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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_Poisson_sections.py:


===========================================================
Plot Poisson ratio as 2D sections
===========================================================

This example shows how to plot the directional dependence of the Poisson ratio in XY, XZ and YZ planes.

.. GENERATED FROM PYTHON SOURCE LINES 9-14

Define the stiffness tensor for NiTi
-------------------------------------

We define the stiffness tensor for a monoclinic NiTi material using its elastic constants. They are taken from the
`Materials Project (mp-1048) <https://github.com/DorianDepriester/Elasticipy>`_.

.. GENERATED FROM PYTHON SOURCE LINES 14-24

.. code-block:: Python

    from elasticipy.tensors.elasticity import StiffnessTensor
    C = StiffnessTensor.monoclinic(
        phase_name='TiNi',
        C11=231, C12=127, C13=104,
        C22=240, C23=131, C33=175,
        C44=81, C55=11, C66=85,
        C15=-18, C25=1, C35=-3, C46=3
    )
    print("Stiffness tensor for NiTi:\n", C)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Stiffness tensor for NiTi:
     Stiffness tensor (in Voigt mapping):
    [[231. 127. 104.   0. -18.   0.]
     [127. 240. 131.   0.   1.   0.]
     [104. 131. 175.   0.  -3.   0.]
     [  0.   0.   0.  81.   0.   3.]
     [-18.   1.  -3.   0.  11.   0.]
     [  0.   0.   0.   3.   0.  85.]]
    Phase: TiNi




.. GENERATED FROM PYTHON SOURCE LINES 25-27

Get the Poisson ratio from the stiffness tensor
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 27-31

.. code-block:: Python

    nu = C.Poisson_ratio
    print("Poisson ratio:")
    print(nu)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Poisson ratio:
    Hyperspherical function
    Min=-0.550188605619326, Max=1.4394343811864985




.. GENERATED FROM PYTHON SOURCE LINES 32-34

Plot it as polar curves in planar sections
------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 34-37

.. code-block:: Python

    fig, ax = nu.plot_xyz_sections()





.. image-sg:: /auto_examples/images/sphx_glr_Poisson_sections_001.png
   :alt: X-Y plane, X-Z plane, Y-Z plane
   :srcset: /auto_examples/images/sphx_glr_Poisson_sections_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.776 seconds)


.. _sphx_glr_download_auto_examples_Poisson_sections.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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