.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/ex19_taylor-hood.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_ex19_taylor-hood.py>`
        to download the full example code.

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

.. _sphx_glr_examples_ex19_taylor-hood.py:


Mixed-field hyperelasticity with quadratic triangles
----------------------------------------------------
A 90° section of a plane-strain circle is subjected to uniaxial compression by a
vertically moved rigid top plate. A mixed-field formulation is used with quadratic
triangles.

.. GENERATED FROM PYTHON SOURCE LINES 8-15

.. code-block:: Python


    from functools import partial

    import numpy as np

    import felupe as fem








.. GENERATED FROM PYTHON SOURCE LINES 17-20

A 90° section of a circle with quadratic triangles is created. The midpoints are
shifted to the outer radius. An additional point, used as center- (control-) point, is
added to the mesh.

.. GENERATED FROM PYTHON SOURCE LINES 20-25

.. code-block:: Python

    mesh = fem.Circle(n=6, sections=[0]).triangulate().add_midpoints_edges()
    mask = np.isclose(mesh.x**2 + mesh.y**2, 1, atol=0.05)
    mesh.points[mask] /= np.linalg.norm(mesh.points[mask], axis=1).reshape(-1, 1)
    mesh.add_points([0, 1.1])








.. GENERATED FROM PYTHON SOURCE LINES 26-29

Let's create a region for quadratic triangles and a mixed-field container with two
dual fields, one for the pressure and another one for the volume ratio. The dual
fields are disconnected.

.. GENERATED FROM PYTHON SOURCE LINES 29-50

.. code-block:: Python

    region = fem.RegionQuadraticTriangle(mesh)
    field = fem.FieldsMixed(
        region, n=3, values=(0.0, 0.0, 1.0), planestrain=True, disconnect=True
    )

    # create a nearly-incompressible hyperelastic solid body and the rigid top plate
    umat = fem.NearlyIncompressible(material=fem.NeoHooke(mu=1), bulk=5000)
    solid = fem.SolidBody(umat=umat, field=field)
    top = fem.ContactRigidPlane(
        field=field,
        points=np.arange(mesh.npoints)[np.isclose(mesh.x**2 + mesh.y**2, 1)],
        centerpoint=-1,
        normal=(0, -1),
        items=[solid],
        friction=0.5,
        multiplier=10,  # increase contact normal multiplier
        multiplier_tangential=2,  # increase contact tangential multiplier
    )
    kwargs = dict(line_width=5, opacity=1, sym=(True, False), size=2)
    mesh.plot(nonlinear_subdivision=4, plotter=top.plot(**kwargs)).show()








.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /examples/images/sphx_glr_ex19_taylor-hood_001.png
        :alt: ex19 taylor hood
        :srcset: /examples/images/sphx_glr_ex19_taylor-hood_001.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/docs/checkouts/readthedocs.org/user_builds/felupe-ja/checkouts/latest/felupe/docs/examples/images/sphx_glr_ex19_taylor-hood_001.vtksz






.. GENERATED FROM PYTHON SOURCE LINES 51-53

A step is used containts the solid body and the rigid top plate as items. The rigid
vertical movement of the top plate is applied in a ramped manner.

.. GENERATED FROM PYTHON SOURCE LINES 53-60

.. code-block:: Python

    boundaries = fem.dof.symmetry(field[0])
    boundaries["move"] = fem.Boundary(field[0], fy=1.1, skip=(1, 0))
    move = fem.math.linsteps([0, -0.4], num=6)
    ramp = {boundaries["move"]: move}
    step = fem.Step(items=[solid, top], ramp=ramp, boundaries=boundaries)
    job = fem.Job(steps=[step]).evaluate()








.. GENERATED FROM PYTHON SOURCE LINES 61-63

The maximum principal values of the Cauchy stress tensor are plotted. The cell-based
means are projected to the mesh-points.

.. GENERATED FROM PYTHON SOURCE LINES 63-69

.. code-block:: Python

    solid.plot(
        "Principal Values of Cauchy Stress",
        nonlinear_subdivision=4,
        plotter=top.plot(**kwargs),
        project=partial(fem.project, mean=True),
    ).show()







.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /examples/images/sphx_glr_ex19_taylor-hood_002.png
        :alt: ex19 taylor hood
        :srcset: /examples/images/sphx_glr_ex19_taylor-hood_002.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/docs/checkouts/readthedocs.org/user_builds/felupe-ja/checkouts/latest/felupe/docs/examples/images/sphx_glr_ex19_taylor-hood_002.vtksz







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

   **Total running time of the script:** (0 minutes 1.763 seconds)


.. _sphx_glr_download_examples_ex19_taylor-hood.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: ex19_taylor-hood.ipynb <ex19_taylor-hood.ipynb>`

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

      :download:`Download Python source code: ex19_taylor-hood.py <ex19_taylor-hood.py>`

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

      :download:`Download zipped: ex19_taylor-hood.zip <ex19_taylor-hood.zip>`


.. only:: html

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

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