C modeling
==============


Characteristics of the mesh and the interface
----------------------------------------------

We consider a structure with dimensions :math:`\mathrm{LX}=5m`, :math:`\mathrm{LY}=5m`, and :math:`\mathrm{LZ}=25m`. This structure is discretized with 5 HEXA8 meshes. We are interested in a normal flat interface

:math:`n=(\begin{array}{}-1\\ 1\\ 1\end{array})`

passing through point :math:`A` with coordinates :math:`(\mathrm{5,}5\delta ,5)`. The [] shows a zoom of the 2nd element where the interface trace is represented in red.

5

N9 ROAD


.. image:: images/10000000000002D6000001E66F238399F736C296.png
    :width: 4.7398in
    :height: 3.1728in


.. _RefImage_10000000000002D6000001E66F238399F736C296.png:

**Figure** 4.1-a **: C mesh and zoom**

The interface is characterized by the normal level set with the cartesian equation:

:math:`\mathrm{lsn}=-x+y+z-5\delta`

**Note:**


.. code-block:: text

    With the new displacement jump enrichment [:ref:`R7.02.12 <R7.02.12>`], we do not see a decrease in precision on the solution when moving in the vicinity of the interface and a conditioning problem, although the interface is flat compared to the nodes of the mesh.


Boundary conditions
----------------------

The boundary conditions are the same as those in modeling B. The nodes on the lower face are embedded and a tensile displacement is imposed on the nodes on the upper face:

Lower side: :math:`\mathrm{DX}=0`, :math:`\mathrm{DY}=0`, and :math:`\mathrm{DZ}=0`

Top side: :math:`\mathrm{DX}=0`, :math:`\mathrm{DY}=0`, and :math:`\mathrm{DZ}={10}^{-6}`


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

The smooth running of the calculation allows *a priori* to validate the case. We therefore test the values of the displacement just above the interface after convergence of the iterations of the operator STAT_NON_LINE.


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    ":math:`\mathit{DZ}` for all nodes just above the interface", ":math:`1.0E-6` ", "1.0E -3%"


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