.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/ex11_notch-stress.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_ex11_notch-stress.py>`
        to download the full example code.

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

.. _sphx_glr_examples_ex11_notch-stress.py:


Notch Stress
------------

.. topic:: Three-dimensional linear-elastic analysis.

   * read a mesh file
   
   * define a linear-elastic solid body
   
   * project the linear-elastic stress tensor to the mesh-points
   
   * plot the max. principal stress component

   * evaluate the fatigue life

.. admonition:: This example requires external packages.
   :class: hint
   
   .. code-block::
      
      pip install pypardiso

A linear-elastic notched plate is subjected to uniaxial tension. The cell-based mean of
the stress tensor is projected to the mesh-points and its maximum principal value is plotted. FElupe has no quadratic wedge element formulation
implemented and hence, the quadratic wedges in the mesh are converted to quadratic
hexahedrons.

.. GENERATED FROM PYTHON SOURCE LINES 29-59

.. code-block:: Python

    import numpy as np
    import pypardiso
    import pyvista as pv

    import felupe as fem

    m = pv.examples.download_notch_displacement()

    hex20 = [0, 2, 1, 1, 3, 5, 4, 4, 8, 7, 1, 6, 11, 10, 4, 9, 12, 14, 13, 13]
    mesh = fem.Mesh(
        m.points * 250,
        np.vstack([m.cells_dict[25], m.cells_dict[26][:, hex20]]),
        "hexahedron20",
    )
    region = fem.RegionQuadraticHexahedron(mesh)
    field = fem.FieldContainer([fem.Field(region, dim=3)])

    boundaries, loadcase = fem.dof.uniaxial(field, clamped=True, sym=False, move=0.02)
    solid = fem.SolidBody(umat=fem.LinearElastic(E=2.1e5, nu=0.30), field=field)
    step = fem.Step(items=[solid], boundaries=boundaries)
    job = fem.Job(steps=[step]).evaluate(parallel=True, solver=pypardiso.spsolve)

    solid.plot(
        "Principal Values of Cauchy Stress",
        show_edges=False,
        view="xy",
        project=fem.topoints,
        show_undeformed=False,
    ).show()








.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /examples/images/sphx_glr_ex11_notch-stress_001.png
        :alt: ex11 notch stress
        :srcset: /examples/images/sphx_glr_ex11_notch-stress_001.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/docs/checkouts/readthedocs.org/user_builds/felupe/checkouts/latest/docs/examples/images/sphx_glr_ex11_notch-stress_001.vtksz






.. GENERATED FROM PYTHON SOURCE LINES 61-74

The number of maximum endurable cycles between zero and the applied displacement is
evaluated with a SN-curve as denoted in Eq. :eq:`sn-curve`. The range of the maximum
principal value of the Cauchy stress tensor is used to evaluate the fatigue life.
For simplicity, the stress is evaluated for the total solid body. To consider only
stresses on points which lie on the surface of the solid body, the cells on faces
:meth:`~felupe.RegionQuadraticHexahedronBoundary.mesh.cells_faces` must be determined
first.

.. math::
   :label: sn-curve

   \frac{N}{N_D} = \left( \frac{S}{S_D} \right)^{-k}


.. GENERATED FROM PYTHON SOURCE LINES 74-93

.. code-block:: Python

    S_D = 100  # MPa
    N_D = 2e6  # cycles
    k = 5  # slope

    S = fem.topoints(fem.math.eigvalsh(solid.evaluate.cauchy_stress())[-1], region)
    N = N_D * (abs(S) / S_D) ** -k

    view = solid.view(point_data={"Endurable Cycles": N})
    plotter = view.plot(
        "Endurable Cycles",
        show_undeformed=False,
        show_edges=False,
        log_scale=True,
        flip_scalars=True,
        clim=[N.min(), 2e6],
        above_color="lightgrey",
    )
    plotter.camera.zoom(6)
    plotter.show()







.. tab-set::



   .. tab-item:: Static Scene



            
     .. image-sg:: /examples/images/sphx_glr_ex11_notch-stress_002.png
        :alt: ex11 notch stress
        :srcset: /examples/images/sphx_glr_ex11_notch-stress_002.png
        :class: sphx-glr-single-img
     


   .. tab-item:: Interactive Scene



       .. offlineviewer:: /home/docs/checkouts/readthedocs.org/user_builds/felupe/checkouts/latest/docs/examples/images/sphx_glr_ex11_notch-stress_002.vtksz







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

   **Total running time of the script:** (0 minutes 7.604 seconds)


.. _sphx_glr_download_examples_ex11_notch-stress.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: ex11_notch-stress.ipynb <ex11_notch-stress.ipynb>`

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

      :download:`Download Python source code: ex11_notch-stress.py <ex11_notch-stress.py>`


.. only:: html

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

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