J modeling
==============


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

The law of behavior tested is' VISC_CIN1_CHAB 'documented in doc [:ref:`R5.03.04 <R5.03.04>`]. It is a viscoplastic Chaboche law with non-linear kinematic work hardening, similar to modeling law :math:`G`, with viscosity in addition. The elastic parameters are as follows:

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

The elastoplastic parameters are as follows:

:math:`{R}_{I}(T)`, :math:`{R}_{0}(T)`, :math:`B(T)`, :math:`{\mathrm{C1}}_{I}(T)`, :math:`{\mathrm{G1}}_{0}(T)`,, :math:`K`, :math:`W`, :math:`{A}_{I}`.

The viscosity parameters are as follows:

:math:`N`, :math:`1/K(T)`, and :math:`1/M(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:`{R}_{I}(T)` "," :math:`300.` :math:`\mathrm{MPa}` "," :math:`150.` :math:`\mathrm{MPa}`"
    ":math:`{R}_{0}(T)` "," :math:`100.` :math:`\mathrm{MPa}` "," :math:`50.` :math:`\mathrm{MPa}`"
    ":math:`B(T)` "," :math:`12.` "," :math:`5.`"
    ":math:`{C}_{I}(T)` "," :math:`2000.` :math:`\mathrm{MPa}` "," :math:`500.` :math:`\mathrm{MPa}`"
    ":math:`{G}_{0}(T)` "," :math:`45.` "," :math:`75.`"
    ":math:`K` "," :math:`1.` "," :math:`1.`"
    ":math:`W` "," :math:`0.` "," :math:`0.`"
    ":math:`{A}_{I}` "," :math:`1.` "," :math:`1.`"
    ":math:`N` "," :math:`24.` "," :math:`16.`"
    ":math:`1/K` "," :math:`1/100.` :math:`{\mathrm{MPa}}^{\text{-1}}` "," :math:`1/150.` :math:`{\mathrm{MPa}}^{\text{-1}}`"
    ":math:`1/M` "," :math:`0.` "," :math:`0.`"



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 ", "171.5016"," 0.10%"
    "RESU_9 "," TRACE "," AUTRE_ASTER "," ", "-171.5016"," 0.10%"
    "RESU_9 ", "V1"," AUTRE_ASTER ", "8.28498E-03"," 0.10%"