Two-step Hashin-Shtrikman interpolated twice

[1]:

import numpy as np
import mechmean
import mechkit
from mechmean.example_input import inp

[2]:

np.set_printoptions(linewidth=140)

[3]:

# Define isotropic constituents
inclusion = mechkit.material.Isotropic(E=inp["E_f"], nu=inp["nu_f"])
matrix = mechkit.material.Isotropic(E=inp["E_m"], nu=inp["nu_m"])

[4]:

# Define orientation averager and polairzation
averager = mechmean.orientation_averager.AdvaniTucker(N4=inp["N4"])
P_func = mechmean.hill_polarization.Factory().needle

[5]:

# Homogenize
input_dict = {
    "phases": {
        "inclusion": {
            "material": inclusion,
            "volume_fraction": inp["c_f"],
        },
        "matrix": {
            "material": matrix,
            "volume_fraction": 1.0 - inp["c_f"],
        },
    },
    "k1": 1.0 / 2.0,
    "k2": 1.0 / 2.0,
    "averaging_func": averager.average,
}
hashin = mechmean.approximation.HSW2StepInterpolatedReferenceMaterial(**input_dict)
C_eff = hashin.calc_C_eff()

[6]:

print("Effective stiffness Hashin Shtrikman two step with two interpolations")
print(C_eff)

Effective stiffness Hashin Shtrikman two step with two interpolations
[[ 1.63102824e+01  6.58025250e+00  5.92268990e+00 -1.30273244e-02 -1.54212831e-01  3.41663919e-01]
 [ 6.58025250e+00  1.47855403e+01  5.97255588e+00 -1.76997935e-02 -2.17124072e-02  3.06640385e-01]
 [ 5.92268990e+00  5.97255588e+00  1.22565235e+01 -1.95743285e-04 -4.24225377e-02 -2.81542424e-02]
 [-1.30273244e-02 -1.76997935e-02 -1.95743285e-04  6.86934068e+00  9.09581576e-02 -8.37665265e-02]
 [-1.54212831e-01 -2.17124072e-02 -4.24225377e-02  9.09581576e-02  7.21591508e+00 -2.59557689e-02]
 [ 3.41663919e-01  3.06640385e-01 -2.81542424e-02 -8.37665265e-02 -2.59557689e-02  9.71821602e+00]]