.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/umats/ELIST.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_ELIST.py>`
        to download the full example code.

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

.. _sphx_glr_examples_umats_ELIST.py:


Transversely Isotropic 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 12-50

In transversely isotropic elastic materials, there is a single axis of symmetry.
The material behaves isotropically in the plane perpendicular to this axis (the transverse plane).
Eight parameters are required:

1. The axis of symmetry (1, 2, or 3)
2. The longitudinal Young modulus :math:`E_L`
3. The transverse Young modulus :math:`E_T`
4. The Poisson ratio in the transverse-longitudinal plane :math:`\nu_{TL}`
5. The Poisson ratio in the transverse-transverse plane :math:`\nu_{TT}`
6. The shear modulus in the longitudinal-transverse plane :math:`G_{LT}`
7. The coefficient of thermal expansion in the longitudinal direction :math:`\alpha_L`
8. The coefficient of thermal expansion in the transverse direction :math:`\alpha_T`

The elastic stiffness tensor for a transversely isotropic material with axis 1 as the symmetry axis
is written in the Voigt notation formalism as:

.. math::

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

where :math:`G_{TT} = E_T / (2(1+\nu_{TT}))` is the shear modulus in the transverse plane.

The thermal expansion tensor is:

.. math::

   \boldsymbol{\alpha} = \begin{pmatrix}
       \alpha_L & 0 & 0 \\
       0 & \alpha_T & 0 \\
       0 & 0 & \alpha_T
   \end{pmatrix}

.. GENERATED FROM PYTHON SOURCE LINES 50-92

.. code-block:: Python


    umat_name = "ELIST"  # 5 character code for transversely isotropic elastic subroutine
    nstatev = 1  # Number of internal variables

    # Material parameters
    axis = 1  # Symmetry axis
    E_L = 4500.0  # Longitudinal Young's modulus (MPa)
    E_T = 2300.0  # Transverse Young's modulus (MPa)
    nu_TL = 0.05  # Poisson ratio (transverse-longitudinal)
    nu_TT = 0.3  # Poisson ratio (transverse-transverse)
    G_LT = 2700.0  # Shear modulus (longitudinal-transverse)
    alpha_L = 1.0e-5  # Thermal expansion (longitudinal)
    alpha_T = 2.5e-5  # Thermal expansion (transverse)

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

    props = np.array([axis, E_L, E_T, nu_TL, nu_TT, G_LT, alpha_L, alpha_T])

    path_data = "data"
    path_results = "results"
    pathfile = "ELIST_path.txt"
    outputfile = "results_ELIST.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 93-97

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

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

.. GENERATED FROM PYTHON SOURCE LINES 97-115

.. code-block:: Python


    outputfile_macro = os.path.join(path_results, "results_ELIST_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_ELIST_001.png
   :alt: ELIST
   :srcset: /examples/umats/images/sphx_glr_ELIST_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_ELIST.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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