Modeling A
==============


Characteristics of modeling
-----------------------------------

This is a D_ PLAN modeling using linear XFEM elements.

The interface is unmeshed and cuts off the center element in :math:`Y={L}_{d}=\frac{13\ast \mathit{LY}}{25}`. So we have 3 XFEM elements and 2 classic elements. As indicated in the Figure, the 3 elements XFEM are subdivided into sub-triangles (to perform the Gauss-Legendre integration on either side of the lips of the interface, but these triangular sub-elements are not mesh elements).


.. image:: images/100000000000028C00000244098F484CCD384DCA.png
    :width: 4.9193in
    :height: 4.2626in


.. _RefImage_100000000000028C00000244098F484CCD384DCA.png:

**Figure** 3.1-a **: Characteristics of modelling**


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

The mesh composed of 5 QUAD4 is shown in Figure.


.. image:: images/1000000000000623000003816525C0585F90CC9B.png
    :width: 6.3374in
    :height: 3.5417in


.. _RefImage_1000000000000623000003816525C0585F90CC9B.png:

**Figure** 3.2-a **: 2D mesh**


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

The results (resolution with STAT_NON_LINE) are summarized in the table below for the :math:`y` direction. We are testing the following :math:`y` movement of the interface nodes.


.. csv-table::

    "**Quantities tested**", "**Reference type**", "**Reference value**", "**Tolerance (%)**"
    "DY (below) MIN ", "'ANALYTIQUE'", "-2.6E-02", "0.001"
    "DY (above) MAX ", "'ANALYTIQUE'", "2.4E-02", "0.001"


We also test the displacement along :math:`x` of the two interface nodes located on the [BC] side and respectively on the lower and upper lip of the crack.


.. csv-table::

    "**Quantities tested**", "**Reference type**", "**Reference value**", "**Tolerance (%)**"
    "DX (below [BC])", "'ANALYTIQUE'", "2.6E-02", "0.001"
    "DX (above [BC] side)", "'ANALYTIQUE'", "-2.4E-02", "0.001"


The displacement fields are presented in the direction :math:`y` (Figure) and :math:`x` (Figure).

**Figure** 3.3-a **: Field of movement by direction (Oy)**


.. image:: images/100000000000047C000002F6E8713E538455E9C8.png
    :width: 5.6665in
    :height: 3.3646in


.. _RefImage_100000000000047C000002F6E8713E538455E9C8.png:

**Figure** 3.3-b **: Field of movement according to direction (Ox)**


.. image:: images/100000000000047C000002F67655F66DA3B549DE.png
    :width: 5.6299in
    :height: 3.6398in


.. _refImage_100000000000047c000002f67655f66 DA3B549DE .png: