.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/heterogeneous/effective_props.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_heterogeneous_effective_props.py: Micromechanics Examples ~~~~~~~~~~~~~~~~~~~~~~~ This example studies the evolution of the mechanical properties of a composite material considering spherical reinforcement. .. GENERATED FROM PYTHON SOURCE LINES 8-15 .. code-block:: Python import numpy as np import matplotlib.pyplot as plt from simcoon import simmit as sim from simcoon import parameter as par import os .. GENERATED FROM PYTHON SOURCE LINES 16-22 In this example we study the evolution of the mechanical properties of a 2-phase composite material considering spherical reinforcement. Two micromechanical schemes are utilized: Mori-Tanaka and Self-consistent. First we define the number of state variables (if any) at the macroscopic level and the material properties. .. GENERATED FROM PYTHON SOURCE LINES 22-34 .. code-block:: Python dir = os.path.dirname(os.path.realpath("__file__")) nstatev = 0 nphases = 2 # The number of phases num_file = 0 # The num of the file that contains the subphases int1 = 50 int2 = 50 n_matrix = 0 props = np.array([nphases, num_file, int1, int2, n_matrix], dtype="float") .. GENERATED FROM PYTHON SOURCE LINES 35-43 There is a possibility to consider a misorientation between the test frame of reference and the composite material orientation, using Euler angles with the zā€“xā€“z convention. The stiffness tensor will be returned in the test frame of reference. We also specify which micromechanical scheme will be used: - ``MIMTN`` ā†’ Mori-Tanaka scheme - ``MISCN`` ā†’ Self-consistent scheme .. GENERATED FROM PYTHON SOURCE LINES 43-53 .. code-block:: Python path_data = dir + "/data" path_keys = dir + "/keys" param_list = par.read_parameters() psi_rve = 0.0 theta_rve = 0.0 phi_rve = 0.0 .. GENERATED FROM PYTHON SOURCE LINES 54-56 Run the simulation to obtain the effective isotropic elastic properties for different volume fractions of reinforcement up to 50%. .. GENERATED FROM PYTHON SOURCE LINES 56-87 .. code-block:: Python concentration = np.arange(0.0, 0.51, 0.01) E_MT = np.zeros(len(concentration)) umat_name = "MIMTN" for i, x in enumerate(concentration): param_list[1].value = x param_list[0].value = 1.0 - x par.copy_parameters(param_list, path_keys, path_data) par.apply_parameters(param_list, path_data) L = sim.L_eff(umat_name, props, nstatev, psi_rve, theta_rve, phi_rve) p = sim.L_iso_props(L).flatten() E_MT[i] = p[0] E_SC = np.zeros(len(concentration)) umat_name = "MISCN" for i, x in enumerate(concentration): param_list[1].value = x param_list[0].value = 1.0 - x par.copy_parameters(param_list, path_keys, path_data) par.apply_parameters(param_list, path_data) L = sim.L_eff(umat_name, props, nstatev, psi_rve, theta_rve, phi_rve) p = sim.L_iso_props(L).flatten() E_SC[i] = p[0] .. GENERATED FROM PYTHON SOURCE LINES 88-93 Plotting the results -------------------- In blue, we plot the effective Young's modulus vs volume fraction curve using the Mori-Tanaka scheme, in red using the Self-Consistent scheme, and with black crosses the experimental data from (Wang 2003). .. GENERATED FROM PYTHON SOURCE LINES 93-114 .. code-block:: Python fig = plt.figure() plt.xlabel(r"Volume fraction (c)", size=15) plt.ylabel(r"Effective Young's modulus ($E$, MPa)", size=15) plt.plot(concentration, E_MT, c="blue", label="Mori-Tanaka") plt.plot(concentration, E_SC, c="red", label="Self-Consistent") expfile = path_data + "/" + "E_exp.txt" c, E = np.loadtxt(expfile, usecols=(0, 1), unpack=True) plt.plot( c, E, linestyle="None", marker="x", color="black", markersize=10, label="Exp. (Wang 2003)", ) plt.legend() plt.tight_layout() plt.show() .. image-sg:: /examples/heterogeneous/images/sphx_glr_effective_props_001.png :alt: effective props :srcset: /examples/heterogeneous/images/sphx_glr_effective_props_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 115-126 Effect of Aspect Ratio on Effective Stiffness --------------------------------------------- The