O modeling
==============


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

The law of behavior tested is' VMIS_JOHN_COOK 'documented in doc [:ref:`R5.03.02 <R5.03.02>`]. It is a Von Mises law of Johnson-Cook isotropic work hardening. The elastic parameters are as follows:

:math:`E(T)`, :math:`\nu (T)`, and :math:`\alpha (T)`

The elastoplastic parameters are as follows:

:math:`A`, :math:`B`, :math:`C`, :math:`{N}_{\mathrm{PUISS}}`, :math:`{M}_{\mathrm{PUISS}}`,, :math:`\mathrm{EPSP0}`, :math:`\mathrm{TROOM}`, and :math:`\mathrm{TMELT}`

Values of the parameters used:


+----------------------------+---------------------------------+---------------------------------+
|Settings                    |:math:`T=20°C`                   |:math:`T=500°C`                  |
+----------------------------+---------------------------------+---------------------------------+
|:math:`E(T)`                |:math:`2.E5` :math:`\mathrm{MPa}`|:math:`1.E5` :math:`\mathrm{MPa}`|
+----------------------------+---------------------------------+---------------------------------+
|:math:`\nu (T)`             |:math:`0.`                       |:math:`0.`                       |
+----------------------------+---------------------------------+---------------------------------+
|:math:`\alpha (T)`          |:math:`1.E-5` :math:`{K}^{-1}`   |:math:`2.E-5` :math:`{K}^{-1}`   |
+----------------------------+---------------------------------+---------------------------------+
|:math:`A`                   |:math:`90.` :math:`\mathrm{MPa}`                                   |
+----------------------------+---------------------------------+---------------------------------+
|:math:`B`                   |:math:`292.` :math:`\mathrm{MPa}`                                  |
+----------------------------+---------------------------------+---------------------------------+
|:math:`C`                   |:math:`0.025`                                                      |
+----------------------------+---------------------------------+---------------------------------+
|:math:`{N}_{\mathrm{PUISS}}`|:math:`0.31`                                                       |
+----------------------------+---------------------------------+---------------------------------+
|:math:`{M}_{\mathrm{PUISS}}`|:math:`1.09`                                                       |
+----------------------------+---------------------------------+---------------------------------+
|:math:`\mathrm{EPSP0}`      |:math:`10000` :math:`{s}^{-1}`                                     |
+----------------------------+---------------------------------+---------------------------------+
|:math:`\mathrm{TROOM}`      |:math:`298` :math:`°K`                                             |
+----------------------------+---------------------------------+---------------------------------+
|:math:`\mathrm{TMELT}`      |:math:`1083` :math:`°K`                                            |
+----------------------------+---------------------------------+---------------------------------+


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


.. csv-table::

    "Result at order number :math:`i` ", "Name of the tested parameter", "Name of the tested parameter", "Reference type", "tolerance"
    "RESU_9 "," VMIS "," AUTRE_ASTER ", "97.5"," 0.10%"
    "RESU_9 "," TRACE "," AUTRE_ASTER ", "-97.5"," 0.10%"
    "RESU_9 ", "V1"," AUTRE_ASTER ", "9.025E-03"," 0.10%"