Modélisation A
==============

Caractéristiques de la modélisation
-----------------------------------


.. image:: images/1000078A00000BFD0000182FBFEF0C26825DC3D2.svg
    :width: 154
    :height: 312


.. _RefImage_1000078A00000BFD0000182FBFEF0C26825DC3D2.svg:

:math:`A=\mathit{N4}` , :math:`B=\mathit{N5}` , :math:`C=\mathit{N13}` , :math:`D=\mathit{N12}` .


Caractéristiques du maillage
----------------------------

Nombre de nœuds: 13.

Nombre de mailles et types: 2 mailles QUAD8, 6mailles SEG3.


Grandeurs testées et résultats
------------------------------

.. csv-table::

    "**Identification**", "**Type de Référence**", "**Référence**", "**Tolérance (** :math:`\text{\%}` **)**"
    ":math:`{\sigma}_{zz}` :math:`t=\mathrm{60s}`", "ANALYTIQUE", "4.0792E8", "0.1"
    ":math:`{\epsilon}_{\gamma}^{\mathit{eff}}` :math:`t=\mathrm{60s}`", "ANALYTIQUE", "3.9604E-3", "0.1"
    ":math:`{\epsilon}_{\alpha}^{\mathit{eff}}` :math:`t=\mathrm{60s}`", "ANALYTIQUE", "0.", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{th}}` :math:`t=60s`", "ANALYTIQUE", "-6.0E-3", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{meca}}` :math:`t=60s`", "ANALYTIQUE", "-2.59208E-3", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{plas}}` :math:`t=60s`", "ANALYTIQUE", "-1.9802E-3", "0.1"
    "", "", "", ""
    ":math:`{\sigma}_{zz}` :math:`t=\mathrm{89s}`", "ANALYTIQUE", "7.0684E8", "0.80"
    ":math:`{\epsilon}_{\gamma}^{\mathit{eff}}` :math:`t=\mathrm{89s}`", "ANALYTIQUE", "3.9604E-3", "0.1"
    ":math:`{\epsilon}_{\alpha}^{\mathit{eff}}` :math:`t=\mathrm{89s}`", "ANALYTIQUE", "0.", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{th}}` :math:`t=89s`", "ANALYTIQUE", "-7.49460E-3", "0.5"
    ":math:`{\epsilon}_{xx}^{\mathit{meca}}` :math:`t=89s`", "ANALYTIQUE", "-3.04046E-3", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{plas}}` :math:`t=89s`", "ANALYTIQUE", "-1.9802E-3", "0.3"
    "", "", "", ""
    ":math:`{\sigma}_{zz}` :math:`t=\mathrm{112s}`", "ANALYTIQUE", "9.4392E8", "0.1"
    ":math:`{\epsilon}_{\gamma}^{\mathit{eff}}` :math:`t=\mathrm{112s}`", "ANALYTIQUE", "0.", "0.1"
    ":math:`{\epsilon}_{\alpha}^{\mathit{eff}}` :math:`t=\mathrm{112s}`", "ANALYTIQUE", "0.", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{th}}` :math:`t=112s`", "ANALYTIQUE", "-8.68E-3", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{meca}}` :math:`t=112s`", "ANALYTIQUE", "-3.39608E-3", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{plas}}` :math:`t=112s`", "ANALYTIQUE", "-1.9802E-3", "0.1"
    "", "", "", ""
    ":math:`{\sigma}_{zz}` :math:`t=\mathrm{176s}`", "ANALYTIQUE", "12.101E8", "0.1"
    ":math:`{\epsilon}_{\gamma}^{\mathit{eff}}` :math:`t=\mathrm{176s}`", "ANALYTIQUE", "0.", "0.1"
    ":math:`{\epsilon}_{\alpha}^{\mathit{eff}}` :math:`t=\mathrm{176s}`", "ANALYTIQUE", "5.068921E-3", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{th}}` :math:`t=176s`", "ANALYTIQUE", "-1.508E-2", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{meca}}` :math:`t=176s`", "ANALYTIQUE", "-6.3298E-3", "0.1"
    ":math:`{\epsilon}_{xx}^{\mathit{plas}}` :math:`t=176s`", "ANALYTIQUE", "-4.51465E-3", "0.1"



Remarques
---------

Dans cette modélisation:

:math:`{\epsilon}_{zz}^{\mathit{pt}}(T,Z)=0`

L'erreur sur :math:`{\sigma}_{zz}` à 89 secondes provient en fait de l'erreur commise sur la description numérique de la transformation métallurgique qui est, à cet instant, d'environ :math:`56\text{\%}` .