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


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

In this modeling, the extended finite element method (:math:`\text{X-FEM}`) is used. We define an enrichment radius :math:`{R}_{\mathit{ENRI}}=0.5`. Finite elements are linear.


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

Same as modeling A.


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'", "0.9648"," 1.0%"
    "CALC_G /K2 ", "'ANALYTIQUE'", "0.00", "0.00", "0.001"
    "CALC_G /G", "'ANALYTIQUE'", "9.3084E-7"," 2.0%"



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

By activating the contact algorithm, we obtain the solution moving in the vicinity of the crack given to [] (to be compared with post-treatment).

On the other hand, we find an analytical conclusion, namely the abscissa of the point at which the crack begins to open:

:math:`c=-\frac{a}{3}\approx -0.33`

Indeed, in post-treatment, we analyzed the contact pressures to determine the abscissa of the last point of contact. Graphically, it is estimated that the pressure falls sharply around the abscissa point :math:`{x}_{c}\approx -0.325`, which validates the estimation hypothesis of :math:`{K}_{I}`.


.. image:: images/100000000000046100000351FE7542CF6FE32CD0.png
    :width: 4.5047in
    :height: 3.4701in


.. _RefImage_100000000000046100000351FE7542CF6FE32CD0.png:

Figure 4.4-1: contact crack closure facies


.. image:: images/10000000000015BD00000F2AD6280212F23A7796.png
    :width: 5.7181in
    :height: 3.9882in


.. _RefImage_10000000000015BD00000F2AD6280212F23A7796.png:

Figure 4.4-2: contact pressure along the crack