F modeling
==============


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

The law of behavior tested is' VMIS_ECMI_LINE 'documented in doc [:ref:`R5.03.16 <R5.03.16>`]. It is a Von Mises law with linear kinematic work hardening and linear 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:`{\sigma }_{y}(T)`, :math:`{E}_{T}(T)`, and :math:`C(T)`.

Values of the parameters used:


.. csv-table::

    "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:`{\sigma }_{y}(T)` "," :math:`100.` :math:`\mathrm{MPa}` "," :math:`50.` :math:`\mathrm{MPa}`"
    ":math:`{E}_{T}(T)` "," :math:`10000.` :math:`\mathrm{MPa}` "," :math:`5000.` :math:`\mathrm{MPa}`"
    ":math:`C(T)` "," :math:`2000.` :math:`\mathrm{MPa}` "," :math:`500.` :math:`\mathrm{MPa}`"



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 (:math:`\mathrm{MPa}`)", "AUTRE_ASTER ", "97.5"," 0.10%"
    "RESU_9 "," TRACE (:math:`\mathrm{MPa}`)", "AUTRE_ASTER "," -97.5", "0.10%"
    "RESU_9 ", "V1"," AUTRE_ASTER ", "9.025E-03"," 0.10%"