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

.. only:: html

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

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

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

.. _sphx_glr_examples_umats_ELORT.py:


Orthotropic Elasticity Example
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 5-11

.. code-block:: Python


    import numpy as np
    from simcoon import simmit as sim
    import matplotlib.pyplot as plt
    import os








.. GENERATED FROM PYTHON SOURCE LINES 12-51

In orthotropic elastic materials, there are three mutually perpendicular planes of symmetry.
The material has different mechanical properties in each of the three directions.
Twelve parameters are required:

1. The Young modulus in direction 1: :math:`E_1`
2. The Young modulus in direction 2: :math:`E_2`
3. The Young modulus in direction 3: :math:`E_3`
4. The Poisson ratio :math:`\nu_{12}`
5. The Poisson ratio :math:`\nu_{13}`
6. The Poisson ratio :math:`\nu_{23}`
7. The shear modulus :math:`G_{12}`
8. The shear modulus :math:`G_{13}`
9. The shear modulus :math:`G_{23}`
10. The coefficient of thermal expansion :math:`\alpha_1`
11. The coefficient of thermal expansion :math:`\alpha_2`
12. The coefficient of thermal expansion :math:`\alpha_3`

The elastic stiffness tensor for an orthotropic material is written in the Voigt notation as:

.. math::

   \mathbf{L} = \begin{pmatrix}
       L_{11} & L_{12} & L_{13} & 0 & 0 & 0 \\
       L_{12} & L_{22} & L_{23} & 0 & 0 & 0 \\
       L_{13} & L_{23} & L_{33} & 0 & 0 & 0 \\
       0 & 0 & 0 & G_{23} & 0 & 0 \\
       0 & 0 & 0 & 0 & G_{13} & 0 \\
       0 & 0 & 0 & 0 & 0 & G_{12}
   \end{pmatrix}

The thermal expansion tensor is:

.. math::

   \boldsymbol{\alpha} = \begin{pmatrix}
       \alpha_1 & 0 & 0 \\
       0 & \alpha_2 & 0 \\
       0 & 0 & \alpha_3
   \end{pmatrix}

.. GENERATED FROM PYTHON SOURCE LINES 51-99

.. code-block:: Python


    umat_name = "ELORT"  # 5 character code for orthotropic elastic subroutine
    nstatev = 1  # Number of internal variables

    # Material parameters
    E_1 = 4500.0  # Young's modulus in direction 1 (MPa)
    E_2 = 2300.0  # Young's modulus in direction 2 (MPa)
    E_3 = 2700.0  # Young's modulus in direction 3 (MPa)
    nu_12 = 0.06  # Poisson ratio 12
    nu_13 = 0.08  # Poisson ratio 13
    nu_23 = 0.30  # Poisson ratio 23
    G_12 = 2200.0  # Shear modulus 12 (MPa)
    G_13 = 2100.0  # Shear modulus 13 (MPa)
    G_23 = 2400.0  # Shear modulus 23 (MPa)
    alpha_1 = 1.0e-5  # Thermal expansion in direction 1
    alpha_2 = 2.5e-5  # Thermal expansion in direction 2
    alpha_3 = 2.2e-5  # Thermal expansion in direction 3

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

    props = np.array(
        [E_1, E_2, E_3, nu_12, nu_13, nu_23, G_12, G_13, G_23, alpha_1, alpha_2, alpha_3]
    )

    path_data = "data"
    path_results = "results"
    pathfile = "ELORT_path.txt"
    outputfile = "results_ELORT.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 100-104

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

We plot the stress-strain curve in the loading direction (direction 1).

.. GENERATED FROM PYTHON SOURCE LINES 104-122

.. code-block:: Python


    outputfile_macro = os.path.join(path_results, "results_ELORT_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,
    )

    plt.grid(True)
    plt.xlabel(r"Strain $\varepsilon_{11}$")
    plt.ylabel(r"Stress $\sigma_{11}$ (MPa)")
    plt.plot(e11, s11, c="blue", label="Loading direction 1")
    plt.legend(loc="best")

    plt.show()



.. image-sg:: /examples/umats/images/sphx_glr_ELORT_001.png
   :alt: ELORT
   :srcset: /examples/umats/images/sphx_glr_ELORT_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.056 seconds)


.. _sphx_glr_download_examples_umats_ELORT.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: ELORT.ipynb <ELORT.ipynb>`

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

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

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

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


.. only:: html

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

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