Modeling A
==============


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

In this modeling, the mesh method is tested for crack propagation. Level-sets are determined by orthogonal projection onto the segments making up the crack.


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

The structure is modelled by a regular mesh composed of :math:`90\times 30` QUAD4, respectively along the axes :math:`x`, :math:`y`. The crack is not meshed.


.. image:: images/10000000000004590000033074BD265CFFB3F105.png
    :width: 5.2638in
    :height: 1.6575in


.. _RefImage_10000000000004590000033074BD265CFFB3F105.png:

**Figure** 3.2-a **: mesh of the cracked plate**


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}` with an accuracy of :math:`{2.10}^{-3}`.


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**difference**"
    "CALC_G ", "", "", ""
    "KI_1 ", "2,43961 10-1", "2,43961 10-1", "-"
    "KI_2 ", "2.90147 10-1", "2.90147 10-1", "-"
    "KI_3 ", "3,30840 10-1", "3,30840 10-1", "-"
    "KI_4 ", "3.75984 10-1", "3.75984 10-1", "-"
    "KI_5 ", "4.33606 10-1", "4.33606 10-1", "-"
    "KI_6 ", "4.96975 10-1", "4.96975 10-1", "-"
    "KI_7 ", "5,73785 10-1", "5,73785 10-1", "-"
    "KI_8 ", "6,70222 10-1", "6,70222 10-1", "-"
    "KI_9 ", "7,89716 10-1", "7,89716 10-1", "-"
    "KI_10 ", "9.39463 10-1", "9.39463 10-1", "-"
    "KI_11 ", "1.15201", "1.15201", "" 1.15201", "-"
    "KI_12 ", "1.45163", "1.45163", "-"
    "KI_13 ", "1.91885", "1.91885", "-"



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 {10}^{-2}`.


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Reference**", "**Difference**"
    "CALC_G ", "", "", ""
    "KII_1 ", "4,27722 10-2", "4,27722 10-2", "-"
    "KII_2 ", "1.21013 10-4", "1.21013 10-4", "-"
    "KII_3 ", "7,10255 10-3", "7,10255 10-3", "-"
    "KII_4 ", "1.94683 10-3", "1.94683 10-3", "-"
    "KII_5 ", "1.20266 10-3", "1.20266 10-3", "-"
    "KII_6 ", "8,82542 10-4", "8,82542 10-4", "-"
    "KII_7 ", "-1,23199 10-3", "-1,23199 10-3", "-"
    "KII_8 ", "-3,54655 10-3", "-3,54655 10-3", "-"
    "KII_9 ", "-4.54122 10-3", "-4.54122 10-3", "-"
    "KII_10 ", "-8,18030 10-3", "-8,18030 10-3", "-"
    "KII_11 ", "-1.55772 10-2", "-1.55772 10-2", "-"
    "KII_12 ", "-2,31849 10-2", "-2,31849 10-2", "-"
    "KII_13 ", "-3,52229 10-2", "-3,52229 10-2", "-"



Additional results
-------------------------


.. image:: images/1000020000000213000000CCCA8374103A6CB74B.png
    :width: 4.7102in
    :height: 1.6146in


.. _RefImage_1000020000000213000000CCCA8374103A6CB74B.png:

**Figure** 3.4-a **: Comparison of the path obtained with the mesh method to the paths of the study by Mariani and Perego**

On this, we can see: in black the numerical results of Mariani and Perego, in dotted lines the experimental results and in blue the results of the Code_Aster mesh method. The mesh method gives results similar to the experimental data.