.. _V1.01.361:

**v1.01.361** ZZZZ361 - Degenerate cutting cases for XFEM quadratic 3D elements
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**Summary:**

In this test case, it is proposed to check the correct progress of particular volume cutting cases in the quadratic XFEM frame. In three-dimensional XFEM, the "parent" finite elements crossed by the crack are cut into "child" tetrahedra, which are then cut back into sub-tetrahedra to conform to the discontinuity.

There are a total of five configurations for cutting "child" tetrahedra into sub-tetrahedra (*cf.* [:ref:`R7.02.12 <R7.02.12>`]), distinguished according to the number of vertex nodes of the child tetrahedron for which the *lsn* is cancelled (npts) and the number of intersection points between the *lsn* =0 surface and the edges of the child tetrahedron (npts) and the number of intersection points between the *lsn* =0 surface and the edges of the child tetrahedron. However, degenerate "grazing" configurations exist. These degenerate configurations can easily be reduced to conventional cutting configurations.

We are interested here in the six degenerate configurations (models A to F) for which the surface *lsn=0* shaves the surface of the child tetrahedron, and which only occur in quadratic XFEM. These situations occur when one or more edges of the child tetrahedron have exactly 2 points such as*lsn=0* (necessarily one end and the middle node according to the adjustment of *level set* in the quadratic case). Finally, in G modeling, we study the case of non-degenerate cutting for which the *lsn=0* surface shaves one of the edges of the tetrahedron.


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence
    Mod_lisation_A
    Mod_lisation_B
    Mod_lisation_C
    Mod_lisation_D
    Mod_lisation_E
    Mod_lisation_F
    Mod_lisation_G
    Synth_se_des_r_sultats