Modeling A: Method MAILLAGE
=================================


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

In this modeling, the crack is not meshed. We use the X- FEM method and a representation of the crack by level sets. The level sets are updated by the operator PROPA_FISS, method MAILLAGE.


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

The initial mesh size of the structure is relatively coarse. It was made in Salomé's module SMESH, with Blsurf and GHS3D. The size defined for the Blsurf surface mesh is :math:`2\mathit{mm}`.

mesh unit: meters

Number of knots: 2268

Number of meshes and type: 10690 TETRA4


.. image:: images/10000000000005150000040542FF5F9D3E811ED7.png
    :width: 2.7083in
    :height: 2.1417in


.. _RefImage_10000000000005150000040542FF5F9D3E811ED7.png:

Figure 3.2-1:

An automatic refinement procedure is put in place. After refinement around the crack bottom, the characteristic length of an element near the crack bottom is :math:`5\mu m`.

The refined mesh has the following characteristics:


* Number of knots: 18325


* Number of meshes and type: 103853 TETRA4


.. image:: images/100000000000051700000405D7469EE9F7A0FF0F.png
    :width: 4.0709in
    :height: 3.2165in


.. _RefImage_100000000000051700000405D7469EE9F7A0FF0F.png:


.. image:: images/100000000000051700000405449FBB0A2C821AA5.png
    :width: 6.889in
    :height: 5.4402in


.. _RefImage_100000000000051700000405449FBB0A2C821AA5.png:


Boundary conditions and loads
-------------------------------------


* A traction force is applied to the upper and lower faces and the one on the right;


* Rigid modes are blocked in the following way:

node :math:`A`: :math:`\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0`, node :math:`B`: :math:`\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0`, and node :math:`C`: :math:`\mathit{DX}\mathrm{=}\mathit{DZ}\mathrm{=}0`


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

The position of the deepest crack bottom point is tested. This is equivalent to testing the maximum coordinate along the :math:`Y` axis of the points at the bottom of the crack after a propagation step.


.. csv-table::

    "**Identification**", "**Reference Type**", "**Reference Value**", "**% Tolerance**"
    ":math:`\mathit{max}(Y)` ", "'SOURCE_EXTERNE'", "173.3 10-6"," 5%"