.. _sphx_glr_examples_poromechanics:

Poromechanics
-------------

Biot poroelasticity of saturated porous media, in small and finite strain.
See :doc:`/poromechanics` for the formulation.


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    <div class="sphx-glr-thumbcontainer" tooltip="A saturated column is loaded by a constant pressure on its drained top face, under lateral confinement, and settles by about 8 %. The skeleton is a compressible Neo-Hookean solid (simcoon NEOHC law) and the permeability decreases with the volume change through the Holmes-Mow model, as is typical for soft biological tissues such as articular cartilage.">

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  .. image:: /examples/poromechanics/images/thumb/sphx_glr_finite_strain_consolidation_thumb.png
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  :doc:`/examples/poromechanics/finite_strain_consolidation`

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      <div class="sphx-glr-thumbnail-title">Finite strain consolidation of a hyperelastic porous column</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="A rigid hemispherical indenter is pressed into a layer of saturated soft tissue lying on a rigid substrate, as when pressing a fingertip on the skin. The indenter is pushed in quickly and then held in place.">

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  .. image:: /examples/poromechanics/images/thumb/sphx_glr_indentation_soft_tissue_thumb.png
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  :doc:`/examples/poromechanics/indentation_soft_tissue`

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      <div class="sphx-glr-thumbnail-title">Indentation of a hyperelastic soft tissue: fluid exudation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In the undrained limit (nearly incompressible fluid, no time to drain), the pore pressure enforces a volume constraint and the Biot system becomes a saddle-point problem. Its discretization is stable only if the pair of displacement and pressure interpolations satisfies the inf-sup (LBB) condition. Equal-order pairs (same element for both fields) violate it, and the pressure shows spurious node-to-node oscillations (&quot;checkerboard&quot;).">

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  .. image:: /examples/poromechanics/images/thumb/sphx_glr_taylor_hood_lbb_thumb.png
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  :doc:`/examples/poromechanics/taylor_hood_lbb`

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      <div class="sphx-glr-thumbnail-title">Inf-sup (LBB) stable elements: Taylor-Hood interpolation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="A column of saturated porous material with a linear elastic skeleton is loaded by a constant pressure on its top face. The top face is drained (``PorePressure = 0``), the bottom and lateral faces are sealed, and the lateral displacements are blocked (oedometric, i.e. 1D, consolidation).">

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  .. image:: /examples/poromechanics/images/thumb/sphx_glr_terzaghi_1d_thumb.png
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  :doc:`/examples/poromechanics/terzaghi_1d`

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      <div class="sphx-glr-thumbnail-title">Terzaghi 1D consolidation (small strain)</div>
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.. toctree::
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   /examples/poromechanics/finite_strain_consolidation
   /examples/poromechanics/indentation_soft_tissue
   /examples/poromechanics/taylor_hood_lbb
   /examples/poromechanics/terzaghi_1d