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


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

2D elements' PLAN '

For reasons of symmetry, we only mesh a quarter of a square section and we refine to :math:`x=L` and :math:`y=L`.


.. image:: images/100003F8000010F30000117718244B578763BF92.svg
    :width: 218
    :height: 225


.. _RefImage_100003F8000010F30000117718244B578763BF92.svg:


.. csv-table::

    "Cutting:", "5 QUAD8 meshes along the :math:`x` axis"
    "", "5 QUAD8 meshes along the :math:`y` axis"



.. csv-table::

    "Boundary conditions:", "on :math:`x=0` and :math:`y=0` "," :math:`\phi \mathrm{=}0`"
    "", "on :math:`x=L` and :math:`y=L` "," :math:`-\lambda \partial T/\partial n=h(T(x,y,t)-{T}_{\infty })`"


Gauss points:


.. csv-table::

    ":math:`A`:", "mesh :math:`\mathit{m13}` point 1"
    ":math:`B`:", "mesh :math:`\mathit{m19}` point 1"
    ":math:`C`:", "mesh :math:`\mathit{m19}` point 3"


Bow:


.. math::
: label: EQ-None

    O


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


.. csv-table::

    "Number of knots:", "96"
    "Number of meshes and types:", "25 QUAD8, 20 SEG3"



notes
---------

165 steps of calculation from :math:`0` to :math:`\mathrm{410 }s` (40 steps of :math:`\mathrm{5 }s`, then 40 steps of :math:`\mathrm{1 }s`, then 85 steps of :math:`\mathrm{2 }s`).


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

Option META_ELNO and DURT_ELNO:


.. csv-table::

    "**Identification**", "**Sizes**", "**Reference**", "**Aster**", "**% difference**"
    ":math:`t\mathrm{=}\mathrm{30 }s` :math:`\mathit{M13}` (:math:`\mathit{PG1}`)", ":math:`P` ", "0.0489", "0.0489", "1.64 10—6 absolute"
    ":math:`t\mathrm{=}\mathrm{140 }s` :math:`\mathit{M13}` (:math:`\mathit{PG1}`)", ":math:`P` ", "0.9505", "0.9505", "4.10 10—5 absolute"
    ":math:`t\mathrm{=}\mathrm{300 }s` :math:`\mathit{M13}` (:math:`\mathit{PG1}`)", ":math:`\mathit{TPG}` ", "464.1", "464.37", "0.058"
    ":math:`t\mathrm{=}\mathrm{300 }s` :math:`\mathit{M19}` (:math:`\mathit{PG1}`)", ":math:`\mathit{TPG}` ", "338.5", "338.79", "0.086"
    ":math:`t\mathrm{=}\mathrm{300 }s` :math:`\mathit{M19}` (:math:`\mathit{PG3}`)", ":math:`\mathit{TPG}` ", "245.4", "245.68", "0.116"
    ":math:`t\mathrm{=}\mathrm{410 }s` :math:`\mathit{M13}` (:math:`\mathit{PG1}`)", ":math:`\mathit{ZB}` ", "", "0.7828", ""
    ":math:`t\mathrm{=}\mathrm{300 }s` :math:`\mathit{M19}` (:math:`\mathit{PG1}`)", ":math:`\mathit{ZB}` ", "", "0.5873", ""
    ":math:`t\mathrm{=}\mathrm{300 }s` :math:`\mathit{M19}` (:math:`\mathit{PG3}`)", ":math:`\mathit{ZB}` ", "", "0.3113", ""
    ":math:`t\mathrm{=}\mathrm{410 }s` :math:`\mathit{M13}` (:math:`\mathit{PG1}`)", ":math:`\mathit{ZM}` ", "", "0.2156", ""
    ":math:`t\mathrm{=}\mathrm{410 }s` :math:`\mathit{M19}` (:math:`\mathit{PG1}`)", ":math:`\mathit{ZM}` ", "", "0.4103", ""
    ":math:`t\mathrm{=}\mathrm{410 }s` :math:`\mathit{M19}` (:math:`\mathit{PG3}`)", ":math:`\mathit{ZM}` ", "", "0.6846", ""
    ":math:`t\mathrm{=}\mathrm{30 }s` :math:`\mathit{N1}` "," :math:`\mathit{HV}` ", "", "223.643", ""
    ":math:`t\mathrm{=}\mathrm{140 }s` :math:`\mathit{N1}` "," :math:`\mathit{HV}` ", "", "106.430", ""
    ":math:`t\mathrm{=}\mathrm{300 }s` :math:`\mathit{N1}` "," :math:`\mathit{HV}` ", "", "100,000", ""
    ":math:`t\mathrm{=}\mathrm{410 }s` :math:`\mathit{N1}` "," :math:`\mathit{HV}` ", "", "308.248", ""



.. csv-table::

    ":math:`\mathit{TPG}`:", "temperature at the point of GAUSS,"
    ":math:`\mathit{ZB}`:", "proportion of bainite,"
    ":math:`\mathit{ZM}`:", "martensite proportion,"
    ":math:`P`:", "austenite proportion."
    ":math:`\mathit{HV}`:", "Vickers hardness"