Modélisation A
==============

L'éprouvette est maillée avec deux éléments TRIA3 à trois nœuds pour toutes les modélisations.


*   2 éléments grilles pour modéliser les fibres dans la direction :math:`\mathrm{OX}`


*   2 éléments grilles pour modéliser les fibres dans la direction :math:`\mathrm{OY}`

Les nœuds des éléments sont communs pour chacune des nappes d'armature.


.. image:: images/100004C6000069D500004D1AFEA1C75A82055C99.svg
    :width: 345
    :height: 252


.. _RefImage_100004C6000069D500004D1AFEA1C75A82055C99.svg:


Résultats modélisation A (écrouissage isotrope linéaire)
--------------------------------------------------------


Chargement thermique pour la modélisation A
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Température de référence: 50

Histoire du chargement: :math:`{\mathrm{Evolution}}_{A}` (cf. [:ref:`§1.4 <§1.4>`])

Les températures sont rentrées comme un champ aux nœuds.


Résultats
~~~~~~~~~

On relève des valeurs de :math:`\mathit{SIXX}` au nœud :math:`\mathrm{NO1}` (dans la direction des armatures longitudinales) et :math:`\mathit{SIXX}` au nœud :math:`\mathrm{NO1}` (dans la direction des armatures transversales) et celles du Maximum et minimum des variables internes :math:`\mathrm{V1}` et :math:`\mathrm{V3}` .


+---------+---------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------+
|         | :math:`\mathit{SIXX}` dans les mailles modélisant les fibres orientées suivant :math:`\mathrm{OX}`                        | :math:`\mathit{SIXX}` dans les mailles modélisant les fibres orientées suivant :math:`\mathrm{OY}`                        |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| Instant | Référence                                                                                          | *Code_Aster* | Ecart | Référence                                                                                          | *Code_Aster* | Ecart |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 1       | 2,0000E+08                                                                                         | 2,0000E+08   | 0     | 2,0000E+08                                                                                         | 2,0000E+08   | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 2       | 2,4000E+08                                                                                         | 2,4000E+08   | 0     | 2,4000E+08                                                                                         | 2,4000E+08   | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 3       | 4,0000E+07                                                                                         | 4,0000E+07   | 0     | 4,0000E+07                                                                                         | 4,0000E+07   | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 4       | 2,4000E+08                                                                                         | 2,4000E+08   | 0     | 2,4000E+08                                                                                         | 2,4000E+08   | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 5       | –1,6000E+08                                                                                        | –1,6000E+08  | 0     | –1,6000E+08                                                                                        | –1,6000E+08  | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 6       | –3,1200E+08                                                                                        | –3,1200E+08  | 0     | –3,1200E+08                                                                                        | –3,1200E+08  | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 7       | 2,8800E+08                                                                                         | 2,8800E+08   | 0     | 2,8800E+08                                                                                         | 2,8800E+08   | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 8       | 4,0960E+08                                                                                         | 4,0960E+08   | 0     | 4,0960E+08                                                                                         | 4,0960E+08   | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 9       | –2,7040E+08                                                                                        | –2,7040E+08  | 0     | –2,7040E+08                                                                                        | –2,7040E+08  | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 10      | –5,2768E+08                                                                                        | –5,2768E+08  | 0     | –5,2768E+08                                                                                        | –5,2768E+08  | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+
| 11      | 4,7232E+08                                                                                         | 4,7232E+08   | 0     | 4,7232E+08                                                                                         | 4,7232E+08   | 0     |
+---------+----------------------------------------------------------------------------------------------------+--------------+-------+----------------------------------------------------------------------------------------------------+--------------+-------+


+---------+--------------------+----------------------------+----------------------------+
| Instant | Variables internes | Minimum                    | Maximum                    |
|         |                    +--------------+-------------+--------------+-------------+
|         |                    | *Code_Aster* | Référence   | *Code_Aster* | Référence   |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 1       | V1                 | 0            | 0           | 0            | 0           |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 0            | 0           | 0            | 0           |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 2       | V1                 | 1.8E-03      | 1.8E-03     | 1.8E-03      | 1.8E-03     |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 1.8E-03      | 1.8E-03     | 1.8E-03      | 1.8E-03     |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 3       | V1                 | 1.8E-03      | 1.8E-03     | 1.8E-03      | 1.8E-03     |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 1.8E-03      | 1.8E-03     | 1.8E-03      | 1.8E-03     |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 4       | V1                 | 1.8E-03      | 1.8E-03     | 1.8E-03      | 1.8E-03     |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 1.8E-03      | 1.8E-03     | 1.8E-03      | 1.8E-03     |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 5       | V1                 | 1.8E-03      | 1.8E-03     | 1.8E-03      | 1.8E-03     |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 1.8E-03      | 1.8E-03     | 1.8E-03      | 1.8E-03     |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 6       | V1                 | 5.04E-03     | 5.04E-03    | 5.04E-03     | 5.04E-03    |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 5.04E-03     | 5.04E-03    | 5.04E-03     | 5.04E-03    |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 7       | V1                 | 5.04E-03     | 5.04E-03    | 5.04E-03     | 5.04E-03    |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 5.04E-03     | 5.04E-03    | 5.04E-03     | 5.04E-03    |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 8       | V1                 | 9.432E-03    | 9.432E-03   | 9.432E-03    | 9.432E-03   |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 9.432E-03    | 9.432E-03   | 9.432E-03    | 9.432E-03   |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 9       | V1                 | 9.432E-03    | 9.432E-03   | 9.432E-03    | 9.432E-03   |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 9.432E-03    | 9.432E-03   | 9.432E-03    | 9.432E-03   |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 10      | V1                 | 1.47456E-02  | 1.47456E-02 | 1.47456E-02  | 1.47456E-02 |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 1.47456E-02  | 1.47456E-02 | 1.47456E-02  | 1.47456E-02 |
+---------+--------------------+--------------+-------------+--------------+-------------+
| 11      | V1                 | 1.47456E-02  | 1.47456E-02 | 1.47456E-02  | 1.47456E-02 |
|         +--------------------+--------------+-------------+--------------+-------------+
|         | V3                 | 1.47456E-02  | 1.47456E-02 | 1.47456E-02  | 1.47456E-02 |
+---------+--------------------+--------------+-------------+--------------+-------------+

**Remarques :**

*Les résultats présentés sont donnés dans le repère de référence* :math:`({X}_{\mathrm{ref}},{Y}_{\mathrm{ref}})` *faisant un angle de* :math:`0°` *par rapport à* :math:`(X,Y)` *.*

*Le cas test étudié correspond au schéma suivant dans un plan contrainte déformation:*


.. image:: images/Object_17.svg
    :width: 345
    :height: 252


.. _RefImage_Object_17.svg: