.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/elements/solid186/example_solid186.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_gallery_elements_solid186_example_solid186.py>`
        to download the full example code.

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

.. _sphx_glr_gallery_elements_solid186_example_solid186.py:


.. _ref_solid186_example:

HEX20 — uniaxial tension on a 20-node hex
============================================

Single HEX20 brick (a unit cube, 20 nodes including the mid-edge
nodes of the serendipity family) loaded in uniaxial tension.  The
consistent-load vector for a serendipity 8-node face has corner weight
:math:`-1/12` and mid-edge weight :math:`+1/3`; applying these produces
a uniform σxx field, so ``εxx = σ/E`` and ``εyy = εzz = −ν·εxx``
exactly at every node.

.. GENERATED FROM PYTHON SOURCE LINES 14-24

.. code-block:: Python


    from __future__ import annotations

    import numpy as np
    import pyvista as pv
    from vtkmodules.util.vtkConstants import VTK_QUADRATIC_HEXAHEDRON

    import femorph_solver
    from femorph_solver import ELEMENTS








.. GENERATED FROM PYTHON SOURCE LINES 25-29

Reference 20-node unit cube
---------------------------
Corners 1-8 in VTK_QUADRATIC_HEXAHEDRON order, then mid-edge nodes 9-20 on the
bottom, top, and vertical edges.

.. GENERATED FROM PYTHON SOURCE LINES 29-59

.. code-block:: Python

    E = 2.1e11  # Pa
    NU = 0.30
    F_TOTAL = 4.2e4  # N

    coords = np.array(
        [
            [0.0, 0.0, 0.0],
            [1.0, 0.0, 0.0],
            [1.0, 1.0, 0.0],
            [0.0, 1.0, 0.0],
            [0.0, 0.0, 1.0],
            [1.0, 0.0, 1.0],
            [1.0, 1.0, 1.0],
            [0.0, 1.0, 1.0],
            [0.5, 0.0, 0.0],
            [1.0, 0.5, 0.0],
            [0.5, 1.0, 0.0],
            [0.0, 0.5, 0.0],
            [0.5, 0.0, 1.0],
            [1.0, 0.5, 1.0],
            [0.5, 1.0, 1.0],
            [0.0, 0.5, 1.0],
            [0.0, 0.0, 0.5],
            [1.0, 0.0, 0.5],
            [1.0, 1.0, 0.5],
            [0.0, 1.0, 0.5],
        ],
        dtype=np.float64,
    )








.. GENERATED FROM PYTHON SOURCE LINES 60-62

Build the model
---------------

.. GENERATED FROM PYTHON SOURCE LINES 62-87

.. code-block:: Python

    cells = np.concatenate([[20], np.arange(20, dtype=np.int64)])
    cell_types = np.array([VTK_QUADRATIC_HEXAHEDRON], dtype=np.uint8)
    grid = pv.UnstructuredGrid(cells, cell_types, coords)

    m = femorph_solver.Model.from_grid(grid)
    m.assign(ELEMENTS.HEX20, material={"EX": E, "PRXY": NU})

    # Symmetry BC: x=0 face UX, y=0 face UY, z=0 face UZ.
    x0 = [1, 4, 5, 8, 12, 16, 17, 20]
    y0 = [1, 2, 5, 6, 9, 13, 17, 18]
    z0 = [1, 2, 3, 4, 9, 10, 11, 12]
    for nn in x0:
        m.fix(nodes=[nn], dof="UX", value=0.0)
    for nn in y0:
        m.fix(nodes=[nn], dof="UY", value=0.0)
    for nn in z0:
        m.fix(nodes=[nn], dof="UZ", value=0.0)

    # Consistent-load on x=1 face: 4 corners × −F/12 + 4 mid-edges × +F/3
    # (integrates to F_TOTAL exactly for a uniform traction).
    for nn in (2, 3, 6, 7):
        m.apply_force(nn, fx=-F_TOTAL / 12.0)
    for nn in (10, 14, 18, 19):
        m.apply_force(nn, fx=F_TOTAL / 3.0)








.. GENERATED FROM PYTHON SOURCE LINES 88-90

Static solve and strain recovery
--------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 90-98

.. code-block:: Python

    res = m.solve()
    eps = m.eel(res.displacement)

    eps_xx_expected = F_TOTAL / E
    eps_yy_expected = -NU * eps_xx_expected
    print(f"εxx expected = {eps_xx_expected:.3e}  |  recovered (mean) = {eps[:, 0].mean():.3e}")
    print(f"εyy expected = {eps_yy_expected:.3e}  |  recovered (mean) = {eps[:, 1].mean():.3e}")





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

 .. code-block:: none

    εxx expected = 2.000e-07  |  recovered (mean) = 2.000e-07
    εyy expected = -6.000e-08  |  recovered (mean) = -6.000e-08




.. GENERATED FROM PYTHON SOURCE LINES 99-101

Plot the deformed cube, coloured by εxx
---------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 101-119

.. code-block:: Python

    grid = femorph_solver.io.static_result_to_grid(m, res)
    node_nums = m.node_numbers
    node_to_idx = {int(nn): i for i, nn in enumerate(node_nums)}
    grid.point_data["eps_xx"] = np.array(
        [eps[node_to_idx[int(nn)], 0] for nn in grid.point_data["ansys_node_num"]]
    )

    plotter = pv.Plotter(off_screen=True)
    plotter.add_mesh(grid, style="wireframe", color="gray", line_width=1, opacity=0.4)
    plotter.add_mesh(
        grid.warp_by_vector("displacement", factor=2.0e5),
        scalars="eps_xx",
        show_edges=True,
        cmap="viridis",
        scalar_bar_args={"title": "εxx"},
    )
    plotter.add_axes()
    plotter.show()



.. image-sg:: /gallery/elements/solid186/images/sphx_glr_example_solid186_001.png
   :alt: example solid186
   :srcset: /gallery/elements/solid186/images/sphx_glr_example_solid186_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.251 seconds)


.. _sphx_glr_download_gallery_elements_solid186_example_solid186.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: example_solid186.ipynb <example_solid186.ipynb>`

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

      :download:`Download Python source code: example_solid186.py <example_solid186.py>`

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

      :download:`Download zipped: example_solid186.zip <example_solid186.zip>`


.. only:: html

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

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