E modeling
==============


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

Modeling AXIS.

Model of DRUCK_PRAG_N_A with linear, parabolic and exponential negative work hardening.


.. image:: images/Shape9.gif


.. _RefSchema_Shape9.gif:


.. csv-table::

    "Number of nodes", ":math:`4` ", "", "", ""
    "Number of meshes", ":math:`5` ", "That is:", "", ""
    "", "", "SEG2 "," :math:`4`"
    "", "", "QUAD4 "," :math:`1`"


The square is in space :math:`[0.\mathrm{,1}\mathrm{.}]\text{x}[0.\mathrm{,1}\mathrm{.}]`.

Coordinates of points :math:`(m)`:

 :math:`A:(0.,0.)`

 :math:`B:(1.,0.)`

 :math:`C:(1.,1.)`

 :math:`D:(0.,1.)`

Knitwear:

 :math:`\mathrm{M1}`: surface :math:`\mathrm{ABDC}`

 :math:`\mathrm{M2}`: segment :math:`\mathrm{AB}`

 :math:`\mathrm{M3}`: segment :math:`\mathrm{BC}`

 :math:`\mathrm{M4}`: segment :math:`\mathrm{CD}`

 :math:`\mathrm{M5}`: segment :math:`\mathrm{DA}`

Node groups:

 :math:`A,B`


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                        |
+--------------------------------+-----+----------+--------------------------------+-----------------------------------+-------------------------------------+---------------------------+