F modeling
==============


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

It is the same modeling as modeling E, but with plane constraints. The intersection is constructed in the same way.


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

The mesh, identical to that of modeling B, is represented in FIG. 4.2-a.


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

The movements at the level of the crack lips are tested after having carried out the post-treatment operations relating to :math:`\text{X-FEM}` (POST_MAIL_XFEM and POST_CHAM_XFEM). The DX displacement should follow function :math:`{u}_{x}` in equation 2.2-7. The displacement DY should follow function :math:`{u}_{y}` in equation 2.2-8. The deformation shown in FIG. 7.4-a is obtained.


+------------------+-------------------+-------------+-+
|**Identification**                    |**Reference**|0|
+------------------+-------------------+-------------+ +
|DEPZON_1          |DX- :math:`{u}_{x}`|MIN          | |
+                  +                   +-------------+-+
|                  |                   |MAX          |0|
+                  +-------------------+-------------+-+
|                  |DY- :math:`{u}_{y}`|MIN          |0|
+                  +                   +-------------+-+
|                  |                   |MAX          |0|
+------------------+-------------------+-------------+-+
|DEPZON_2          |DX- :math:`{u}_{x}`|MIN          |0|
+                  +                   +-------------+-+
|                  |                   |MAX          |0|
+                  +-------------------+-------------+-+
|                  |DY- :math:`{u}_{y}`|MIN          |0|
+                  +                   +-------------+-+
|                  |                   |MAX          |0|
+------------------+-------------------+-------------+-+
|DEPZON_3          |DX- :math:`{u}_{x}`|MIN          |0|
+                  +                   +-------------+-+
|                  |                   |MAX          |0|
+                  +-------------------+-------------+-+
|                  |DY- :math:`{u}_{y}`|MIN          |0|
+                  +                   +-------------+-+
|                  |                   |MAX          |0|
+------------------+-------------------+-------------+-+
|DEPZON_4          |DX- :math:`{u}_{x}`|MIN          |0|
+                  +                   +-------------+-+
|                  |                   |MAX          |0|
+                  +-------------------+-------------+-+
|                  |DY- :math:`{u}_{y}`|MIN          |0|
+                  +                   +-------------+-+
|                  |                   |MAX          |0|
+------------------+-------------------+-------------+-+

Table 8.3-1

The deformation is shown in Figure 8.4-a.


.. image:: images/1000000000000312000002827155F606701B9A58.jpg
    :width: 3.9366in
    :height: 3.2165in


.. _RefImage_1000000000000312000002827155F606701B9A58.jpg:

Figure 8.4-a: Deformed structure (Exaggeration 10).

We test the value of :math:`{E}^{e}` produced by the POST_ERREUR operator (expressed in :math:`\text{J}\times {\text{m}}^{-1}`).


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**"
    "Ee", "'ANALYTIQUE'", "1,825106"


We test the value of :math:`{\Vert u\Vert }_{{L}^{2}}` produced by the POST_ERREUR operator.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "L2 standard, "'ANALYTIQUE'", "0.992051745962"," 0.1%"



notes
---------

The remarks are identical to those formulated for modeling E.