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

The crack bottom is closed. We calculate :math:`G`.


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


.. image:: images/10000000000002EC00000242F33EBCD25DBBD74F.png
    :width: 5.6591in
    :height: 4.3547in


.. _RefImage_10000000000002EC00000242F33EBCD25DBBD74F.png:

The advantage of this modeling is to represent the entire crack background, which is a closed curve, without taking advantage of the symmetries of the problem.

Only traction loading is taken into account.


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

Number of knots: 11114

Number of meshes and type: 2432 PENTA15

The middle nodes of the edges of the elements touching the bottom of the crack are moved to a quarter of these edges.


note
--------

     The values of :math:`G` are tested for :math:`\mathrm{\theta }` fields defined as a function of radius (R_ INF and R_ SUP)

     and the number of layers (NB_COUCHE_INFet NB_COUCHE_SUP).

The keyword SYME is used in the CALC_G operator to automatically multiply by two the energy restoration rate calculated on a single lip of the crack, when the FOND_FISS operand is absent. When FOND_FISS is present, symmetry information is retrieved directly from the fond_fiss concept created via DEFI_FOND_FISS.

The principle is the same for POST_K1_K2_K3. The indication of the symmetry induces the calculation of the stress intensity factors and the energy restoration rate G_ IRWIN by interpolation of the movements of a single lip of the crack. Moving the middle nodes of the edges of the elements touching the bottom of the crack to a quarter of these edges would improve the accuracy of the calculation.


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


.. csv-table::

    "**Identification**", "**Reference**", "**Reference type**", ":math:`\text{\%}` **tolerance**"
    "G local Node :math:`N403` - Discretization LINEAIRE, R_ INF and R_ SUP ", "11.586"," ANALYTIQUE ", "3.0"
    "G local Node :math:`N2862` - Discretization LINEAIRE, R_ INF and R_ SUP ", "11.586"," ANALYTIQUE ", "2.0"
    "G local Node :math:`N375` - Discretization LINEAIRE, R_ INF and R_ SUP ", "11.586"," ANALYTIQUE ", "3.0"
    "G local Node :math:`N292` - Discretization LINEAIRE, R_ INF and R_ SUP ", "11.586"," ANALYTIQUE ", "2,4"
    ":math:`\mathit{max}(G\mathit{local})` - Discretization LINEAIRE, R_ INF R_ SUP ", "11.59"," ANALYTIQUE ", "2.5"
    ":math:`\mathit{min}(G\mathit{local})` - Discretization LINEAIRE, R_ INF R_ SUP ", "11.59"," ANALYTIQUE ", "2.0"
    "G local point :math:`1` Discretization LINEAIRE/NB_POINT_FOND =33, R_ INF and R_ SUP ", "11.586"," ANALYTIQUE ", "1.0"
    "G local point :math:`13` Discretization LINEAIRE/NB_POINT_FOND =33, R_ INF and R_ SUP ", "11.586"," ANALYTIQUE ", "1.0"
    "G local point :math:`21` Discretization LINEAIRE/NB_POINT_FOND =33, R_ INF and R_ SUP ", "11.586"," ANALYTIQUE ", "1.0"
    "G local point :math:`33` Discretization LINEAIRE/NB_POINT_FOND =33, R_ INF and R_ SUP ", "11.586"," ANALYTIQUE ", "1.0"
    "G local Node :math:`N403` - Discretization LINEAIRE, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.586"," ANALYTIQUE ", "3.0"
    "G local Node :math:`N2862` - Discretization LINEAIRE, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.586"," ANALYTIQUE ", "2.0"
    "G local Node :math:`N375` - Discretization LINEAIRE, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.586"," ANALYTIQUE ", "3.0"
    "G local Node :math:`N292` - Discretization LINEAIRE, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.586"," ANALYTIQUE ", "2,4"
    ":math:`\mathit{max}(G\mathit{local})` - Discretization LINEAIRE, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.59"," ANALYTIQUE ", "2.5"
    ":math:`\mathit{min}(G\mathit{local})` - Discretization LINEAIRE, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.59"," ANALYTIQUE ", "2.0"
    "G local point :math:`1` Discretization LINEAIRE/NB_POINT_FOND =33/=33, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.586"," ANALYTIQUE ", "1.0"
    "G local point :math:`13` Discretization LINEAIRE/NB_POINT_FOND =33/=33, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.586"," ANALYTIQUE ", "1.0"
    "G local point :math:`21` Discretization LINEAIRE/NB_POINT_FOND =33/=33, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.586"," ANALYTIQUE ", "1.0"
    "G local point :math:`33` Discretization LINEAIRE/NB_POINT_FOND =33/=33, NB_COUCHE_INF and NB_COUCHE_SUP ", "11.586"," ANALYTIQUE ", "1.0"