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

Behavioral law and material parameters
--------------------------------------------

The law of behavior tested is' BETON_BURGER ', it is documented in doc [:ref:`R7.01.35 <R7.01.35>`]. This law, implemented under Mfront, is used to model the natural creep of concrete, taking into account the distinction between volume creep and deviatoric creep in order to account for phenomena in cases of multi-axial creep. The test is carried out using D_ PLAN modeling (mesh QUAD4) with the command STAT_NON_LINE. The elastic parameters are as follows:

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

The parameters of the visco-plastic law are as follows:

:math:`{K}_{R}^{S}`, :math:`{K}_{R}^{D}`, :math:`{\eta }_{R}^{S}`, :math:`{\eta }_{I}^{S}`, :math:`{\eta }_{R}^{D}`,, :math:`{\eta }_{I}^{D}`, and :math:`\kappa`.

Values of the parameters used:

.. csv-table::

    "Settings", ":math:`T\mathrm{=}0°C` "," :math:`T=500°C`"
    ":math:`E(T)` "," :math:`11000\mathit{MPa}` "," :math:`31000\mathit{MPa}`"
    ":math:`\nu (T)` "," :math:`0.` "," :math:`0.`"
    ":math:`\alpha (T)` "," :math:`\mathrm{1,0}\times {10}^{-4}{K}^{-1}` "," :math:`\mathrm{2,0}\times {10}^{-4}{K}^{-1}`"
    ":math:`{K}_{R}^{S}` "," :math:`4360\mathit{MPa}` "," :math:`4360\mathit{MPa}`"
    ":math:`\kappa` "," :math:`\mathrm{3,3}\times {10}^{-3}` "," :math:`\mathrm{3,3}\times {10}^{-3}`"
    ":math:`{K}_{R}^{D}` "," :math:`3270\mathit{MPa}` "," :math:`3270\mathit{MPa}`"
    ":math:`{\eta }_{R}^{S}` "," :math:`\mathrm{3,41}\times {10}^{9}\mathit{MPa}\mathrm{.}s` "," :math:`\mathrm{3,41}\times {10}^{9}\mathit{MPa}\mathrm{.}s`"
    ":math:`{\eta }_{I}^{S}` "," :math:`\mathrm{5,76}\times {10}^{12}\mathit{MPa}\mathrm{.}s` "," :math:`\mathrm{5,76}\times {10}^{12}\mathit{MPa}\mathrm{.}s`"
    ":math:`{\eta }_{R}^{D}` "," :math:`\mathrm{2,55}\times {10}^{9}\mathit{MPa}\mathrm{.}s` "," :math:`\mathrm{2,55}\times {10}^{9}\mathit{MPa}\mathrm{.}s`"
    ":math:`{\eta }_{I}^{D}` "," :math:`\mathrm{4,32}\times {10}^{12}\mathit{MPa}\mathrm{.}s` "," :math:`\mathrm{4,32}\times {10}^{12}\mathit{MPa}\mathrm{.}s`"



Results
---------

.. csv-table::

    "Result at order number :math:`i` ", "Name of the tested parameter", "Name of the tested parameter", "Reference type", "Tolerance"
    "RESU_0 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -31.50", "0.10%"
    "RESU_1 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -71.50", "0.10%"
    "RESU_2 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -120.75", "0.10%"
    "RESU_3 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -180.00", "0.10%"
    "RESU_4 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -250.00", "0.10%"
    "RESU_5 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -331.50", "0.10%"
    "RESU_6 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER ", "-425.25"," 0.10%"
    "RESU_7 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -532.00", "0.10%"
    "RESU_8 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -652.50", "0.10%"
    "RESU_9 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -787.50", "0.10%"
    "RESU_10 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -937.75", "0.10%"
    "RESU_11 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -1104.00", "0.10%"
    "RESU_12 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -1287.00", "0.10%"
    "RESU_13 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -1487.50", "0.10%"
    "RESU_14 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -1706.25", "0.10%"
    "RESU_15 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -1944.00", "0.10%"
    "RESU_16 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER ", "-2201.50"," 0.10%"
    "RESU_17 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -2479.50", "0.10%"
    "RESU_18 "," PRIN_1 (:math:`\mathrm{Pa}`)", "AUTRE_ASTER "," -2778.75", "0.10%"
    "RESU_19 "," PRIN_1 (:math:`\mathit{Pa}`)", "AUTRE_ASTER "," -3100.00", "0.10%"