Original Mori-Tanaka vs. Tandon-Weng

import numpy as np
import matplotlib.pyplot as plt
from fiberpy.mechanics import A2Eij, FiberComposite

params = {
    "figure.figsize": (6, 4),
    "figure.dpi": 72,
    "axes.titlesize": 14,
    "axes.labelsize": 14,
    "font.size": 14,
    "xtick.labelsize": 14,
    "ytick.labelsize": 14,
    "legend.fontsize": 14,
    "savefig.bbox": "tight",
    "figure.constrained_layout.use": True,
}
plt.rcParams.update(params)

# Example RVE data
rve_data = {
    "rho0": 1.14e-9,
    "E0": 631.66,
    "nu0": 0.42925,
    "alpha0": 5.86e-5,
    "rho1": 2.55e-9,
    "E1": 72000,
    "nu1": 0.22,
    "alpha1": 5e-6,
    "mf": 0.5,
    "aspect_ratio": 17.983,
}
fiber = FiberComposite(rve_data)

Original Mori-Tanaka vs. Tandon-Weng#

a11 = np.linspace(1 / 3, 1, 20)
MT = np.zeros((len(a11), 9))
TW = np.zeros((len(a11), 9))
for i in range(len(a11)):
    a = np.array([a11[i], (1 - a11[i]) / 2, (1 - a11[i]) / 2])
    A = fiber.ABar(a, "MoriTanaka")
    MT[i, :] = A2Eij(A)
    A = fiber.ABar(a, "TandonWeng")
    TW[i, :] = A2Eij(A)

plt.figure(figsize=(12, 4))
plt.subplot(121)
plt.plot(a11, MT[:, 0] / 1e3, "C0-", label="$E_1$ MT")
plt.plot(a11, MT[:, 1] / 1e3, "C1-", label="$E_2$ MT")
plt.plot(a11, TW[:, 0] / 1e3, "C0--", label="$E_1$ TW")
plt.plot(a11, TW[:, 1] / 1e3, "C1--", label="$E_2$ TW")
plt.xlabel("$a_{11}$")
plt.ylabel("$E$ (GPa)")
plt.title(r"$a=\mathrm{diag}\,(a_{11}, (1-a_{11})/2, (1-a_{11})/2)$").set_y(1.02)
plt.grid()
plt.legend()

plt.subplot(122)
plt.plot(a11, MT[:, 6], "C0-", label=r"$\nu_{12}$ MT")
plt.plot(a11, MT[:, 7], "C1-", label=r"$\nu_{23}$ MT")
plt.plot(a11, TW[:, 6], "C0--", label=r"$\nu_{12}$ TW")
plt.plot(a11, TW[:, 7], "C1--", label=r"$\nu_{23}$ TW")
plt.xlabel("$a_{11}$")
plt.ylabel(r"$\nu$")
plt.title(r"$a=\mathrm{diag}\,(a_{11}, (1-a_{11})/2, (1-a_{11})/2)$").set_y(1.02)
plt.grid()
plt.legend()

plt.show()
../_images/567158cf3820461b936421bba67e000bc457016fef45386805b9b953f179250f.png

Closures#

a11 = np.linspace(1 / 3, 1, 20)
HYB = np.zeros((len(a11), 9))
ORT = np.zeros((len(a11), 9))
IBOF = np.zeros((len(a11), 9))
for i in range(len(a11)):
    a = np.array([a11[i], (1 - a11[i]) / 2, (1 - a11[i]) / 2])
    A = fiber.ABar(a, closure="hybrid")
    HYB[i, :] = A2Eij(A)
    A = fiber.ABar(a, closure="orthotropic")
    ORT[i, :] = A2Eij(A)
    A = fiber.ABar(a, closure="invariants")
    IBOF[i, :] = A2Eij(A)

