J modeling
==============

This modeling is exactly the same as modeling B. The only difference is that the finite elements used are quadratic elements instead of linear elements.


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

The displacement values are tested after convergence of the iterations of the operator STAT_NON_LINE. We check that we find the values determined in [§ :ref:`3.3 <Ref76289108>`] for the 2 load cases.

The following table is obtained for the first loading case.


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    ":math:`\mathit{DX}` for all nodes just below the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DY}` for all nodes just below the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DZ}` for all nodes just below the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DX}` for all nodes just above the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DY}` for all nodes just above the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DZ}` for all nodes just above the interface", "1.0E-6", "1.0E -9%"


The following table is obtained for the 2nd load case.


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    ":math:`\mathit{DX}` for all nodes just below the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DY}` for all nodes just below the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DZ}` for all nodes just below the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DX}` for all nodes just above the interface", "1.0E-6", "1.0E -9%"
    ":math:`\mathit{DY}` for all nodes just above the interface", "2.0E-6", "1.0E -9%"
    ":math:`\mathit{DZ}` for all nodes just above the interface", "3.0E-6", "1.0E -9%"


To test all the nodes at once, we test the MINIMUM and the MAXIMUM of the column.

We also test the values of the displacement from the command POST_CHAM_XFEM. We are in fact testing the value of the sum of the absolute values of the movements of the nodes of the cracked mesh. It is a non-regression test compared to the values obtained with version 8.2.13 for :math:`\mathit{DX}` and 9.0.21 for :math:`\mathit{DY}`


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    "SOMM_ABS (DX)", "0.000", "1.0E-12"
    "SOMM_ABS (DY)", "1.3E-05", "1.0E -04%"