F modeling
==============


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

3D modeling.


.. image:: images/Shape10.gif


.. _RefSchema_Shape10.gif:

DRUCK_PRAG_N_A model with linear, parabolic and exponential negative work hardening.


.. csv-table::

    "Number of nodes", ":math:`20` ", "", "", ""
    "Number of meshes", ":math:`7` ", "That is:", "", ""
    "", "", "QUAD8 "," :math:`6`"
    "", "", "HEXA20 "," :math:`1`"


Cube geometry :math:`(m)`:

Center :math:`O(0.\mathrm{,0}\mathrm{.}\mathrm{,0}\mathrm{.})`

Side :math:`C=1m`

Mesh groups:

:math:`\mathrm{BAS}`: surface of the cube belonging to the :math:`Z=-0.5` plane

:math:`\mathrm{HAUT}`: surface of the cube belonging to the :math:`Z=+0.5` plane

:math:`\mathrm{DROITE}`: surface of the cube belonging to the :math:`Y=+0.5` plane

:math:`\mathrm{GAUCHE}`: surface of the cube belonging to the :math:`Y=-0.5` plane

:math:`\mathrm{DERRIERE}`: surface of the cube belonging to the :math:`X=-0.5` plane

:math:`\mathrm{DEVANT}`: surface of the cube belonging to the :math:`X=+0.5` plane


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


+--------------------------------+-----+----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|Grandeur                        |Point|NUME_ORDRE|Reference, linear work hardening|Reference, parabolic work hardening|Reference, exponential work hardening|Tolerance :math:`\text{\%}`|
+--------------------------------+-----+----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|:math:`\mathit{SIZZ}(N/{m}^{2})`|A    |9         |:math:`-8.77\mathrm{.}{10}^{6}` |:math:`-8.76\mathrm{.}{10}^{6}`    |:math:`-8.77\mathrm{.}{10}^{6}`      |0.1                        |
+                                +     +----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|                                |     |34        |:math:`-7.20\mathrm{.}{10}^{6}` |:math:`-6.44\mathrm{.}{10}^{6}`    |:math:`-7.55\mathrm{.}{10}^{6}`      |0.1                        |
+                                +     +----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|                                |     |60        |:math:`-5.86\mathrm{.}{10}^{6}` |:math:`-5.80\mathrm{.}{10}^{6}`    |/                                    |0.1                        |
+--------------------------------+-----+----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|:math:`\mathrm{V1}`             |A    |9         |:math:`4.69\mathrm{.}{10}^{-5}` |:math:`5.11\mathrm{.}{10}^{-5}`    |:math:`4.69\mathrm{.}{10}^{-5}`      |0.1                        |
+                                +     +----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|                                |     |34        |:math:`5.3\mathrm{.}{10}^{-3}`  |:math:`5.4\mathrm{.}{10}^{-3}`     |:math:`5.3\mathrm{.}{10}^{-3}`       |0.1                        |
+                                +     +----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|                                |     |60        |:math:`9.8\mathrm{.}{10}^{-3}`  |:math:`9.8\mathrm{.}{10}^{-3}`     |/                                    |0.1                        |
+--------------------------------+-----+----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|:math:`\mathrm{DY}(m)`          |A    |9         |:math:`-1.2\mathrm{.}{10}^{-3}` |:math:`-1.2\mathrm{.}{10}^{-3}`    |:math:`-1.2\mathrm{.}{10}^{-3}`      |0.1                        |
+                                +     +----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|                                |     |34        |:math:`-4.9\mathrm{.}{10}^{-3}` |:math:`-4.9\mathrm{.}{10}^{-3}`    |:math:`-4.9\mathrm{.}{10}^{-3}`      |0.1                        |
+                                +     +----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+
|                                |     |60        |:math:`-8.8\mathrm{.}{10}^{-3}` |:math:`-8.8\mathrm{.}{10}^{-3}`    |/                                    |0.1                        |
+--------------------------------+-----+----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+