shape of the reinforcement significantly affects the effective properties. Let's study how the aspect ratio of prolate (fiber-like) and oblate (disc-like) inclusions influences the effective Young's modulus using the Mori-Tanaka scheme. The aspect ratio is defined as :math:`ar = a_1/a_3`, where: - :math:`ar > 1`: prolate ellipsoid (fiber-like) - :math:`ar = 1`: sphere - :math:`ar < 1`: oblate ellipsoid (disc-like) .. GENERATED FROM PYTHON SOURCE LINES 126-173 .. code-block:: Python # Fixed volume fraction of 20% c_reinf = 0.20 param_list[1].value = c_reinf param_list[0].value = 1.0 - c_reinf par.copy_parameters(param_list, path_keys, path_data) par.apply_parameters(param_list, path_data) # Aspect ratios from oblate (0.1) to prolate (10) aspect_ratios = np.logspace(-1, 1, 50) E_eff_ar = np.zeros(len(aspect_ratios)) umat_name = "MIMTN" # Save original phase file phase_file = path_data + "/Nellipsoids0.dat" with open(phase_file, "r") as f: original_content = f.read() print(f"\nComputing effective properties for c={c_reinf * 100:.0f}% reinforcement...") for i, ar in enumerate(aspect_ratios): # Read and modify the phase file to set the aspect ratio with open(phase_file, "r") as f: lines = f.readlines() # Update semi-axes in reinforcement phase (line 2): a1/a3 = ar, a2 = a3 = 1 parts = lines[2].split() parts[8] = str(ar) # a1 parts[9] = "1" # a2 parts[10] = "1" # a3 lines[2] = "\t".join(parts) + "\n" with open(phase_file, "w") as f: f.writelines(lines) L = sim.L_eff(umat_name, props, nstatev, psi_rve, theta_rve, phi_rve) p = sim.L_iso_props(L).flatten() E_eff_ar[i] = p[0] # Restore original phase file with open(phase_file, "w") as f: f.write(original_content) # Get reference value for spherical inclusion (ar=1) idx_sphere = np.argmin(np.abs(aspect_ratios - 1.0)) E_sphere_ref = E_eff_ar[idx_sphere] .. rst-class:: sphx-glr-script-out .. code-block:: none Computing effective properties for c=20% reinforcement... .. GENERATED FROM PYTHON SOURCE LINES 174-179 Plot: Effective Young's modulus vs aspect ratio ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This plot shows how inclusion shape dramatically affects composite stiffness. Prolate (fiber-like) inclusions are more effective at reinforcing the composite than oblate (disc-like) inclusions at the same volume fraction. .. GENERATED FROM PYTHON SOURCE LINES 179-209 .. code-block:: Python fig, ax = plt.subplots(figsize=(10, 6)) ax.semilogx(aspect_ratios, E_eff_ar / 1000, "b-", linewidth=2, label="Mori-Tanaka") ax.axvline(x=1, color="k", linestyle=":", alpha=0.5, label="Sphere (ar=1)") ax.axhline( y=E_sphere_ref / 1000, color="r", linestyle="--", alpha=0.7, label=f"Sphere ref (E={E_sphere_ref / 1000:.1f} GPa)", ) # Add shaded regions for oblate/prolate ymin, ymax = ax.get_ylim() ax.axvspan(0.1, 1, alpha=0.1, color="orange") ax.axvspan(1, 10, alpha=0.1, color="green") ax.text(0.2, ymax - 0.1 * (ymax - ymin), "Oblate\n(disc-like)", fontsize=9, ha="center") ax.text(5, ymax - 0.1 * (ymax - ymin), "Prolate\n(fiber-like)", fontsize=9, ha="center") ax.set_xlabel("Aspect ratio $a_1/a_3$", fontsize=12) ax.set_ylabel("Effective Young's modulus $E_{eff}$ (GPa)", fontsize=12) ax.set_title( f"Effect of inclusion shape on composite stiffness (c={c_reinf * 100:.0f}%, Mori-Tanaka)", fontsize=14, ) ax.legend(fontsize=10, loc="lower right") ax.grid(True, alpha=0.3) ax.set_xlim([0.1, 10]) plt.tight_layout() plt.show() .. image-sg:: /examples/heterogeneous/images/sphx_glr_effective_props_002.png :alt: Effect of inclusion shape on composite stiffness (c=20%, Mori-Tanaka) :srcset: /examples/heterogeneous/images/sphx_glr_effective_props_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.229 seconds) .. _sphx_glr_download_examples_heterogeneous_effective_props.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: effective_props.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: effective_props.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: effective_props.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_