slices(
radii=["0", "1/2", "9/10"],
la1s=list(map(eval, la1_values)) + ["1"],
numeric=True,
)
[5]:
# Get fiber orientation tensors
parameterizations = vofotensors.fabric_tensors.N4s_parametric
parameterization = parameterizations["planar"]["la1_d1_d8"]
N4_func = sp.lambdify([la1, d1, d8], parameterization)
df["N4"] = df.apply(
lambda row: N4_func(la1=row["la1"], d1=row["d_1"], d8=row["d_8"]), axis=1
)
[6]:
# Define angle discretization
angles = np.linspace(0, 2 * np.pi, 120)
[7]:
# Homogenize
df["stiffness"] = df.apply(
lambda row: homogenization_function(N4=row["N4"], inp=None),
axis=1,
)
[8]:
# Define helper func to explicitly select either Youngs or generalized compression mod.
def get_Youngs_modulus(stiffness, angles):
projector = planarfibers.utils.PlanarStiffnesProjector()
E, K = projector.get_planar_E_K(stiffness=stiffness, angles=angles)
if key_quantity == "E_modulus":
return E
elif key_quantity == "K_modulus":
return K
[9]:
# Get Youngs-Modulus for direction in plane
df[key_quantity] = df.apply(
lambda row: get_Youngs_modulus(stiffness=row["stiffness"], angles=angles),
axis=1,
)
[10]:
# Define layout
la1_key_extensions = {f"-la1-{index}": value for index, value in enumerate(la1_values)}
# la1_key_extensions = {
# "-la1-0": "3 / 6",
# "-la1-1": "4 / 6",
# "-la1-2": "5 / 6",
# }
grid_indices = {
"vshc-central": (2, 0),
"vshc-m90-0": (3, 0),
"vshc-m90-1": (4, 0),
"vshc-m45-0": (3, 1),
"vshc-m45-1": (4, 2),
"vshc-0-0": (2, 1),
"vshc-0-1": (2, 2),
"vshc-45-0": (1, 1),
"vshc-45-1": (0, 2),
"vshc-90-0": (1, 0),
"vshc-90-1": (0, 0),
}
legend_axis_indices = (4, 1)
empty_axes_indices = [(0, 1), (1, 2), (3, 2), legend_axis_indices]
[11]:
# Plot first view
nbr_slices = len(la1_key_extensions)
fig = plt.figure(figsize=(6 * nbr_slices, 10))
subfigs = fig.subfigures(1, nbr_slices, wspace=0.0)
for index, (key_extension, la1val) in enumerate(la1_key_extensions.items()):
subfig = subfigs[index]
subfig.suptitle(f"la1 = {la1val}")
axs = subfig.subplots(ncols=3, nrows=5, subplot_kw={"projection": "polar"})
lines = [] # Initialize legend lines
for key_N4_start, grid_index in grid_indices.items():
ax = axs[grid_index]
key = key_N4_start + key_extension
ax.plot(angles, df.loc[key][key_quantity], label=key_quantity, color="red")
# Update legend if something has been plotted
lines_tmp, labels_tmp = ax.get_legend_handles_labels()
if len(lines_tmp) > len(lines):
lines, labels = lines_tmp, labels_tmp
for ax in axs.flatten():
ax.set_xticklabels([])
if SCALE_HOMOGENEOUS:
ax.set_ylim(
bottom=0,
top=1.2,
)
ax.set_yticks([0, 0.5, 1])
legend_axis = axs[legend_axis_indices]
legend_axis.legend(lines, labels, loc="center")
for indice in empty_axes_indices:
ax = axs[indice]
ax.axis("off")
fig.tight_layout()
[12]:
# Define layout second view
grid_indices = {
"v00-upper-0": (0, 0),
"v00-upper-1": (0, 1),
"v00-upper-2": (0, 2),
#
"v00-mid-0": (1, 0),
"v00-mid-1": (1, 1),
"v00-mid-2": (1, 2),
#
"v00-lower-0": (2, 0),
"v00-lower-1": (2, 1),
"v00-lower-2": (2, 2),
#
"v00-mid-3": (1, 3),
#
}
legend_axis_indices = (0, 3)
empty_axes_indices = [(2, 3), legend_axis_indices]
[13]:
# Plot second dview
fig, axs = plt.subplots(
figsize=(12, 9), ncols=4, nrows=3, subplot_kw={"projection": "polar"}
)
lines = [] # Initialize legend lines
for key_N4_start, grid_index in grid_indices.items():
ax = axs[grid_index]
key = key_N4_start
ax.plot(angles, df.loc[key][key_quantity], label=key_quantity, color="red")
# Update legend if something has been plotted
lines_tmp, labels_tmp = ax.get_legend_handles_labels()
if len(lines_tmp) > len(lines):
lines, labels = lines_tmp, labels_tmp
for ax in axs.flatten():
ax.set_xticklabels([])
if SCALE_HOMOGENEOUS:
ax.set_ylim(
bottom=0,
top=1.2,
)
ax.set_yticks([0, 0.5, 1])
legend_axis = axs[legend_axis_indices]
legend_axis.legend(lines, labels, loc="center")
for indice in empty_axes_indices:
ax = axs[indice]
ax.axis("off")
fig.tight_layout()
plt.show()
Integrate random planar FODF with numerical averager
[1]:
import planarfibers
import pandas as pd
import numpy as np
[2]:
pd.set_option("display.max_columns", 100)
pd.set_option("display.width", 1000)
np.set_printoptions(linewidth=400)
[3]:
# Select random FODF: choose exact closre FODF, see equation (77) in "Fiber orientation distributions based on planar fiber orientation tensors of fourth order. Math. Mech. Solids (to appear 2022)"".
la1 = 5 / 6
odf_func = lambda phi: ((1.0 - la1) * la1) / (
2.0 * np.pi * (la1**2 + (1.0 - 2.0 * la1) * np.cos(phi) ** 2)
)
[4]:
# Select quantity which is to be averaged
quantity = planarfibers.approximation.calc_MT_UD()
print(quantity)
[[24.52696446 4.87908133 4.87908133 0. 0. 0. ]
[ 4.87908133 9.12135685 5.36895671 0. 0. 0. ]
[ 4.87908133 5.36895671 9.12135685 0. 0. 0. ]
[ 0. 0. 0. 3.75240015 0. 0. ]
[ 0. 0. 0. 0. 3.97000178 0. ]
[ 0. 0. 0. 0. 0. 3.97000178]]
[5]:
# Average
averager = planarfibers.averager.AveragerPlanar(odf_planar=odf_func)
average = averager.average(quantity)
print(average)
[[ 2.08517135e+01 5.98673099e+00 4.96072722e+00 0.00000000e+00 0.00000000e+00 8.54110020e-16]
[ 5.98673099e+00 1.05813085e+01 5.28731081e+00 0.00000000e+00 0.00000000e+00 -6.43671067e-17]
[ 4.96072722e+00 5.28731081e+00 9.12135685e+00 0.00000000e+00 0.00000000e+00 -8.74005141e-18]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 3.78866709e+00 1.53209539e-17 0.00000000e+00]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 5.77997479e-18 3.93373484e+00 0.00000000e+00]
[ 1.01914811e-15 -1.51996602e-16 -1.44620409e-17 0.00000000e+00 0.00000000e+00 6.18530110e+00]]