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

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

.. _sphx_glr_examples_umats_ELISO.py:


Isotropic elasticity examples
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. 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 12-92

In thermoelastic isotropic materials three parameters are required:

1. The Young modulus :math:`E`,
2. The Poisson ratio :math:`\nu`,
3. The coefficient of thermal expansion :math:`\alpha`.

The elastic stiffness tensor and the thermal expansion coefficients tensor are 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},
   \quad
   \boldsymbol{\alpha} = \begin{pmatrix}
       \alpha & 0 & 0 \\
       0 & \alpha & 0 \\
       0 & 0 & \alpha
   \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 tangent stiffness tensor in this case is :math:`\mathbf{L}^t = \mathbf{L}`.
Moreover, 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},

where :math:`\delta_{ij}` implies the Kronecker delta operator.
In the 1D case only one component of stress is computed, through the relation

.. math::

   \sigma^{\mathrm{fin}}_{11} = \sigma^{\mathrm{init}}_{11} + E \Delta\varepsilon^{\mathrm{el}}_{11}.

In the plane stress case only three components of stress are computed, through the relations

.. math::

   \begin{pmatrix}
       \sigma^{\mathrm{fin}}_{11} \\
       \sigma^{\mathrm{fin}}_{22} \\
       \sigma^{\mathrm{fin}}_{12}
   \end{pmatrix}
   =
   \begin{pmatrix}
       \sigma^{\mathrm{init}}_{11} \\
       \sigma^{\mathrm{init}}_{22} \\
       \sigma^{\mathrm{init}}_{12}
   \end{pmatrix}
   +
   \frac{E}{1-\nu^2}
   \begin{pmatrix}
       1 & \nu & 0 \\
       \nu & 1 & 0 \\
       0 & 0 & \frac{1-\nu}{2}
   \end{pmatrix}
   \begin{pmatrix}
       \Delta\varepsilon^{\mathrm{el}}_{11} \\
       \Delta\varepsilon^{\mathrm{el}}_{22} \\
       2\Delta\varepsilon^{\mathrm{el}}_{12}
   \end{pmatrix}

In the generalized plane strain/3D analysis case the stress tensor is computed through the relation

.. math::

   \sigma^{\mathrm{fin}}_{ij} = \sigma^{\mathrm{init}}_{ij} + L_{ijkl}~\Delta\varepsilon^{\mathrm{el}}_{kl}.

.. GENERATED FROM PYTHON SOURCE LINES 92-146

.. code-block:: Python



    umat_name = "ELISO"  # This is the 5 character code for the elastic-isotropic subroutine
    nstatev = 1  # The number of scalar variables required, only the initial temperature is stored here

    E = 700000.0
    nu = 0.2
    alpha = 1.0e-5

    psi_rve = 0.0
    theta_rve = 0.0
    phi_rve = 0.0
    solver_type = 0
    corate_type = 2

    props = np.array([E, nu, alpha])

    path_data = "data"
    path_results = "results"
    pathfile = "ELISO_path.txt"
    outputfile = "results_ELISO.txt"

    sim.solver(
        umat_name,
        props,
        nstatev,
        psi_rve,
        theta_rve,
        phi_rve,
        solver_type,
        corate_type,
        path_data,
        path_results,
        pathfile,
        outputfile,
    )

    outputfile_macro = os.path.join(path_results, "results_ELISO_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.plot(e11, s11, c="blue")
    plt.xlabel("Strain")
    plt.ylabel("Stress (MPa)")

    plt.show()



.. image-sg:: /examples/umats/images/sphx_glr_ELISO_001.png
   :alt: ELISO
   :srcset: /examples/umats/images/sphx_glr_ELISO_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.052 seconds)


.. _sphx_glr_download_examples_umats_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 <ELISO.ipynb>`

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

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

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

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


.. only:: html

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

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