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


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

In this modeling, the upwind fast marching UPWIND method is tested for crack propagation.

Level-sets are determined by solving the updating equations by schema with finite differences.


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

The same mesh as in modeling 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 KI:
~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**difference**"
    "CALC_G ", "", "", ""
    "KI_1 ", "4.174911 106", "4.205998 106", "4.174911 106", "0.739%"
    "KI_2 ", "4.602545 106", "4.632857 106", "4.602545 106", "0.654%"
    "KI_3 ", "5.067525 106", "5.094923 106", "5.067525 106", "0.538%"
    "KI_4 ", "5.575881 106", "5.599079 106", "5.575881 106", "0.414%"
    "KI_5 ", "6.134452 106", "6.153487 106", "6.153487 106", "0.309%"
    "KI_6 ", "6.751139 106", "6.767759 106", "0.24%"
    "KI_7 ", "7.435204 106", "7.453097 106", "7.435204 106", "0.24%"
    "KI_8 ", "8.197634 106", "8.222429 106", "8.197634 106", "0.302%"
    "KI_9 ", "9.051616 106", "9.090524 106", "9.051616 106", "0.428%"
    "KI_10 ", "1.0013134 107", "1.0074102 107", "1.0013134 107", "0.605%"
    "KI_11 ", "1.1101774 107", "1.1191940 107", "1.1101774 107", "0.805%"
    "KI_12 ", "1.2341792 107", "1.2464967 107", "1.2341792 107", "0.99%"
    "KI_13 ", "1.3763566 107", "1.3916354 107", "1.3763566 107", "1.098%"
    "KI_14 ", "1.5405615 107", "1.5571606 107", "1.5571606 107", "1.065%"
    "KI_15 ", "1.7317423 107", "1.7317423 107", "1.7317423 107", "0.809%"



Results on KII:
~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**"
    "CALC_G ", "", ""
    "KII_1 ", "-294.54", "0"
    "KII_2 ", "-310.00", "0"
    "KII_3 ", "-330.90", "0"
    "KII_4 ", "-357.05", "0"
    "KII_5 ", "-389.44", "0"
    "KII_6 ", "-428.98", "0"
    "KII_7 ", "-476.90", "0"
    "KII_8 ", "-534.75", "0"
    "KII_9 ", "-604.47", "0"
    "KII_10 ", "-68,57", "0"
    "KII_11 ", "-790,30", "0"
    "KII_12 ", "-913.84", "0"
    "KII_13 ", "-1064.72", "0"
    "KII_14 ", "-1250.30", "0"
    "KII_15 ", "-1480.53", "0"