M modeling
==============


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

The temperature here varies from :math:`{T}_{0}=51.7°C` to :math:`{T}_{\mathrm{max}}=101.7°C`. The law of behavior tested is' ELAS '. This elastic law is associated with a transverse isotropic material. The elastic parameters are as follows:

:math:`{E}_{L}(T)`, :math:`{E}_{N}(T)`, :math:`{\nu }_{\text{LN}}(T)`, :math:`{\nu }_{\text{LT}}(T)`, :math:`{G}_{\text{LN}}(T)`,, :math:`{\alpha }_{L}(T)`, and :math:`{\alpha }_{N}(T)`

Values of the parameters used:


.. csv-table::

    "Settings", ":math:`T=51.7°C` "," :math:`T=76.7°C` "," :math:`T=101.7°C`"
    ":math:`{E}_{L}(T)` "," :math:`1.0` :math:`\mathrm{MPa}` "," :math:`1.1` :math:`\mathrm{MPa}` "," :math:`1.2` :math:`\mathrm{MPa}`"
    ":math:`{E}_{N}(T)` "," :math:`1.0` :math:`\mathrm{MPa}` "," :math:`1.1` :math:`\mathrm{MPa}` "," :math:`1.2` :math:`\mathrm{MPa}`"
    ":math:`{\nu }_{\text{LN}}(T)` "," :math:`0.0` "," :math:`0.0` "," :math:`0.0`"
    ":math:`{\nu }_{\text{LT}}(T)` "," :math:`0.0` "," :math:`0.0` "," :math:`0.0`"
    ":math:`{G}_{\text{LN}}(T)` "," :math:`0.5` :math:`\mathrm{MPa}` "," :math:`0.55` :math:`\mathrm{MPa}` "," :math:`0.6` :math:`\mathrm{MPa}`"
    ":math:`{\alpha }_{L}(T)` "," :math:`1.\times {10}^{-5}` :math:`{K}^{-1}` "," :math:`1.5\times {10}^{-5}` :math:`{K}^{-1}` "," :math:`2.\times {10}^{-5}` :math:`{K}^{-1}`"
    ":math:`{\alpha }_{N}(T)` "," :math:`1.\times {10}^{-5}` :math:`{K}^{-1}` "," :math:`1.5\times {10}^{-5}` :math:`{K}^{-1}` "," :math:`2.\times {10}^{-5}` :math:`{K}^{-1}`"



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_4 "," VMIS "," AUTRE_ASTER "," ", "1.2E-3"," 0.10%"
    "RESU_4 "," TRACE "," AUTRE_ASTER "," ", "-1.2E-3"," 0.10%"