plt.figure(figsize=(12, 4))
plt.subplot(121)
plt.plot(a11, HYB[:, 0] / 1e3, "C0-", label="$E_1$ HYB")
plt.plot(a11, HYB[:, 1] / 1e3, "C1-", label="$E_2$ HYB")
plt.plot(a11, ORT[:, 0] / 1e3, "C0--", label="$E_1$ ORT")
plt.plot(a11, ORT[:, 1] / 1e3, "C1--", label="$E_2$ ORT")
plt.plot(a11, IBOF[:, 0] / 1e3, "C0-.", label="$E_1$ IBOF")
plt.plot(a11, IBOF[:, 1] / 1e3, "C1-.", label="$E_2$ IBOF")
plt.xlabel("$a_{11}$")
plt.ylabel("$E$ (GPa)")
plt.title(r"$a=\mathrm{diag}\,(a_{11}, (1-a_{11})/2, (1-a_{11})/2)$").set_y(1.02)
plt.grid()
plt.legend()

plt.subplot(122)
plt.plot(a11, HYB[:, 6], "C0-", label=r"$\nu_{12}$ HYB")
plt.plot(a11, HYB[:, 7], "C1-", label=r"$\nu_{23}$ HYB")
plt.plot(a11, ORT[:, 6], "C0--", label=r"$\nu_{12}$ ORT")
plt.plot(a11, ORT[:, 7], "C1--", label=r"$\nu_{23}$ ORT")
plt.plot(a11, IBOF[:, 6], "C0-.", label=r"$\nu_{12}$ IBOF")
plt.plot(a11, IBOF[:, 7], "C1-.", label=r"$\nu_{23}$ IBOF")
plt.xlabel("$a_{11}$")
plt.ylabel(r"$\nu$")
plt.title(r"$a=\mathrm{diag}\,(a_{11}, (1-a_{11})/2, (1-a_{11})/2)$").set_y(1.02)
plt.grid()
plt.legend()

plt.show()
../_images/d887d226640d4d1499b68bdfb442d94974db571010c6c739b4770158837c3da7.png

Volume fraction dependence#

vf = np.linspace(0, 1, 100)
Random = np.zeros((len(vf), 12))
UD = np.zeros((len(vf), 12))
for i in range(len(vf)):
    fiber.vf = vf[i]
    A = fiber.ABar(np.ones(3) / 3, recompute_UD=True)
    Random[i, :9] = A2Eij(A)
    Random[i, 9:] = fiber.alphaBar(A)

    A = fiber.TandonWeng()
    UD[i, :9] = A2Eij(A)
    UD[i, 9:] = fiber.alphaBar(A)

plt.figure(figsize=(12, 4))
plt.subplot(121)
plt.semilogy(vf, Random[:, 0] / 1e3, "C0-", label="Random")
plt.semilogy(vf, UD[:, 0] / 1e3, "C1-", label="UD")
plt.xlabel("Volume fraction")
plt.ylabel("$E_1$ (GPa)")
plt.grid()
plt.legend()

plt.subplot(122)
plt.semilogy(vf, Random[:, 9], "C0-", label="Random")
plt.semilogy(vf, UD[:, 9], "C1-", label="UD")
plt.xlabel("Volume fraction")
plt.ylabel(r"$\alpha_{1}$")
plt.grid()
plt.legend()

plt.show()
../_images/a659edbf1bfc0fc355c071a281eb95af6d269b60a8a1ca2c5c34e47527ce20a4.png 
vf = np.linspace(0, 1, 100)
UD_MT = np.zeros((len(vf), 9))
UD_Balanced = np.zeros((len(vf), 9))
for i in range(len(vf)):
    fiber.vf = vf[i]
    UD_MT[i] = A2Eij(fiber.MoriTanaka())
    UD_Balanced[i] = A2Eij(fiber.Balanced())

plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.semilogy(vf, UD_MT[:, 0] / 1e3, "C0-", label="Mori-Tanaka")
plt.semilogy(vf, UD_Balanced[:, 0] / 1e3, "C1-", label="Balanced")
plt.xlabel("Volume fraction")
plt.ylabel("$E_1$ (GPa)")
plt.grid()
plt.legend()

plt.subplot(1, 2, 2)
plt.semilogy(vf, UD_MT[:, 1] / 1e3, "C0-", label="Mori-Tanaka")
plt.semilogy(vf, UD_Balanced[:, 1] / 1e3, "C1-", label="Balanced")
plt.xlabel("Volume fraction")
plt.ylabel("$E_2$ (GPa)")
plt.grid()
plt.legend()
plt.show()
../_images/877498c5cca4b6ef69d030ee456ca9b4629fb363b6c227404721ffb199976bf2.png
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