Modeling A
==============

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


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


.. _RefImage_1000078A00000BFD0000182FBFEF0C26825DC3D2.svg:

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


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

Number of knots: 13

Number of meshes and types: 2 QUAD8 meshes, 6 SEG3 meshes.


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

.. csv-table::

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



notes
---------

In this modeling:

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

The error on :math:`{\sigma }_{\mathit{zz}}` at 89 seconds is in fact due to the error made in the numerical description of metallurgical transformation which is, at this moment, approximately :math:`56\text{\%}`.