.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/mechanical/ZENER.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_mechanical_ZENER.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_mechanical_ZENER.py:


Zener viscoelastic model
=========================

.. 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 14-31

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).

Seven parameters are required:

1. The thermoelastic Young's modulus :math:`E_0`
2. The thermoelastic Poisson's ratio :math:`\nu_0`
3. The coefficient of thermal expansion :math:`\alpha`
4. The viscoelastic Young's modulus of the Zener branch :math:`E_1`
5. The viscoelastic Poisson's ratio of the Zener branch :math:`\nu_1`
6. The bulk viscosity of the Zener branch :math:`\eta_B`
7. 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.

.. GENERATED FROM PYTHON SOURCE LINES 31-72

.. code-block:: Python


    umat_name = "ZENER"  # 5 character code for the Zener model
    nstatev = 8  # Number of internal variables

    # Material parameters
    E_0 = 3000.0  # Thermoelastic Young's modulus (MPa)
    nu_0 = 0.4  # Thermoelastic Poisson's ratio
    alpha = 0.0  # Thermal expansion coefficient
    E_1 = 100.0  # Viscoelastic Young's modulus (MPa)
    nu_1 = 0.3  # Viscoelastic Poisson's ratio
    eta_S = 4000.0  # Shear viscosity
    eta_B = eta_S / 4.0  # Bulk viscosity

    psi_rve = 0.0
    theta_rve = 0.0
    phi_rve = 0.0
    solver_type = 0
    corate_type = 1

    props = np.array([E_0, nu_0, alpha, E_1, nu_1, eta_B, eta_S])

    path_data = "../data"
    path_results = "results"
    pathfile = "ZENER_path.txt"
    outputfile = "results_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 73-78

Plotting the results
----------------------

We plot the stress-strain response which exhibits the characteristic
rate-dependent behavior of the Zener viscoelastic model.

.. GENERATED FROM PYTHON SOURCE LINES 78-115

.. code-block:: Python


    outputfile_macro = os.path.join(path_results, "results_ZENER_global-0.txt")

    fig = plt.figure()

    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_out, r = np.loadtxt(outputfile_macro, usecols=(4, 5, 6, 7), unpack=True)
    Wm, Wm_r, Wm_ir, Wm_d = np.loadtxt(
        outputfile_macro, usecols=(20, 21, 22, 23), unpack=True
    )

    # First subplot: Stress vs Strain
    ax1 = fig.add_subplot(1, 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="blue", label="Zener model")
    plt.legend(loc="best")

    # Second subplot: Work terms vs Time
    ax2 = fig.add_subplot(1, 2, 2)
    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")

    plt.show()



.. image-sg:: /examples/mechanical/images/sphx_glr_ZENER_001.png
   :alt: ZENER
   :srcset: /examples/mechanical/images/sphx_glr_ZENER_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.273 seconds)


.. _sphx_glr_download_examples_mechanical_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 <ZENER.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: ZENER.py <ZENER.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: ZENER.zip <ZENER.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_