Modeling A: Modeling FEM 2d-AXI
========================================


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

In this modeling, the crack is meshed (case FEM) and the structure is modeled using 2D-axisymmetry.


.. image:: images/10000000000001930000031E48D3803877FFB38C.png
    :width: 2.0984in
    :height: 4.1575in


.. _RefImage_10000000000001930000031E48D3803877FFB38C.png:

Figure 3.1-1:2D-axi mesh (FEM)


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

Number of knots: 5211

Number of meshes and type: 2550 TRIA6

The characteristic length of an element near the crack bottom is h = 0.025m.

The middle nodes of the edges of the elements touching the bottom of the crack are moved to a quarter of these edges (Barsoum elements).


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


* A surface tensile force is applied to the upper, lower and right sides;


* The movements following :math:`\mathit{Ox}` of the nodes of the axis of rotation are blocked, as recommended for axisymmetric models;


* The rigid mode of movement along the :math:`\mathit{Oy}` axis is blocked by blocking a node along this axis.


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

The values of :math:`{K}_{I}` and :math:`{K}_{\mathit{II}}` at the bottom of the crack obtained with the operators CALC_G and POST_K1_K2_K3 are tested. These values are compared to the analytical solution.

The theta field integration crowns for command CALC_G are:

:math:`{R}_{\text{inf}}\mathrm{=}2h` and :math:`{R}_{\text{sup}}\mathrm{=}5h`.

The ABS_CURV_MAXI parameter for the POST_K1_K2_K3 operator is chosen by default.


Values from CALC_G
~~~~~~~~~~~~~~~~~~~~~~~~~~~

The values are in :math:`\mathit{Pa}\mathrm{.}\sqrt{m}`.


.. csv-table::

    "**Identification**", "**Reference Type**", "**Reference Value**", "**% Tolerance**"
    ":math:`{K}_{I}` ", "'ANALYTIQUE'", "1.177 106"," 2%"
    ":math:`{K}_{\mathit{II}}` ", "'ANALYTIQUE'", "0.3153 106"," 2%"



Values from POST_K1_K2_K3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The values are in :math:`\mathit{Pa}\mathrm{.}\sqrt{m}`.


.. csv-table::

    "**Identification**", "**Reference Type**", "**Reference Value**", "**% Tolerance**"
    ":math:`{K}_{I}` ", "'ANALYTIQUE'", "1.177 106"," 2%"
    ":math:`{K}_{\mathit{II}}` ", "'ANALYTIQUE'", "0.3153 106"," 12%"