D modeling
===============



This modeling is based on modeling A.

The type of element chosen for the mesh is the only difference between these two models.


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

We discretize the structure into 6 finite elements TETRA4

The interface is present within these 6 elements through the level sets.


.. image:: images/1000000000000239000004238C5733C18C337071.jpg
    :width: 2.9634in
    :height: 4.302in


.. _RefImage_1000000000000239000004238C5733C18C337071.jpg:

**Figure** 5.1-a **: Mesh**


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

The boundary conditions are those of modeling A: we embed the nodes on the lower face and we impose a displacement of the nodes on the upper face.


Analytical resolution
---------------------

The analytical solution is the one presented in modeling A [§ :ref:`2.3 <Ref76285195>`]: all the degrees of freedom following :math:`x` and :math:`y` are zero and all the degrees of freedom following :math:`z` are equal to :math:`\mathrm{uz}/2`, where :math:`\mathrm{uz}={10}^{-6}`


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

We test the values of the displacement just below and above the interface after convergence of the iterations of the operator STAT_NON_LINE. We check that we find the values determined in [§ :ref:`2.3 <Ref76285195>`].


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    "DX for all nodes just below the interface", "0.00", "1.0E-16"
    "DY for all nodes just below the interface", "0.00", "1.0E-16"
    "DZ for all nodes just below the interface", "0.00", "1.0E-16"
    "DX for all nodes just above the interface", "0.00", "1.0E-16"
    "DY for all nodes just above the interface", "0.00", "1.0E-16"
    "DZ for all nodes just above the interface", "1.0E-6", "1.0E -9%"


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


Comments
------------

We notice the discontinuity of the field of movement when crossing the interface, which is possible thanks to the enrichment of the elements with the Heaviside degree of freedom.