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


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

It is a nonlinear elasticity calculation under the hypothesis of small displacements, in plane deformations. The crack is opened in mixed mode. The entire structure is shown.


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

The mesh at the input of the test case into a linear mesh with the following characteristics:

 -Number of knots: 17691

 -Number of elements:

     -Triangles: 12988

     -quadrangles: 10816

The radius of the radiating domain at the bottom of the crack is :math:`25\mathit{mm}`. The size of the elements connected to the bottom of the crack is :math:`{10}^{-3}\mathit{mm}`

It is obtained by "mirroring" the modeling A mesh.

At the execution of the test case, a new quadratic mesh with elements of BARSOUM at the bottom of the crack is created by executing the commands CREA_MAILLAGE (keyword LINE_QUAD) then MODI_MAILLAGE (keyword MODI_MAILLE, option NOEUD_QUART).


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

The results obtained for three different integration rings are compared:


.. csv-table::

    "* crown 1: :math:`{R}_{\mathit{inf}}=10\mathit{mm}` ", ", "; :math:`{R}_{\text{sup}}=15\mathit{mm}`"
    "* crown 2: :math:`{R}_{\mathit{inf}}=15\mathit{mm}` ", ", "; :math:`{R}_{\text{sup}}=20\mathit{mm}`"
    "* crown 3: :math:`{R}_{\mathit{inf}}=20\mathit{mm}` ", ", "; :math:`{R}_{\text{sup}}=25\mathit{mm}`"


The reference values of G from method 3 POST_K1_K2_K3 selected as well as the associated details are provided in the table below.


.. csv-table::

    "**Calculation instant**", "**Imposed relocation** :math:`\mathrm{\delta }`
    **(in mm)**", "**Reference**: :math:`G(N/m)`
    From POST_K1_K2_K3 (method 3)", "**Tolerance**
    **(%)**"
    "1"," :math:`\mathrm{0,7}\ast \text{Dp}=200` ", "1.36596E+04", "0, 5"
    "2"," :math:`\text{Dp}=286` ", "2.74150E+04", "0, 4"
    "3"," :math:`3\ast \text{Dp}=857` ", "1.68193E+05", "0, 3"


Where :math:`\mathit{Dp}=L\mathrm{.}\mathit{SY}/E`.