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

Modeling A corresponds to the case **a/b = 0.4**.


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

Z

R


.. image:: images/10004EF6000027CA000027CA38D683EFDCEE0232.svg
    :width: 482
    :height: 474


.. _RefImage_10004EF6000027CA000027CA38D683EFDCEE0232.svg:

**Full mesh**


.. image:: images/10002CD60000293D0000166D10599F27CA33D43E.svg
    :width: 482
    :height: 474


.. _RefImage_10002CD60000293D0000166D10599F27CA33D43E.svg:

**Zoom of the crack point**


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

1756 knots and 569 elements including 529 QUA8 and 40 TRI6


Tested features
------------------------


.. 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. 1", "Crown No. 2", "Crown No. 2", "Crown No. 3", "Crown No. 4"
    "", "ring", "1.E-6", "2.5E-5", "5.E-5", "7.5E-5", "7.5E-5"
    "", "rsup", "2.5E-5", "5.E-5", "7.5E-5", "1.E-4"


Benchmark solutions
----------------------

For a ratio a/b = 0.4 (and a = 10-3 m), the reference solution for KI is:

:math:`{K}_{I}=4.7419\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}}={\mathrm{1.0231.10}}^{2}{\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", "1,0231.102", "0,9701.10 2", "6"
    "G", "J.m-1", "G_ EPSI ", "crown No. 2", "1,0231.102", "1,0051.10 2", "2"
    "G", "J.m-1", "G_ EPSI ", "crown No. 3", "1,0231.10 2", "1,0055.10 2", "2"
    "G", "J.m-1", "G_ EPSI ", "crown No. 4", "1,0231.102", "1.01.102", "2"
    "K1"," MPa .m-2", "K", "crown No. 1", "4.7419", "4.4145", "8"
    "K1"," MPa .m-2", "K", "crown No. 2", "4.7419", "4.7571", "2"
    "K1"," MPa .m-2", "K", "crown No. 3", "4.7419", "4.7913", "2"
    "K1"," MPa .m-2", "K", "crown No. 4", "4.7419", "4.8244", "2"