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


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


.. image:: images/100000000000045F0000030353DEDBF695FE6177.png
    :width: 6.889in
    :height: 4.5811in


.. _RefImage_100000000000045F0000030353DEDBF695FE6177.png:

The field :math:`\theta` is calculated then the energy release rate :math:`G`, the stress coefficients :math:`{K}_{1}` and :math:`{K}_{2}`, the energy recovery rate obtained by the formula d'IRWIN, the direction of propagation of the crack, are calculated.


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

Number of knots: 673

Number of meshes and types: 112 QUAD8 meshes and 142 TRIA6 meshes


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

The values tested are the energy recovery rate calculated by the theta method and the energy recovery rate calculated by the formula IRWIN using the stress intensity coefficients :math:`{K}_{1}` and :math:`{K}_{2}`.


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    "Crowns 1 to 6 :math:`G` "," :math:`2.3093{10}^{\mathrm{-}3}` ", "< 1%"
    "Crowns 1 to 6 :math:`G` (IRWIN)", ":math:`2.3093{10}^{\mathrm{-}3}` ", "< 1%"
    "Crowns 1 to 6 :math:`{K}_{1}` "," :math:`24.491` ", "< 1%"
    "Crowns 1 to 6 :math:`{K}_{2}` "," :math:`0.` ", "absolute"



note
--------

The calculation of :math:`G`, :math:`{K}_{1}`, :math:`{K}_{2}`, :math:`G` (IRWIN) :math:`\mathrm{=}\frac{1}{E}({K}_{1}^{2}+{K}_{2}^{2})` was carried out from 6 different :math:`\theta` fields, each corresponding to a circular crown centered in :math:`C`.