Modeling E
==============


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

The law of behavior tested is' VENDOCHAB '. It is a law of viscoplastic behavior coupled with isotropic Lemaitre-Chaboche damage [:ref:`R5.03.15 <R5.03.15>`]. The elastic parameters are as follows:


.. csv-table::

    "Settings", ":math:`T=20°C` "," :math:`T=500°C`"
    ":math:`E(T)` "," :math:`150000` :math:`\mathrm{MPa}` "," :math:`100000` :math:`\mathrm{MPa}`"
    ":math:`\nu (T)` "," :math:`0.` "," :math:`0.`"
    ":math:`\alpha (T)` "," :math:`1.\times {10}^{-5}` :math:`{K}^{-1}` "," :math:`2.\times {10}^{-5}` :math:`{K}^{-1}`"


The parameters of the viscoplastic law are as follows:

:math:`S(T)`, :math:`{\alpha }_{D}(T)`, :math:`{\beta }_{D}(T)`, :math:`1\mathrm{/}K(T)`, :math:`{A}_{D}(T)`,, :math:`{R}_{D}(T)`, and :math:`{K}_{D}(T)`

:math:`N(T)`, :math:`1\mathrm{/}K(T)`, and :math:`1\mathrm{/}M(T)`

Values of the parameters used:


.. csv-table::

    "Settings", ":math:`T=20°C` "," :math:`T=500°C`"
    ":math:`S(T)` "," :math:`0.` :math:`\mathrm{MPa}` "," :math:`900.` :math:`\mathrm{MPa}`"
    ":math:`{\alpha }_{D}(T)` "," :math:`0.` "," :math:`1.`"
    ":math:`{\beta }_{D}(T)` "," :math:`0.` "," :math:`1.`"
    ":math:`{A}_{D}(T)` "," :math:`3.\times {10}^{3}` :math:`\mathrm{MPa}` "," :math:`3.5\times {10}^{3}` :math:`\mathrm{MPa}`"
    ":math:`{R}_{D}(T)` "," :math:`6` "," :math:`7`"
    ":math:`{K}_{D}(T)` "," :math:`15` "," :math:`10`"



.. csv-table::

    "Settings", ":math:`T=20°C` "," :math:`T=500°C`"
    ":math:`N(T)` "," :math:`12` "," :math:`15`"
    ":math:`1\mathrm{/}K(T)` "," :math:`5.\times {10}^{-3}{(\mathrm{Mpa})}^{\text{-1}}` "," :math:`1.\times {10}^{-3}{(\mathrm{Mpa})}^{\text{-1}}`"
    ":math:`1\mathrm{/}M(T)` "," :math:`0.` "," :math:`0.1111`"



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 ", "959.9793"," 0.10%"
    "RESU_9 "," TRACE (:math:`\mathrm{MPa}`)", "AUTRE_ASTER "," -959.9802", "0.10%"
    "RESU_9 ", "V1"," AUTRE_ASTER ", "-9.8381E-08"," 0.10%"