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


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

In this modeling, the extended finite element method (:math:`\text{X-FEM}`) is used. Finite elements are linear.

We define a radius of enrichment of elements X- FEM crack bottom :math:`{R}_{\mathit{ENRI}}=0.5`. This enrichment radius makes it possible to more accurately capture the singular asymptotic solution at the bottom of the crack. The relatively large radius size (25% of the crack length) does not introduce conditioning problems, taking into account the new approximation at the bottom of the crack [:ref:`R7.02.12 <R7.02.12>`].


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

The mesh at the center of the test piece is refined in order to optimize the calculation of the solution moving in the vicinity of the crack [].

NOMBRE OF NOEUDS 4088

NOMBRE OF MAILLES 4360

SEG2 80

TRIA3 466

QUAD4 3814


.. image:: images/10000000000000F4000001E9763A66D7B72C0409.png
    :width: 2.3972in
    :height: 4.8043in


.. _RefImage_10000000000000F4000001E9763A66D7B72C0409.png:

Figure 3.2-1: Domain mesh


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

On the background of the crack in opening :math:`P2=(a\mathrm{,0})`, the stress intensity factor :math:`{K}_{I}` given by the command CALC_G is tested, compared to the analytical value explained in paragraph [:ref:`5 <RefNumPara__20359_821110035>`].

For method :math:`G-\mathit{thêta}` (command CALC_G), the following crowns of the theta field are chosen:


.. csv-table::

    "", "Crown 1", "Crown 2", "Crown 3", "Crown 3", "Crown 4", "Crown 5", "Crown 6"
    "Rinf", "0.1", "0.2", "0.2", "0.3", "0.3", "0.1", "0.2"
    "Rsup", "0.2", "0.3", "0.3", "0.3", "0.4", "0.4", "0.4"



.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Precision**"
    "CALC_G /K1 ", "'ANALYTIQUE'", "0.88629"," 1.0%"
    "CALC_G /K2 ", "'ANALYTIQUE'", "0.00"," 0.001%"
    "CALC_G /G ", "'ANALYTIQUE'", "7.85514E-07"," 2.0%"



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

Here is the displacement field calculated by Aster, without activating the crack lip contact algorithm:


.. image:: images/10000201000000FF0000018D5C94DA5B3DFF8B8D.png
    :width: 2.3972in
    :height: 3.7327in


.. _RefImage_10000201000000FF0000018D5C94DA5B3DFF8B8D.png:

Figure 3.4-1: Field of movement (with offset)