:orphan:

.. _easyfea-examples:

Examples
========

Contains example scripts demonstrating the use of numerous simulations that can be run with EasyFEA.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A cantilever beam undergoing bending deformation.">

.. only:: html

  .. image:: /examples/images/thumb/sphx_glr_HelloWorld_thumb.png
    :alt:

  :doc:`/examples/HelloWorld`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">HelloWorld</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/HelloWorld


Euler-Bernoulli beam simulations
================================

Contains examples for ``static`` simulations.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Beam subjected to pure tensile loading.">

.. only:: html

  .. image:: /examples/Beam/images/thumb/sphx_glr_Beam1_thumb.png
    :alt:

  :doc:`/examples/Beam/Beam1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Beam1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A cantilever beam undergoing bending deformation.">

.. only:: html

  .. image:: /examples/Beam/images/thumb/sphx_glr_Beam2_thumb.png
    :alt:

  :doc:`/examples/Beam/Beam2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Beam2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A bi-fixed beam undergoing bending deformation.">

.. only:: html

  .. image:: /examples/Beam/images/thumb/sphx_glr_Beam3_thumb.png
    :alt:

  :doc:`/examples/Beam/Beam3`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Beam3</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Frame with two beams.">

.. only:: html

  .. image:: /examples/Beam/images/thumb/sphx_glr_Beam4_thumb.png
    :alt:

  :doc:`/examples/Beam/Beam4`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Beam4</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Frame with six beams">

.. only:: html

  .. image:: /examples/Beam/images/thumb/sphx_glr_Beam5_thumb.png
    :alt:

  :doc:`/examples/Beam/Beam5`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Beam5</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


Hyperelastic simulations
========================

Contains examples for ``static`` and ``dynamic`` simulations in the ``Lagrangian`` framework.

Also includes ``sympy`` scripts to construct new ``hyperelastic`` laws.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Compute hyperelastic constitutive laws.">

.. only:: html

  .. image:: /examples/Hyperelasticity/images/thumb/sphx_glr_ComputeHyperelasticLaws_thumb.png
    :alt:

  :doc:`/examples/Hyperelasticity/ComputeHyperelasticLaws`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ComputeHyperelasticLaws</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Compute invariants used in hyperelastic constitutive laws.">

.. only:: html

  .. image:: /examples/Hyperelasticity/images/thumb/sphx_glr_ComputeInvariants_thumb.png
    :alt:

  :doc:`/examples/Hyperelasticity/ComputeInvariants`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ComputeInvariants</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A cantilever beam undergoing bending deformation.">

.. only:: html

  .. image:: /examples/Hyperelasticity/images/thumb/sphx_glr_Hyperelas1_thumb.png
    :alt:

  :doc:`/examples/Hyperelasticity/Hyperelas1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hyperelas1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A hyper elastic cube in compression.">

.. only:: html

  .. image:: /examples/Hyperelasticity/images/thumb/sphx_glr_Hyperelas2_thumb.png
    :alt:

  :doc:`/examples/Hyperelasticity/Hyperelas2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hyperelas2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A L shape part undergoing bending deformation.">

.. only:: html

  .. image:: /examples/Hyperelasticity/images/thumb/sphx_glr_Hyperelas3_thumb.png
    :alt:

  :doc:`/examples/Hyperelasticity/Hyperelas3`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hyperelas3</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A cantilever beam undergoing bending deformation in dynamic.">

.. only:: html

  .. image:: /examples/Hyperelasticity/images/thumb/sphx_glr_Hyperelas4_thumb.gif
    :alt:

  :doc:`/examples/Hyperelasticity/Hyperelas4`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hyperelas4</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


Linearized elastic simulations
==============================

Contains examples for ``static``, ``dynamic``, ``contact``, ``homogenization`` and ``mesh optimization``.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Performing a &#x27;Hertz contact problem&#x27; with the assumption of frictionless contact The master mesh is considered non-deformable.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Contact1_thumb.gif
    :alt:

  :doc:`/examples/LinearizedElasticity/Contact1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Contact1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A cantilever beam undergoing bending deformation.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas1_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Bending bracket component.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas2_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Hydraulic dam subjected to water pressure and its own weight.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas3_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas3`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas3</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Plate with a hole subjected to uniform tensile loading.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas4_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas4`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas4</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A cylindrical conduit exposed to uniform pressure.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas5_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas5`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas5</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A bi-fixed beam undergoing bending deformation.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas6_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas6`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas6</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Control lever for a molding machine used to blow plastic bottles.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas7_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas7`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas7</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A cantilever beam undergoing dynamic bending deformation.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas8_thumb.gif
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas8`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas8</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Wave propagation.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Elas9_thumb.gif
    :alt:

