.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/thermomechanical/ZENER.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_thermomechanical_ZENER.py: Zener viscoelastic model (thermomechanical) ============================================= .. GENERATED FROM PYTHON SOURCE LINES 5-13 .. code-block:: Python import numpy as np import matplotlib.pyplot as plt import simcoon as sim import os plt.rcParams["figure.figsize"] = (18, 10) .. GENERATED FROM PYTHON SOURCE LINES 14-35 The Poynting-Thomson (Zener) constitutive law is a rate-dependent, isotropic, linear viscoelastic model that accounts for thermal strains. It consists of an elastic spring in parallel with a Maxwell element (spring + dashpot in series). Nine parameters are required for the thermomechanical version: 1. The density :math:`\rho` 2. The specific heat :math:`c_p` 3. The thermoelastic Young's modulus :math:`E_0` 4. The thermoelastic Poisson's ratio :math:`\nu_0` 5. The coefficient of thermal expansion :math:`\alpha` 6. The viscoelastic Young's modulus of the Zener branch :math:`E_1` 7. The viscoelastic Poisson's ratio of the Zener branch :math:`\nu_1` 8. The bulk viscosity of the Zener branch :math:`\eta_B` 9. The shear viscosity of the Zener branch :math:`\eta_S` The viscoelastic material constitutive law is implemented using a *fast scalar updating method*. The updated stress is provided for 1D, plane stress, and generalized plane strain/3D analysis. The updated work terms and internal heat production :math:`r` are determined with the thermomechanical algorithm. .. GENERATED FROM PYTHON SOURCE LINES 35-81 .. code-block:: Python umat_name = "ZENER" # 5 character code for the Zener model nstatev = 8 # Number of internal variables # Material parameters rho = 4.4 # Density c_p = 0.656 # Specific heat capacity E_0 = 3000.0 # Thermoelastic Young's modulus (MPa) nu_0 = 0.4 # Thermoelastic Poisson's ratio alpha = 0.86e-5 # Thermal expansion coefficient E_1 = 1200.0 # Viscoelastic Young's modulus (MPa) nu_1 = 0.3 # Viscoelastic Poisson's ratio eta_B = 12500.0 # Bulk viscosity eta_S = 400.0 # Shear viscosity psi_rve = 0.0 theta_rve = 0.0 phi_rve = 0.0 solver_type = 0 corate_type = 0 # Define the properties props = np.array([rho, c_p, E_0, nu_0, alpha, E_1, nu_1, eta_B, eta_S]) path_data = "../data" path_results = "results" # Run the simulation pathfile = "THERM_ZENER_path.txt" outputfile = "results_THERM_ZENER.txt" sim.solver( umat_name, props, nstatev, psi_rve, theta_rve, phi_rve, solver_type, corate_type, path_data, path_results, pathfile, outputfile, ) .. GENERATED FROM PYTHON SOURCE LINES 82-87 Plotting the results ---------------------- We plot the stress-strain response, the temperature evolution, the mechanical work terms and the thermal work terms. .. GENERATED FROM PYTHON SOURCE LINES 87-145 .. code-block:: Python fig = plt.figure() outputfile_macro = os.path.join(path_results, "results_THERM_ZENER_global-0.txt") # Get the data e11, e22, e33, e12, e13, e23, s11, s22, s33, s12, s13, s23 = np.loadtxt( outputfile_macro, usecols=(8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19), unpack=True, ) time, T, Q, r = np.loadtxt(outputfile_macro, usecols=(4, 5, 6, 7), unpack=True) Wm, Wm_r, Wm_ir, Wm_d, Wt, Wt_r, Wt_ir = np.loadtxt( outputfile_macro, usecols=(20, 21, 22, 23, 24, 25, 26), unpack=True ) # Stress vs Strain ax = fig.add_subplot(2, 2, 1) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel(r"Strain $\varepsilon_{11}$", size=15) plt.ylabel(r"Stress $\sigma_{11}$ (MPa)", size=15) plt.plot(e11, s11, c="black", label="direction 1") plt.legend(loc="best") # Temperature vs Time ax = fig.add_subplot(2, 2, 2) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"Temperature $\theta$ (K)", size=15) plt.plot(time, T, c="black", label="temperature") plt.legend(loc="best") # Mechanical work vs Time ax = fig.add_subplot(2, 2, 3) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"$W_m$", size=15) plt.plot(time, Wm, c="black", label=r"$W_m$") plt.plot(time, Wm_r, c="green", label=r"$W_m^r$") plt.plot(time, Wm_ir, c="blue", label=r"$W_m^{ir}$") plt.plot(time, Wm_d, c="red", label=r"$W_m^d$") plt.legend(loc="best") # Thermal work vs Time ax = fig.add_subplot(2, 2, 4) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"$W_t$", size=15) plt.plot(time, Wt, c="black", label=r"$W_t$") plt.plot(time, Wt_r, c="green", label=r"$W_t^r$") plt.plot(time, Wt_ir, c="blue", label=r"$W_t^{ir}$") plt.legend(loc="best") plt.show() .. image-sg:: /examples/thermomechanical/images/sphx_glr_ZENER_001.png :alt: ZENER :srcset: /examples/thermomechanical/images/sphx_glr_ZENER_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 146-150 Increment size effect ----------------------- Here we test the effect of the increment size on the results. .. GENERATED FROM PYTHON SOURCE LINES 150-192 .. code-block:: Python increments = [1, 10, 100, 1000] outputfile_globals = {} for inc in increments: pathfile = f"THERM_ZENER_path_{inc}.txt" outputfile = f"results_THERM_ZENER_{inc}.txt" sim.solver( umat_name, props, nstatev, psi_rve, theta_rve, phi_rve, solver_type, corate_type, path_data, path_results, pathfile, outputfile, ) outputfile_globals[inc] = f"results_THERM_ZENER_{inc}_global-0.txt" # Load data for each increment data = [] for inc in increments: path = os.path.join(path_results, outputfile_globals[inc]) e11, e22, e33, e12, e13, e23, s11, s22, s33, s12, s13, s23 = np.loadtxt( path, usecols=range(8, 20), unpack=True ) time, T, Q, r = np.loadtxt(path, usecols=range(4, 8), unpack=True) Wm, Wm_r, Wm_ir, Wm_d, Wt, Wt_r, Wt_ir = np.loadtxt( path, usecols=range(20, 27), unpack=True ) data.append( { "e11": e11, "s11": s11, "time": time, "T": T, "Wm": Wm, "Wm_r": Wm_r, "Wm_ir": Wm_ir, "Wm_d": Wm_d, "Wt": Wt, "Wt_r": Wt_r, "Wt_ir": Wt_ir, } ) .. GENERATED FROM PYTHON SOURCE LINES 193-195 Plotting the increment size comparison ----------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 195-266 .. code-block:: Python fig = plt.figure() markers = ["D", "o", "x", None] labels = ["1 increment", "10 increments", "100 increments", "1000 increments"] # Stress vs Strain ax = fig.add_subplot(2, 2, 1) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel(r"Strain $\varepsilon_{11}$", size=15) plt.ylabel(r"Stress $\sigma_{11}$ (MPa)", size=15) for i, d in enumerate(data): if markers[i] is not None: plt.plot(d["e11"], d["s11"], linestyle="None", marker=markers[i], color="black", markersize=10, label=labels[i]) else: plt.plot(d["e11"], d["s11"], c="black", label=labels[i]) plt.legend(loc="best") # Temperature vs Time ax = fig.add_subplot(2, 2, 2) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"Temperature $\theta$ (K)", size=15) for i, d in enumerate(data): if markers[i] is not None: plt.plot(d["time"], d["T"], linestyle="None", marker=markers[i], color="black", markersize=10, label=labels[i]) else: plt.plot(d["time"], d["T"], c="black", label=labels[i]) plt.legend(loc="best") # Mechanical work vs Time ax = fig.add_subplot(2, 2, 3) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"$W_m$", size=15) work_colors = ["black", "green", "blue", "red"] work_keys = ["Wm", "Wm_r", "Wm_ir", "Wm_d"] work_labels = [r"$W_m$", r"$W_m^r$", r"$W_m^{ir}$", r"$W_m^d$"] for i, d in enumerate(data): for j, (wk, wc, wl) in enumerate(zip(work_keys, work_colors, work_labels)): if markers[i] is not None: plt.plot(d["time"], d[wk], linestyle="None", marker=markers[i], color=wc, markersize=10) else: plt.plot(d["time"], d[wk], c=wc, label=wl) plt.legend(loc="best") # Thermal work vs Time ax = fig.add_subplot(2, 2, 4) plt.grid(True) plt.tick_params(axis="both", which="major", labelsize=15) plt.xlabel("time (s)", size=15) plt.ylabel(r"$W_t$", size=15) therm_keys = ["Wt", "Wt_r", "Wt_ir"] therm_labels = [r"$W_t$", r"$W_t^r$", r"$W_t^{ir}$"] therm_colors = ["black", "green", "blue"] for i, d in enumerate(data): for j, (wk, wc, wl) in enumerate(zip(therm_keys, therm_colors, therm_labels)): if markers[i] is not None: plt.plot(d["time"], d[wk], linestyle="None", marker=markers[i], color=wc, markersize=10) else: plt.plot(d["time"], d[wk], c=wc, label=wl) plt.legend(loc="best") plt.show() .. image-sg:: /examples/thermomechanical/images/sphx_glr_ZENER_002.png :alt: ZENER :srcset: /examples/thermomechanical/images/sphx_glr_ZENER_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.133 seconds) .. _sphx_glr_download_examples_thermomechanical_ZENER.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: ZENER.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: ZENER.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: ZENER.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_