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


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

In this modeling, the geometric method is tested for crack propagation. The level-sets are recalculated at each propagation step.


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

Here we use the same mesh as in modeling :math:`A`.


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

For each propagation step, we test the value of the stress intensity factors :math:`{K}_{I}` and :math:`{K}_{\mathrm{II}}` given by CALC_G.


Results on :math:`{K}_{I}`:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A relative non-regression test is carried out on :math:`{K}_{I}` compared to :math:`{K}_{I\mathrm{maillage}}` with an accuracy of :math:`\text{3\%}`.


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**Difference (** :math:`\text{\%}` **)**"
    "CALC_G ", "", "", ""
    "KI_1 ", "2.4396 10-1", "2.43961 10-1", "2.43961 10-1", "-2.03 10-4%"
    "KI_2 ", "2.9026 10-1", "2.90147 10-1"," 0.04%"
    "KI_3 ", "3.3057 10-1", "3.30840 10-1"," 0.08%"
    "KI_4 ", "3.7665 10-1", "3.75984 10-1"," 0.18%"
    "KI_5 ", "4.3352 10-1", "4.33606 10-1"," 0.01%"
    "KI_6 ", "4.966710-1", "4.96975 10-1"," 0.06%"
    "KI_7 ", "5,7348 10-1", "5,73785 10-1"," 0.05%"
    "KI_8 ", "6.7175 10-1", "6.70222 10-1"," 0.23%"
    "KI_9 ", "7,8989 10-1", "7,89716 10-1"," 0.02%"
    "KI_10 ", "9.3925 10-1", "9.39463 10-1"," 0.02%"
    "KI_11 ", "1.15158", "1.15201"," 0.04%"
    "KI_12 ", "1.45290", "1.45163"," 0.09%"
    "KI_13 ", "1.92063", "1.91885"," 0.09%"



Results on :math:`{K}_{\mathrm{II}}`:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For this test, we want :math:`{K}_{\mathrm{II}}` to be such as :math:`{K}_{\mathrm{II}}={K}_{\mathrm{IIref}}\pm {3.10}^{-2}` (test in absolute).


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**Difference %**"
    "CALC_G ", "", "", ""
    "KII_1 ", "4,27721 10-2", "4,27722 10-2", "3,92 10-8"
    "KII_2 ", "5,49728 10-5", "1,21013 10-4", "6,6 10-5"
    "KII_3 ", "8,31292 10-3", "7,10255 10-3", "1,21 10-3", "1,21 10-3"
    "KII_4 ", "1.41042 10-3", "1.94683 10-3", "5.36 10-4"
    "KII_5 ", "1.93652 10-4", "1.20266 10-3", "7.34 10-4"
    "KII_6 ", "7.04563 10-4", "8.82542 10-4", "1.78 10-4", "1.78 10-4"
    "KII_7 ", "0.0", "-1.23199 10-3", "1.23 10-3", "1.23 10-3"
    "KII_8 ", "0.0", "-3.54655 10-3", "3.55 10-3", "3.55 10-3"
    "KII_9 ", "0.0", "-4.54122 10-3", "4.54 10-3", "4.54 10-3"
    "KII_10 ", "0.0", "-8,18030 10-3", "8,18 10-3", "8,18 10-3"
    "KII_11 ", "0.0", "-1.55772 10-2", "1.56"
    "KII_12 ", "0.0", "-2.31849 10-2", "2.32"
    "KII_13 ", "0.0", "-3.52229 10-2", "3.52"