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


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

In this modeling, the simplex method is tested for crack propagation.

Level-sets are determined by solving the updating equations.


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 KI:
~~~~~~~~~~~~~~~~~~~

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{5\%}`.


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**Difference (** :math:`\text{\%}` **)**"
    "CALC_G ", "", "", ""
    "KI_1 ", "2.43961 10-1", "2.43961 10-1", "2.43961 10-1", "2.03 10-4%"
    "KI_2 ", "0.29056", "2.90147 10-1"," 0.1%"
    "KI_3 ", "0.3308", "3.30840 10-1", "3.910-4%"
    "KI_4 ", "0.3759", "3.75984 10-1"," 0.02%"
    "KI_5 ", "0.43355", "4.33606 10-1", "7.9 10-4%"
    "KI_6 ", "0.497", "4,96975 10-1"," 0.025%"
    "KI_7 ", "0.573", "5,73785 10-1"," 0.12%"
    "KI_8 ", "0.6705", "6,70222 10-1"," 0.03%"
    "KI_9 ", "0.7899", "7,89716 10-1"," 0.03%"
    "KI_10 ", "0.93757", "9.39463 10-1"," 0.2%"
    "KI_11 ", "1.1508", "1.15201", "1.15201"," 0.11%"
    "KI_12 ", "1.4472", "1.45163"," 0.30%"
    "KI_13 ", "1.8923", "1.91885"," 1.38%"



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

For this test, we want :math:`{K}_{\mathrm{II}}` to be as :math:`{K}_{\mathrm{II}}={K}_{\mathrm{IIref}}\pm {5.10}^{-2}`. (absolute test)


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**Difference**"
    "CALC_G ", "", "", ""
    "KII_1 ", "0.04277", "4.27722 10-2", "3.92 10-8"
    "KII_2 ", "-0.00019", "1.21013 10-4", "3.1 10-4", "3.1 10-4"
    "KII_3 ", "0.00864", "7,10255 10-3", "1,54 10-3", "1,54 10-3"
    "KII_4 ", "0.00068", "1.94683 10-3", "0.0013"
    "KII_5 ", "0.001988", "1.20266 10-3", "7.85 10-4"
    "KII_6 ", "-0.0003965", "8.82542 10-4", "1.27 10-3", "8.82542 10-3"
    "KII_7 ", "-0.001049", "-1.23199 10-3", "1.82 10-4", "-1.82 10-4"
    "KII_8 ", "-0.01141", "-3,54655 10-3", "7,86 10-3", "7,86 10-3"
    "KII_9 ", "0.006572", "-4.54122 10-3", "0.0111"
    "KII_10 ", "0.001981", "-8,18030 10-3", "0.01"
    "KII_11 ", "-0.038036", "-1.55772 10-2", "0.0224"
    "KII_12 ", "-0.012783", "-2,31849 10-2", "0.0104"
    "KII_13 ", "-0.02314", "-3,52229 10-2", "0.012"