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


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

Method MAILLAGE is used by PROPA_FISS to calculate the new position of the bottom of the crack. Stress intensity factors are calculated using operator POST_K1_K2_K3.

The same model as that described for modeling A is used.


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

The same mesh as that of modeling A. is used.


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

The position of the bottom of the crack after four propagations is as follows:


.. csv-table::

    "**Propagation**", "**Coordinate** :math:`x` ", "**Coordinate** :math:`y`"
    "4", "42.05", "20.62"


The non-regression of these values is tested with a relative precision of 0.1%.

For information, we can calculate the error on the coordinates of the crack bottom with respect to the reference solution (modeling :math:`A`):


.. csv-table::

    "**Coord**", "**Current Value**
    [:math:`\mathit{mm}` **]**", "**Reference value**
    [:math:`\mathit{mm}` **]**", "**Error**
    [:math:`\mathit{mm}` **]**"
    ":math:`x` ", "42.05", "42.14", "-0.09"
    ":math:`y` ", "20.62", "20.6", "0.02"


For consistency, we use a tolerance equal to that which will be used for models :math:`C`, :math:`D` and :math:`E`, i.e. :math:`2.0\mathrm{mm}` (see these models for more details).

It can be considered here that the position of the bottom calculated by this modeling is almost the same as the reference position.


notes
---------

The calculated background position respects the tolerance used. This means that the position of the crack bottom calculated by the mesh plus POST_K1_K2_K3 method is very close to the reference one.