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


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

It is a nonlinear elasticity calculation under the hypothesis of small displacements, in plane deformations. The crack is opened in pure I mode. Only half of the structure is represented by symmetry.


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

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

 -Number of knots: 8936

 -Number of elements:

     -Triangles: 6494

     -quadrangles: 5408

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}`

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).


.. image:: images/10000201000001700000026D166DD6E2353657AC.png
    :width: 2.5866in
    :height: 4.3646in


.. _RefImage_10000201000001700000026D166DD6E2353657AC.png:


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**", "**Surface effort**
    **taxed**
    (MPa)", "**Reference**: :math:`G(N/m)`
    From POST_K1_K2_K3 (method 3)", "**Tolerance**
    **(%)**"
    "1"," :math:`\mathrm{0,7}\ast \text{SY}=105` ", "1.13702E+05", "0.3"
    "2"," :math:`\text{SY}=150` ", "2.85869E+05", "0.3"
    "3"," :math:`3\ast \text{SY}=450` ", "3.42359E+06", "0.2"