C modeling
==============


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

In this modeling, the upwind method is tested for crack propagation. Level-sets are determined by solving the updating equations by schema with finite differences.


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

The same mesh as in modeling :math:`A` (§2.1) is used here.


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

For each propagation step, we test the value of the stress intensity factors :math:`{K}_{I}` and :math:`{K}_{\mathit{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\mathit{maillage}}` with an accuracy of :math:`\text{3\%}`.

.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**Difference (** :math:`\text{\%}` **)**"
    "CALC_G ", "", "", ""
    "KI_1 ", "0.243960", "2,43961 10-1", "2.03E -04%"
    "KI_2 ", "0.290552", "2.90147 10-1", "0.14%"
    "KI_3 ", "0.330871", "3,30840 10-1", "9.645E -03%"
    "KI_4 ", "0.375936", "3.75984 10-1", "0.0126%"
    "KI_5 ", "0.433524", "4.33606 10-1", "0.02%"
    "KI_6 ", "0.496884", "4.96975 10-1", "0.02%"
    "KI_7 ", "0.572963", "5.73785 10-1", "0.14%"
    "KI_8 ", "0.673340", "6.70222 10-1", "0.46%"
    "KI_9 ", "0.788694", "7.89716 10-1", "0.13%"
    "KI_10 ", "0.94306", "9.39463 10-1", "0.39%"
    "KI_11 ", "1.151406", "1.15201", "1.15201", "0.05%"
    "KI_12 ", "1.44998", "1.45163", "0.11%"
    "KI_13 ", "1.92206", "1.9185", "0.17%"



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

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


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**Difference**"
    "CALC_G ", "", "", ""
    "KII_1 ", "0.0427721", "4.27722 10-2", "3.92E-08", "4.27721"
    "KII_2 ", "-0.0001827", "1.21013 10-4", "3.04 E-04", "3.04 E-04"
    "KII_3 ", "0.0086350", "7.10255 10-3", "1.53E-03", "1.53E-03"
    "KII_4 ", "0.0006797", "1.94683 10-3", "1.27E-03", "1.27E-03"
    "KII_5 ", "0.0019676", "1.20266 10-3", "7.64E-04", "1.20266 10-3"
    "KII_6 ", "-0.0001195", "8,82542 10-4", "1.00E-03"
    "KII_7 ", "-0.0009619", "-1.23199 10-3", "2.70E-04", "-1.23199 10-3"
    "KII_8 ", "-0.0002964", "-3,54655 10-3", "3.84E-03", "3.84E-03"
    "KII_9 ", "-0.0027228", "-4.54122 10-3", "1.82E-03", "1.82E-03"
    "KII_10 ", "-0.0258299", "-8,18030 10-3", "0.017"
    "KII_11 ", "-0.0041077", "-1.55772 10-2", "0.01146"
    "KII_12 ", "-0.0283523", "-2,31849 10-2", "-2.31849 10-2", "5.17E-03"
    "KII_13 ", "-0.0304681", "-3,52229 10-2", "4.75E-03"