  :doc:`/examples/LinearizedElasticity/Elas9`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Elas9</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Conduct homogenization using an example outlined in Computational Homogenization of Heterogeneous Materials with Finite Elements.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Homog1_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Homog1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Homog1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Perform homogenization on several RVE.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Homog2_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Homog2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Homog2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Conduct full-field homogenization.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Homog3_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Homog3`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Homog3</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Conduct 3d homogenization on a simple RVE.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Homog4_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Homog4`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Homog4</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Conduct 3d homogenization on a periodic mesh generated with microgen.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Homog5_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Homog5`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Homog5</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Verification of energy convergence for a bending beam for all available elements.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_MeshConvergence_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/MeshConvergence`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MeshConvergence</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Optimization of a happy mesh with quality criteria.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_MeshOptim0_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/MeshOptim0`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MeshOptim0</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mesh optimization using the ZZ1 criterion for a bending bracket.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_MeshOptim1_thumb.gif
    :alt:

  :doc:`/examples/LinearizedElasticity/MeshOptim1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MeshOptim1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mesh optimization with the ZZ1 criterion for a bending part.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_MeshOptim2_thumb.gif
    :alt:

  :doc:`/examples/LinearizedElasticity/MeshOptim2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MeshOptim2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mesh optimization using the ZZ1 criterion for a letter weigher.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_MeshOptim3_thumb.gif
    :alt:

  :doc:`/examples/LinearizedElasticity/MeshOptim3`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MeshOptim3</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Modal analysis of a wall structure.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Modal1_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Modal1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Modal1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Modal analysis of a structure.">

.. only:: html

  .. image:: /examples/LinearizedElasticity/images/thumb/sphx_glr_Modal2_thumb.png
    :alt:

  :doc:`/examples/LinearizedElasticity/Modal2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Modal2</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


"MachineLearning" tests
=======================



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="KMeans using scikit-learn according to https://www.youtube.com/watch?v=i-gxm_ofjBo.">

.. only:: html

  .. image:: /examples/MachineLearning/images/thumb/sphx_glr_k_means_thumb.png
    :alt:

  :doc:`/examples/MachineLearning/k_means`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">k_means</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


Meshes
======

Scripts demonstrating how to construct :py:class:`~EasyFEA.fem._mesh.Mesh`.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a 2D domain.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh1_2D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh1_2D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh1_2D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a 3D domain.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh1_3D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh1_3D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh1_3D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a triangle.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh2_2D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh2_2D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh2_2D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a hydraulic dam.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh2_3D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh2_3D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh2_3D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a 2D domain with hole.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh3_2D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh3_2D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh3_2D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a 3D domain with hole.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh3_3D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh3_3D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh3_3D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a 2D bracket.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh4_2D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh4_2D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh4_2D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a 3D bracket.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh4_3D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh4_3D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh4_3D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mesh of a 2D cracked part.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh5_2D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh5_2D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh5_2D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mesh of a 3D cracked part.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh5_3D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh5_3D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh5_3D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Refined 2D mesh in zones.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh6_2D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh6_2D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh6_2D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Refined 3D mesh in zones.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh6_3D_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh6_3D`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh6_3D</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing a 3D part in revolution.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh7_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh7`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh7</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing of a grooved 3D part with calculation of element quality.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh8_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh8`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh8</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing of a perforated plate with a structured mesh.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh9_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh9`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh9</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Simplified turbine mesh with data extraction in matlab.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh10_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh10`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh10</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing of a specimen for a spatially oriented tensile test.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh11_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh11`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh11</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Meshing of a part designed by cad software.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh12_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh12`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh12</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mesh a heterogeneous RVE with cracks.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_Mesh13_thumb.png
    :alt:

  :doc:`/examples/Meshes/Mesh13`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mesh13</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create Lagrange finite element shape functions.">

.. only:: html

  .. image:: /examples/Meshes/images/thumb/sphx_glr_ShapeFunctions_thumb.png
    :alt:

  :doc:`/examples/Meshes/ShapeFunctions`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ShapeFunctions</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


PhaseField damage simulations for quasi-static brittle fracture
===============================================================

Scripts that demonstrate phase-field damage simulations.

To enable fast execution, these examples use coarse meshes and large loading steps.
In practice, fine meshes and smaller increments are essential to obtain realistic and accurate results.

For more realistic simulations, make sure you use a finer mesh and smaller loading steps by setting ``meshTest=False``.



