Modeling B: crack X- FEM
==============================

In this modeling, the crack is no longer meshed, but it is represented by level sets: :math:`\mathit{LSN}\mathrm{=}z\mathrm{-}1\mathrm{/}2` and :math:`\mathit{LST}\mathrm{=}\mathrm{-}y\mathrm{-}x\mathrm{/}2+1`.


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

The structure is modelled by a mesh composed of 15872 tetrahedra (see [:ref:`Figure 2.1-a <Figure 2.1-a>`]).


.. image:: images/10000000000003BA000002950DC2C5BFF7EDF7F2.png
    :width: 4.6173in
    :height: 3.1929in


.. _RefImage_10000000000003BA000002950DC2C5BFF7EDF7F2.png:

**Figure 2.1-a: Healthy mesh**


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

The values of :math:`\mathit{K1}` are tested on the second point and on the last three points of the crack bottom. Indeed, the orientation of the crack implies that :math:`\mathit{K1}` cannot be calculated on certain points. We test the points concerned to verify that *Code_Aster* assigns them the value of the nearest neighbor node or the calculation of :math:`\mathit{K1}` could be performed.


.. csv-table::

    "Identification", "Reference Type", "Reference Value"
    "Point 2", "'NON_REGRESSION'", "1324885.20838"
    "Dot 22", "'NON_REGRESSION'", "851382.586304"
    "Dot 23", "'NON_REGRESSION'", "851382.586304"
    "Dot 24", "'NON_REGRESSION'", "851382.586304"


We also test the values of :math:`\mathit{COOR}\text{\_}X`, :math:`\mathit{COOR}\text{\_}Y`, :math:`\mathit{COOR}\text{\_}Z`, :math:`\mathit{TEMP}` and :math:`\mathit{NEUT}1` at node 1 in order to verify that these components are indeed present in the output table for the case X- FEM.