D modeling
==============


Simulation 1
------------

This is a thermomechanical test with zero imposed deformation along axis :math:`x`. The test is performed on a hardware point with the SIMU_POINT_MAT command. The temperature varies from :math:`{T}_{0}=20°C` to :math:`{T}_{\mathrm{max}}=500°C`. 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.


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

The law of behavior tested is' ELAS_VMIS_TRAC ', documented in the documentation [:ref:`R7.02.03 <R7.02.03>`].

It is a "non-linear" law of elastic behavior (law of HENCKY), from VON MISES to non-linear isotropic work hardening.

The elastic parameters are as follows:

:math:`E(T)`, :math:`\nu (T)`, :math:`\alpha (T)`, :math:`\sigma (\varepsilon ,T)`

Values of the parameters used:


.. csv-table::

    "Parameter", ":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.\times {10}^{-4}` :math:`{K}^{-1}` "," :math:`2.\times {10}^{-4}` :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 thermomechanical 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 serial number i", "Name of the tested parameter", "Reference type", "Reference value", "tolerance"
    "RESU_i "," NOM_PARA ", "", "VALE_REF "," TOLE"
    "RESU_19 "," VMIS "," NON_REGRESSION ", "905.918"," 0.1%"
    "RESU_19 "," TRACE "," NON_REGRESSION "," ", "-905.918"," 0.1%"
    "RESU_19 ", "V1"," NON_REGRESSION ", "0.08694"," 0.1%"