B modeling
==============


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

In this modeling, the crack is not meshed (case X- FEM).

In order to obtain better precision on the results, the initial free mesh was refined at the crack bottom using the MACR_ADAP_MAIL command.


.. image:: images/10000000000003070000032A997B60CD244DA00A.png
    :width: 4.0354in
    :height: 4.2201in


.. _RefImage_10000000000003070000032A997B60CD244DA00A.png:

Figure 4.1-1: Refined structure mesh


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

Number of knots: 1146

Number of meshes and type: 64573 TETRA4

The characteristic length of an element near the crack bottom is :math:`\mathrm{0,07}m`.


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

The choice of numerical parameters for post-processing SIFs is identical to that made for modeling A.

In addition, in order to smooth the results of CALC_G_XFEM (unavoidable on a free mesh), it is necessary to post-treat SIFs only at a limited number of points, distributed uniformly along the crack bottom. Here 21 post-treatment points are selected (initially, there are 289 points along the crack bottom). It also reduces post-processing time CPU.

In the same way, 21 post-processing points are chosen for POST_K1_K2_K3.


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

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


.. csv-table::

    "**Identification**", "**Reference Type**", "**Reference Value**", "**% Tolerance**"
    ":math:`\mathit{max}({K}_{I})` ", "'ANALYTIQUE'", "7,978 105"," 6%"
    ":math:`\mathit{min}({K}_{I})` ", "'ANALYTIQUE'", "7,978 105"," 3%"
    ":math:`{K}_{\mathit{II}}` in :math:`\omega \mathrm{=}0°` ", "'ANALYTIQUE'", "9,386 105"," 14%"
    ":math:`{K}_{\mathit{III}}` in :math:`\omega \mathrm{=}90°` ", "'ANALYTIQUE'", "6,570 105"," 10%"



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:`\mathit{max}({K}_{I})` ", "'ANALYTIQUE'", "7,978 105"," 1%"
    ":math:`\mathit{min}({K}_{I})` ", "'ANALYTIQUE'", "7,978 105"," 3%"
    ":math:`{K}_{\mathit{II}}` in :math:`\omega \mathrm{=}0°` ", "'ANALYTIQUE'", "9,386 105"," 2%"
    ":math:`{K}_{\mathit{III}}` in :math:`\omega \mathrm{=}90°` ", "'ANALYTIQUE'", "6,570 105"," 2%"



notes
---------

It can be seen that, as for modeling A, CALC_K_G_XFEM gives less accurate results than POST_K1_K2_K3. For curved fronts, it is better to prefer the post-treatment of SIF with POST_K1_K2_K3, to maintain an acceptable error in propagating a crack. The X- FEM results are as accurate as the results with a mesh crack (modeling A), which further reinforces the value of using X- FEM compared to the FEM method.

A very good agreement is obtained between the values of K2 and K3 calculated with POST_K1_K2_K3 and the values of the analytical solution (see).

In addition, no interference effect is observed at the edges, as is the case in modeling A. With a meshed crack, we in fact note the appearance of shear at the through points of the crack that is difficult to explain (see).


.. image:: images/10000000000019C8000013ECA8F5A5925B6ECE56.png
    :width: 5.7402in
    :height: 3.9453in


.. _RefImage_10000000000019C8000013ECA8F5A5925B6ECE56.png:

Figure 4.4-1: mode 2 along the forehead as a function of the curvilinear abscissa


.. image:: images/1000000000001B680000135EAA8CEF53BD2D6182.png
    :width: 5.3626in
    :height: 3.5665in


.. _RefImage_1000000000001B680000135EAA8CEF53BD2D6182.png:

Figure 4.4-2: mode 3 along the forehead as a function of the curvilinear abscissa