C modeling
==============


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


Simulation 1
~~~~~~~~~~~~

This is a thermomechanical test with zero imposed deformation along axis :math:`x`. The test is performed on an element of BARRE with the STAT_NON_LINE command. The temperature varies from :math:`{T}_{0}=20°C` to :math:`{T}_{\mathrm{max}}=500°C`. The material is able to be plasticized. The transition consists of NCAL steps. The reference temperature is :math:`{T}_{\mathrm{ref}}=20°C`.


Simulation 2
~~~~~~~~~~~~

It's about looping on NCALcalculs mechanics. For each calculation :math:`i`, the imposed load consists of the thermal deformation :math:`{\varepsilon }_{\mathrm{xx}}=-{\varepsilon }_{\mathrm{th}}=-\alpha (T)({T}_{i}-{T}_{\mathrm{Ref}})`. The initial load consists of the deformations, stresses and internal variables from the previous mechanical calculation.


Material properties
----------------------

The law of behavior tested is' VMIS_ISOT_TRAC 'documented in doc [:ref:`R5.03.09 <R5.03.09>`]. This law involves non-linear isotropic work hardening.

The elastic parameters are as follows:

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

The elastoplastic parameters are as follows:

:math:`\sigma (\varepsilon ,T)`

Values of the parameters used:


.. csv-table::

    "Settings", ":math:`T=20°C` "," :math:`T=500°C`"
    ":math:`E(T)` "," :math:`200000.` MPa "," :math:`100000.` 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}`"



+-------------------------------+-------------+--------------------------+--------------------------+
|Parameter                      |Temperature  |:math:`\varepsilon =0.005`|:math:`\varepsilon =1.005`|
+-------------------------------+-------------+--------------------------+--------------------------+
|:math:`\sigma (\varepsilon ,T)`|:math:`20°C` |:math:`1000.` MPa         |:math:`3000.` MPa         |
+                               +-------------+--------------------------+--------------------------+
|                               |:math:`500°C`|:math:`800.` MPa          |:math:`2000.` MPa         |
+-------------------------------+-------------+--------------------------+--------------------------+


Tested sizes and results
------------------------------

Validation is carried out by comparing the fields calculated at each step of the transient on the one hand and the result of a mechanical calculation on the other hand.

The command used is TEST_TABLE which tests the reference value against the calculated value.

The reference value being the field component extracted at a given time :math:`i` from the first thermo-mechanical simulation performed over NCAL times. The calculated value is the one obtained at the end of the mechanical calculation :math:`i+1` of the loop on the NCAL.


.. csv-table::

    "Result at order number :math:`i` ", "Name of the tested parameter", "Name of the tested parameter", "Reference type", "Tolerance"
    "RESU_i "," NOM_PARA ", "", "VALE_REF "," TOLE"
    "RESU_19 ", "N", "NON_REGRESSION ", "-801.926"," 0.1%"
    "RESU_19 ", "V1"," NON_REGRESSION ", "1.5807E-3"," 0.1%"