.. _sphx_glr_examples_Inelasticity:

.. _easyfea-examples-inelasticity:

Inelastic simulations
=====================

Scripts that demonstrate small-strain materials whose stress depends on the history of strain:
plasticity, viscoplasticity and viscoelasticity.

:py:class:`~EasyFEA.Models.InElastic.Behavior` is assembled from independent pieces rather than chosen
from a list, and driven by :py:class:`~EasyFEA.Simulations.InElastic`. Each piece is optional and
turns on one behavior:

.. list-table::
    :header-rows: 1

    * - Piece
      - What it adds
    * - *(none)*
      - linear elasticity
    * - :py:class:`Models.InElastic.Yield <EasyFEA.Models.InElastic.Yield>`
      - plasticity — von Mises, Hill, Drucker-Prager
    * - :py:class:`Models.InElastic.IsotropicHardening <EasyFEA.Models.InElastic.IsotropicHardening>`
      - the surface grows — linear, Voce, Swift
    * - :py:class:`Models.InElastic.KinematicHardening <EasyFEA.Models.InElastic.KinematicHardening>`
      - the surface moves, giving the Bauschinger effect — Prager, Armstrong-Frederick, Chaboche
    * - :py:class:`Models.InElastic.ViscoPlastic <EasyFEA.Models.InElastic.ViscoPlastic>`
      - it creeps and relaxes once yielded — Norton, Perzyna
    * - :py:class:`Models.InElastic.ViscoElastic <EasyFEA.Models.InElastic.ViscoElastic>`
      - it relaxes without ever yielding — Maxwell branches

Several scripts use :py:class:`~EasyFEA.Models.InElastic.MaterialPoint`, which drives a behaviour at a
single Gauss point with no mesh and no solver. The two solvers behind it are described in
:ref:`simulations-inelastic`.



.. raw:: html

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

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="A rectangular section bent past yield.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_BeamBending_thumb.gif
    :alt:

  :doc:`/examples/Inelasticity/BeamBending`

.. raw:: html

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


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    <div class="sphx-glr-thumbcontainer" tooltip="A single Armstrong-Frederick back-stress is one exponential, saturating at 2C/3\gamma with a single rate. A measured hysteresis loop has both a sharp knee after yield and a long, nearly linear tail, and no single exponential fits both.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_Chaboche_thumb.png
    :alt:

  :doc:`/examples/Inelasticity/Chaboche`

.. raw:: html

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


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    <div class="sphx-glr-thumbcontainer" tooltip="Isotropic hardening grows the yield surface, so reversing the load finds it harder to yield in compression. Real metals do the opposite — the Bauschinger effect — because the surface translates rather than grows.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_CyclicLoading_thumb.png
    :alt:

  :doc:`/examples/Inelasticity/CyclicLoading`

.. raw:: html

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


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    <div class="sphx-glr-thumbcontainer" tooltip="A perforated plate pulled past yield. The hole concentrates the stress, so plasticity starts there and spreads outwards as the load increases.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_PlasticPlate_thumb.gif
    :alt:

  :doc:`/examples/Inelasticity/PlasticPlate`

.. raw:: html

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


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    <div class="sphx-glr-thumbcontainer" tooltip="Viscoelastic relaxation on a mesh, with an exact check.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_RelaxationPlate_thumb.gif
    :alt:

  :doc:`/examples/Inelasticity/RelaxationPlate`

.. raw:: html

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


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    <div class="sphx-glr-thumbcontainer" tooltip="Uniaxial curves for the shipped hardening laws, against their closed forms.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_StressStrain_thumb.png
    :alt:

  :doc:`/examples/Inelasticity/StressStrain`

.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The specimen of Mesh11 pulled past yield, in 3D.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_TensileTest_thumb.gif
    :alt:

  :doc:`/examples/Inelasticity/TensileTest`

.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The classic elastic-plastic benchmark: a thick-walled cylinder under internal pressure, with three independent analytical landmarks on one problem.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_ThickCylinder_thumb.gif
    :alt:

  :doc:`/examples/Inelasticity/ThickCylinder`

.. raw:: html

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


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Two time-dependent mechanisms, three closed forms.">

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  .. image:: /examples/Inelasticity/images/thumb/sphx_glr_TimeDependent_thumb.png
    :alt:

  :doc:`/examples/Inelasticity/TimeDependent`

.. raw:: html

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


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /examples/Inelasticity/BeamBending
   /examples/Inelasticity/Chaboche
   /examples/Inelasticity/CyclicLoading
   /examples/Inelasticity/PlasticPlate
   /examples/Inelasticity/RelaxationPlate
   /examples/Inelasticity/StressStrain
   /examples/Inelasticity/TensileTest
   /examples/Inelasticity/ThickCylinder
   /examples/Inelasticity/TimeDependent