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


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


Meshing of the test piece and the test tube holder
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. image:: images/100000000000011D000001048B4CE7B53993EB84.png
    :width: 3.9575in
    :height: 3.6102in


.. _RefImage_100000000000011D000001048B4CE7B53993EB84.png:

**Meshing of the test piece and the test piece holder**


.. image:: images/100000000000010E000000FCECA1829102115825.png
    :width: 3.7492in
    :height: 3.4992in


.. _RefImage_100000000000010E000000FCECA1829102115825.png:

**Zoom on the crack bottom**


Definition of crown radii
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We define the values of the upper and lower radii, to be specified in the CALC_G command:


.. csv-table::

    "", "1st crown", "2nd crown", "3rd crown", "4th crown"
    ":math:`\text{rinf}(\mathit{mm})` ", "1", "2", "2", "3", "4"
    ":math:`\text{rsup}(\mathit{mm})` ", "2", "3", "3", "4", "5"



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

The mesh consists of two objects:


* the specimen holder consists of 718 knots and 200 QUA8 elements.


* the test piece consists of 1741 knots and 576 elements including 496 QUA8 and 80 TRI6.


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



Note that in this test case, the operator CALC_G replaces the STAT_NON_LINE VMIS_ISOT_TRAC behavior law in ELAS_VMIS_TRAC. This is because we want to calculate :math:`G` assuming that the load is monotonic proportional (see document U2.82.03).


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", ":math:`\text{\%}` **difference**"
    "Load increment no. 22", "", "", ""
    ":math:`G`, crown #1 (:math:`\mathrm{KN}/\mathrm{mm}`)", "6,7451", "7,005", "3,868"
    ":math:`G`, crown #2 (:math:`\mathrm{KN}/\mathrm{mm}`)", "6,7451", "6,99728", "3,739"
    ":math:`G`, crown #3 (:math:`\mathrm{KN}/\mathrm{mm}`)", "6,7451", "6,7451", "6,9964", "3,726"
    "G, crown no. 4 (:math:`\mathrm{KN}/\mathrm{mm}`)", "6,7451", "6,998", "3,75"
    "Load increment No. 36", "", "", ""
    ":math:`G`, crown no. 1 (:math:`\mathrm{KN}/\mathrm{mm}`)", "12,473", "13,069", "4,786"
    ":math:`G`, crown #2 (:math:`\mathrm{KN}/\mathrm{mm}`)", "12,473", "13,094", "4,977"
    ":math:`G`, crown #3 (:math:`\mathrm{KN}/\mathrm{mm}`)", "12,473", "13,083", "4,887"
    ":math:`G`, crown no. 4 (:math:`\mathrm{KN}/\mathrm{mm}`)", "12,473", "13,071", "4,795"
    "Load increment No. 50", "", "", ""
    ":math:`G`, crown no. 1 (:math:`\mathrm{KN}/\mathrm{mm}`)", "18.433", "19.49", "5.744"
    ":math:`G`, crown #2 (:math:`\mathrm{KN}/\mathrm{mm}`)", "18.433", "19.573", "6.184"
    ":math:`G`, crown #3 (:math:`\mathrm{KN}/\mathrm{mm}`)", "18.433", "19.577", "6.204"
    ":math:`G`, crown no. 4 (:math:`\mathrm{KN}/\mathrm{mm}`)", "18.433", "19.574", "6.194"
    "Load increment #64", "", "", ""
    ":math:`G`, crown no. 1 (:math:`\mathrm{KN}/\mathrm{mm}`)", "24,601", "26,84", "9,105"
    ":math:`G`, crown #2 (:math:`\mathrm{KN}/\mathrm{mm}`)", "24,601", "26,977", "9,657"
    ":math:`G`, crown #3 (:math:`\mathrm{KN}/\mathrm{mm}`)", "24,601", "26,981", "9,672"
    ":math:`G`, crown no. 4 (:math:`\mathrm{KN}/\mathrm{mm}`)", "24,601", "26,983", "9,684"