D modeling
==============


Characteristics of modeling
-----------------------------------

We use a MEMBRANE modeling in large deformations (DEFORMATION =' GROT_GDEP ') with the Neo-Hookian law of behavior (RELATION =' ELAS_MEMBRANE_NH'). Linear elements are used.


Characteristics of the mesh
----------------------------

The mesh is the same as for modeling A.


Tested sizes and results
------------------------------

The pressure applied during loading is tested.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Precision**"
    "Instant 0.1 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "109.55 :math:`N/{m}^{2}` "," 7%"
    "Instant 0.2 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "531.73 :math:`N/{m}^{2}` "," 3%"
    "Instant 0.3 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "995.8 :math:`N/{m}^{2}` "," 2%"
    "Instant 0.4 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "1276.2 :math:`N/{m}^{2}` "," 3%"
    "Instant 0.5 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "1366.9 :math:`N/{m}^{2}` "," 3%"
    "Instant 0.6 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "1344.7 :math:`N/{m}^{2}` "," 4%"
    "Instant 0.7 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "1280.6 :math:`N/{m}^{2}` "," 5%"
    "Instant 0.8 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "1203.0 :math:`N/{m}^{2}` "," 6%"
    "Instant 0.9 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "1124.4 :math:`N/{m}^{2}` "," 6%"
    "Instant 1.0 - :math:`\mathit{ETA}\text{\_}\mathit{PILO}` ", "'SOURCE_EXTERNE'", "1049.0 :math:`N/{m}^{2}` "," 7%"



.. image:: images/10000201000006CF00000512C0A4CF01AC1AC796.png
    :width: 5.8098in
    :height: 4.3264in


.. _RefImage_10000201000006CF00000512C0A4CF01AC1AC796.png:

Figure 6.2-a: Results of the D modeling vs numerical reference in figure :ref:`2.1 <RefNumPara__1789_3608235943>` -a.


.. image:: images/100002010000016C00000155BE11931C25F14331.png
    :width: 2.0984in
    :height: 1.9646in


.. _RefImage_100002010000016C00000155BE11931C25F14331.png:


.. image:: images/100002010000016C000001557FE462F79BE08394.png
    :width: 2.0984in
    :height: 1.9602in


.. _RefImage_100002010000016C000001557FE462F79BE08394.png:


.. image:: images/100002010000016C000001557169D5AF344BD6E3.png
    :width: 2.0984in
    :height: 1.9646in


.. _RefImage_100002010000016C000001557169D5AF344BD6E3.png:

Figure 6.2-b: Initial state (left), deformed at time 0.5 (center) and deformed at final state (right).


notes
---------

We used on-the-go piloting (SUIV_PILO) to achieve convergence. The Neo-Hookian law of behavior reveals a *snap-through* at around 1.4kPa. This leads to strong non-linearities around this value that can be overcome by controlling the follower pressure.

The mesh is approximately 2 times coarser than that of the reference and the meshes are linear and not quadratic. This explains the differences observed compared to the reference solution for this modeling.