Modeling E
==============


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

QUAD4 - Axisymmetric.

Testing the variation of the coefficients of VMIS_CINE_LINE as a function of temperature, in this case :math:`{E}_{T}` (given by D_ SIGM_EPSI) varies as: :math:`{E}_{T}={10}^{5}(1–{10}^{-2}(T–{T}_{0}))`. The Prager constant is equal to: :math:`C=\frac{2}{3}\frac{E{E}_{T}}{E-{E}_{T}}`


.. image:: images/1000020000000176000001AB65655726BCBC4D18.png
    :width: 1.7244in
    :height: 1.9689in


.. _RefImage_1000020000000176000001AB65655726BCBC4D18.png:


Characteristics of the mesh
----------------------------

Number of knots: 4

Number of meshes and types: 1 QUAD4, 4 SEG2


note
--------

The variation of :math:`{E}_{T}` (D_ SIGM_EPSI) with the temperature is tested by comparison with the behavior VMIS_ECMI_TRAC where :math:`C` (Prager constant) varies with the temperature in a similar manner (no analytical solution).


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


+--------------------------------------------------------------------+-----------------------+---------------------------------------------------------------+
|**Variables**                                                       |**Moments** :math:`(s)`|**Reference (** **Aster** ****) **** **(** VMIS_ECMI_TRAC **)**|
+--------------------------------------------------------------------+-----------------------+---------------------------------------------------------------+
|:math:`{\varepsilon }_{\mathrm{rr}}={\varepsilon }_{\theta \theta }`|:math:`t=66.666`       |8.6666 10—4                                                    |
+                                                                    +-----------------------+---------------------------------------------------------------+
|                                                                    |:math:`t=80`           |1.112 10—3                                                     |
+                                                                    +-----------------------+---------------------------------------------------------------+
|                                                                    |:math:`t=90`           |1.303 10—3                                                     |
+--------------------------------------------------------------------+-----------------------+---------------------------------------------------------------+
|:math:`{\sigma }_{\mathrm{zz}}` :math:`(\mathrm{MPa})`              |:math:`t=66.666`       |—133.333                                                       |
+                                                                    +-----------------------+---------------------------------------------------------------+
|                                                                    |:math:`t=80`           |—88                                                            |
+                                                                    +-----------------------+---------------------------------------------------------------+
|                                                                    |:math:`t=90`           |—47                                                            |
+--------------------------------------------------------------------+-----------------------+---------------------------------------------------------------+


note
--------

The same results are obtained with behavior VMIS_CINE_LINE as with behavior VMIS_ECMI_TRAC, which validates the consideration of temperature in this model.