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

In this modeling, the extended finite element method (:math:`\text{X-FEM}`) is used. A radius of geometric enrichment is defined with a number of element layers equal to 3.


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

The structure is modelled by a regular mesh (identical to modeling :math:`A`) composed of :math:`100\times 100` QUAD4, respectively along the :math:`x,y` axes. The crack is not meshed.


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

For each value of the angle :math:`\theta` (:math:`0°` and :math:`45°`), and for each load: internal force (:math:`\mathrm{FI}`) and gravity (:math:`\mathrm{PESA}`), we test the value of the stress intensity factor :math:`\mathrm{KI}` given by CALC_G (for the two crack bottoms) as well as that given by K1 of POST_K1_K2_K3 (for the 2nd crack bottom). We also test the value of :math:`G` given by CALC_G, option CALC_G, which we compare to that obtained by CALC_G, option CALC_K_G.

For method :math:`G-\mathrm{thêta}` (command CALC_G), the following theta field crowns are chosen: :math:`{R}_{\mathrm{inf}}=\mathrm{0,1}a` and :math:`{R}_{\text{sup}}=\mathrm{0,3}a`;

For the method by extrapolation of movement jumps (POST_K1_K2_K3), the maximum curvilinear abscissa is equal to :math:`\mathrm{0,3}a`.


Results for :math:`\theta \mathrm{=}0°`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Tolerance**"
    "CALC_G ", "", ""
    "FI background 1: K1", "5013.598", "0.1%"
    "FI background 2: K1", "5013.586", "0.1%"
    "PES background1: K1", "5013.598", "0.1%"
    "PES background2: K1", "5013.586", "0.1%"
    "FI background 1: G", "1.19751E-04"," 0.1%"
    "PES background 1: G", "1.19751E-04"," 0.1%"
    "POST_K1_K2_K3 ", "", ""
    "FI background 2: K1", "5069.12"," 0.1%"
    "PES background2: K1", "5069.12"," 0.1%"



Results for :math:`\theta =45°`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Identification**", "**Code_Aster**", "**Tolerance**"
    "CALC_G ", "", ""
    "FI background 1: K1", "2454.40"," 0.1%"
    "FI background 2: K1", "2592.14","" 0.1%"
    "PES background1: K1", "2454.40"," 0.1%"
    "PES background2: K1", "2592.14"," 0.1%"
    "FI background 1: G", "5.644E-05"," 0.1%"
    "PES background 1: G", "5.644E-05"," 0.1%"
    "POST_K1_K2_K3 ", "", ""
    "FI background 2: K1", "2589.86"," 0.1%"
    "PES background2: K1", "2589.86"," 0.1%"