.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/thermomechanical/ELISO.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_ELISO.py: Isotropic elasticity (thermomechanical) ======================================= .. GENERATED FROM PYTHON SOURCE LINES 5-13 .. code-block:: Python import numpy as np import simcoon as sim import matplotlib.pyplot as plt import os plt.rcParams["figure.figsize"] = (18, 10) .. GENERATED FROM PYTHON SOURCE LINES 14-52 In thermoelastic isotropic materials three mechanical parameters and two thermal parameters are required: 1. The density :math:`\rho` 2. The specific heat :math:`c_p` 3. The Young modulus :math:`E` 4. The Poisson ratio :math:`\nu` 5. The coefficient of thermal expansion :math:`\alpha` The elastic stiffness tensor is written in the Voigt notation formalism as .. math:: \mathbf{L} = \begin{pmatrix} L_{1111} & L_{1122} & L_{1122} & 0 & 0 & 0 \\ L_{1122} & L_{1111} & L_{1122} & 0 & 0 & 0 \\ L_{1122} & L_{1122} & L_{1111} & 0 & 0 & 0 \\ 0 & 0 & 0 & L_{1212} & 0 & 0 \\ 0 & 0 & 0 & 0 & L_{1212} & 0 \\ 0 & 0 & 0 & 0 & 0 & L_{1212} \end{pmatrix} with .. math:: L_{1111} = \frac{E(1-\nu)}{(1+\nu)(1-2\nu)}, \quad L_{1122} = \frac{E\nu}{(1+\nu)(1-2\nu)}, \quad L_{1212} = \frac{E}{2(1+\nu)}. The increment of the elastic strain is given by .. math:: \Delta\varepsilon^{\mathrm{el}}_{ij} = \Delta\varepsilon^{\mathrm{tot}}_{ij} - \alpha \Delta T \delta_{ij} In the thermomechanical framework, the thermal work terms :math:`W_t`, :math:`W_t^r` and :math:`W_t^{ir}` are also computed alongside the mechanical work terms. .. GENERATED FROM PYTHON SOURCE LINES 52-91 .. code-block:: Python umat_name = "ELISO" # 5 character code for the elastic-isotropic subroutine nstatev = 1 # Number of internal variables # Material parameters rho = 4.4 # Density c_p = 0.656 # Specific heat capacity E = 70000.0 # Young's modulus (MPa) nu = 0.2 # Poisson ratio alpha = 1.0e-5 # Thermal expansion coefficient psi_rve = 0.0 theta_rve = 0.0 phi_rve = 0.0 solver_type = 0 corate_type = 2 props = np.array([rho, c_p, E, nu, alpha]) path_data = "../data" path_results = "results" pathfile = "THERM_ELISO_path.txt" outputfile = "results_THERM_ELISO.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 92-97 Plotting the results ---------------------- We plot the stress-strain curve, the temperature evolution, the mechanical work terms and the thermal work terms. .. GENERATED FROM PYTHON SOURCE LINES 97-155 .. code-block:: Python outputfile_macro = os.path.join(path_results, "results_THERM_ELISO_global-0.txt") fig = plt.figure() # 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_ELISO_001.png :alt: ELISO :srcset: /examples/thermomechanical/images/sphx_glr_ELISO_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.221 seconds) .. _sphx_glr_download_examples_thermomechanical_ELISO.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: ELISO.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: ELISO.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: ELISO.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_