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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Performs damage simulation on a CT specimen.">

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  .. image:: /examples/PhaseField/images/thumb/sphx_glr_CT_thumb.gif
    :alt:

  :doc:`/examples/PhaseField/CT`

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      <div class="sphx-glr-thumbnail-title">CT</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Damage simulation for a L-part.">

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  .. image:: /examples/PhaseField/images/thumb/sphx_glr_LShape_thumb.gif
    :alt:

  :doc:`/examples/PhaseField/LShape`

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      <div class="sphx-glr-thumbnail-title">LShape</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Damage simulation for a plate with a hole subjected to compression.">

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  .. image:: /examples/PhaseField/images/thumb/sphx_glr_PlateWithHole_thumb.gif
    :alt:

  :doc:`/examples/PhaseField/PlateWithHole`

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      <div class="sphx-glr-thumbnail-title">PlateWithHole</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Damage simulation for a plate subjected to shear.">

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  .. image:: /examples/PhaseField/images/thumb/sphx_glr_Shear_thumb.gif
    :alt:

  :doc:`/examples/PhaseField/Shear`

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      <div class="sphx-glr-thumbnail-title">Shear</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Damage simulation for a plate subjected to tension.">

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  .. image:: /examples/PhaseField/images/thumb/sphx_glr_Tension_thumb.gif
    :alt:

  :doc:`/examples/PhaseField/Tension`

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      <div class="sphx-glr-thumbnail-title">Tension</div>
    </div>


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    </div>


Thermal simulations
===================

Contains examples for ``static`` and ``transient`` simulations.



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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Thermal simulation.">

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  .. image:: /examples/Thermal/images/thumb/sphx_glr_Thermal1_thumb.png
    :alt:

  :doc:`/examples/Thermal/Thermal1`

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      <div class="sphx-glr-thumbnail-title">Thermal1</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Transient thermal simulation.">

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  .. image:: /examples/Thermal/images/thumb/sphx_glr_Thermal2_thumb.gif
    :alt:

  :doc:`/examples/Thermal/Thermal2`

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      <div class="sphx-glr-thumbnail-title">Thermal2</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Transient thermal simulation.">

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  .. image:: /examples/Thermal/images/thumb/sphx_glr_Thermal3_thumb.gif
    :alt:

  :doc:`/examples/Thermal/Thermal3`

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      <div class="sphx-glr-thumbnail-title">Thermal3</div>
    </div>


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    </div>


Weak forms simulations
======================

Contains examples for ``static``, ``transient`` and ``dynamic`` simulations for ``linear`` or ``non-linear`` problems.



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    <div class="sphx-glr-thumbcontainer" tooltip="A cantilever beam undergoing bending deformation.">

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  .. image:: /examples/WeakForms/images/thumb/sphx_glr_LinearElasticity1_thumb.png
    :alt:

  :doc:`/examples/WeakForms/LinearElasticity1`

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      <div class="sphx-glr-thumbnail-title">LinearElasticity1</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A cantilever beam undergoing bending deformation in dynamic.">

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  .. image:: /examples/WeakForms/images/thumb/sphx_glr_LinearElasticity2_thumb.gif
    :alt:

  :doc:`/examples/WeakForms/LinearElasticity2`

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      <div class="sphx-glr-thumbnail-title">LinearElasticity2</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Poisson equation with unit load.">

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  .. image:: /examples/WeakForms/images/thumb/sphx_glr_Poisson1_thumb.png
    :alt:

  :doc:`/examples/WeakForms/Poisson1`

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      <div class="sphx-glr-thumbnail-title">Poisson1</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Poisson equation with unit load.">

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  .. image:: /examples/WeakForms/images/thumb/sphx_glr_Poisson2_thumb.png
    :alt:

  :doc:`/examples/WeakForms/Poisson2`

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      <div class="sphx-glr-thumbnail-title">Poisson2</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="An educational implementation of topology optimization inspired by Week 10- Topology Optimisation — A Step-by-Step Tutorial created by (Dr Wei Tan, Queen Mary University of London), which in turn builds upon the seminal 88-line topology optimization MATLAB code by Ole Sigmund (2001), published in Structural and Multidisciplinary Optimization, 21(2), pp. 120–127.">

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  .. image:: /examples/WeakForms/images/thumb/sphx_glr_TopologyOptimisation1_thumb.png
    :alt:

  :doc:`/examples/WeakForms/TopologyOptimisation1`

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      <div class="sphx-glr-thumbnail-title">TopologyOptimisation1</div>
    </div>


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    </div>


.. toctree::
   :hidden:
   :includehidden:


   /examples/Beam/index.rst
   /examples/Hyperelasticity/index.rst
   /examples/LinearizedElasticity/index.rst
   /examples/MachineLearning/index.rst
   /examples/Meshes/index.rst
   /examples/PhaseField/index.rst
   /examples/Thermal/index.rst
   /examples/WeakForms/index.rst



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

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