Two-step Hashin-Shtrikman interpolated once

[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"],
        },
    },
    "k": 1.0 / 2.0,
    "averaging_func": averager.average,
}
hashin = mechmean.approximation.Kehrer2019(**input_dict)
C_eff = hashin.calc_C_eff()

[6]:

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

Effective stiffness two step Hashin Shtrikman
Effective_stiffness(upper=array([[ 1.79306622e+01,  6.79183199e+00,  6.44049100e+00, -7.92491438e-03, -1.22458610e-01,  2.79693636e-01],
       [ 6.79183199e+00,  1.66571351e+01,  6.50198561e+00, -1.44257800e-02, -9.10987462e-03,  2.56586798e-01],
       [ 6.44049100e+00,  6.50198561e+00,  1.43808190e+01, -2.85337268e-03, -4.82239343e-02, -3.03802346e-02],
       [-7.92491438e-03, -1.44257800e-02, -2.85337268e-03,  8.56565464e+00,  1.06716825e-01, -7.33643806e-02],
       [-1.22458610e-01, -9.10987462e-03, -4.82239343e-02,  1.06716825e-01,  8.95472773e+00, -1.95087657e-02],
       [ 2.79693636e-01,  2.56586798e-01, -3.03802346e-02, -7.33643806e-02, -1.95087657e-02,  1.09913269e+01]]), lower=array([[ 1.31958542e+01,  6.53652351e+00,  5.06275498e+00, -2.56586400e-02, -2.11023481e-01,  4.35412759e-01],
       [ 6.53652351e+00,  1.13419501e+01,  5.07695238e+00, -2.30964777e-02, -5.61794756e-02,  3.73083046e-01],
       [ 5.06275498e+00,  5.07695238e+00,  8.76711885e+00,  8.96494982e-03, -8.82286689e-03, -1.95238689e-02],
       [-2.56586400e-02, -2.30964777e-02,  8.96494982e-03,  3.73696055e+00,  1.40581209e-02, -9.26497992e-02],
       [-2.11023481e-01, -5.61794756e-02, -8.82286689e-03,  1.40581209e-02,  3.84729163e+00, -3.93273718e-02],
       [ 4.35412759e-01,  3.73083046e-01, -1.95238689e-02, -9.26497992e-02, -3.93273718e-02,  7.12215158e+00]]))