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

Modeling B corresponds to the case **a/b = 0.01**.


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


.. image:: images/10005166000029570000290872590073BD5BE461.svg
    :width: 377
    :height: 365


.. _RefImage_10005166000029570000290872590073BD5BE461.svg:

**Full mesh**


.. image:: images/10004532000026C2000025B960DF6D62BFCC3611.svg
    :width: 377
    :height: 365


.. _RefImage_10004532000026C2000025B960DF6D62BFCC3611.svg:

**Zoom**


.. image:: images/100025BA00002C2200001177EA2F86BAF4B15A5D.svg
    :width: 377
    :height: 365


.. _RefImage_100025BA00002C2200001177EA2F86BAF4B15A5D.svg:

**Zoom of the crack point**


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

2095 nodes and 680 elements including 640 QUA8 and 40 TRI6


Features tested
------------------------


.. csv-table::

    "**Orders**", "", "", ""
    "AFFE_MODELE "," THERMIQUE "," AXIS ", ", ""
    "AFFE_CHAR_THER "," TEMP_IMPO ", "", "", ""
    "AFFE_MODELE "," MECANIQUE "," AXIS ", ", ""
    "AFFE_MATERIAU "," AFFE_VARC "," NOM_VARC =' TEMP '", "", ""
    "CALC_G "," OPTION ", "G_ EPSI ", "", ""
    "CALC_G "," OPTION ", "K", "", ""
    "", "", "", "", ""


In this test, the mechanical result post-processed by the operator CALC_G comes from a CREA_RESU. As this type of result contains only displacements and no constraints, it is necessary to calculate these constraints within the CALC_G operator from the displacement fields. This operation is carried out by choosing to calculate the option G_ EPSI.


Definition of crown radii
-----------------------------------

Several successive pairs of radii for the lower and upper integration rings are retained. These rays should be specified in the CALC_G keyword factor THETA:


.. csv-table::

    "", "", "Crown No. 0", "Crown No. 1", "Crown No. 1", "Crown No. 2", "Crown No. 3", "Crown No. 4"
    "", "ring", "1.E-6", "1.5E-5", "1.75E-5", "2.E-5", "2.25E-5"
    "", "rsup", "2.5E-5", "1.75E-5", "1.75E-5", "2.25E-5", "2.5E-5", "2.5E-5"



Reference solutions
----------------------

For an a/b ratio = 0.01 (and a = 2.5.10-5 m), the reference solution for KI is:

:math:`{K}_{I}=0.9609\text{MPa}\cdot \sqrt{(\text{m})}`

To calculate the energy return rate, we use the formulas of IRWIN in plane deformations:

:math:`{G}_{\mathrm{réf}}=\frac{1-{\nu }^{2}}{E}({K}_{I}^{2}+{K}_{\mathrm{II}}^{2})`, with :math:`{K}_{\mathrm{II}}^{2}=0`

either:

:math:`{G}_{\mathrm{réf}}=4.2019{\text{J.m}}^{-2}`


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


.. csv-table::

    "**Parameter**", "**Unit**", "**Option**", "**Option**", "**Crown**", "**Aster**", "**%** Tolerance"
    "G", "J.m-1", "G_ EPSI ", "crown No. 1", "4.2019", "4.1567", "2"
    "G", "J.m-1", "G_ EPSI ", "crown No. 2", "4.2019", "4.1554", "2"
    "G", "J.m-1", "G_ EPSI ", "crown No. 3", "4.2019", "4.1544", "2"
    "G", "J.m-1", "G_ EPSI ", "crown No. 4", "4.2019", "4.1554", "2"
    "K1"," MPa .m-2", "K", "crown No. 0", "0.9609", "0.9653", "2"