N modeling
==============


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

The law of behavior tested is' ROUSS_PR '. It is an elastoplastic law modeling damage due to the growth of cavities, used in modeling the ductile failure of metals. The temperature here varies from :math:`{T}_{0}=20°C` to :math:`{T}_{\mathrm{max}}=800°C`

Values of the parameters used:


.. csv-table::

    "Settings", ":math:`T=20°C` "," :math:`T=800°C`"
    ":math:`E(T)` "," :math:`2.1E5` :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:`D(T)` "," :math:`\mathrm{1,5}` "," :math:`\mathrm{1,5}`"
    ":math:`\mathrm{BETA}` "," :math:`1` "," :math:`1`"
    ":math:`\text{PORO\_INIT}` "," :math:`{5.10}^{\text{-4}}` "," :math:`{5.10}^{\text{-4}}`"
    ":math:`\text{S\_1}(T)` "," :math:`500.` :math:`\mathrm{MPa}` "," :math:`500.` :math:`\mathrm{MPa}`"
    "Traction curves", ":math:`\varepsilon ;\sigma (\mathrm{MPa})` "," :math:`\varepsilon ;\sigma (\mathrm{MPa})`"
    "First point", ":math:`\frac{800}{2.1{10}^{5}};800.0` "," :math:`\frac{600}{1.0{10}^{5}};600.0`"
    "Second point", ":math:`\mathrm{1,005};\mathrm{1600,}` "," :math:`\mathrm{1,005};\mathrm{1200,}`"



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_29 (t=1, T=800°C)", "VMIS "," "," AUTRE_ASTER "," :math:`605.5` "," 0.10%"
    "RESU_29 (t=1, T=800°C)", "TRACE "," "," AUTRE_ASTER "," :math:`-605.5` "," 0.10%"
    "RESU_29 (t=1, T=800°C)", "V1"," AUTRE_ASTER "," :math:`9.546E-03` "," 0.10%"
    "RESU_29 (t=1, T=800°C)", "V2"," AUTRE_ASTER "," :math:`5.046E-04` "," 0.10%"