B modeling
==============


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

D_ PLAN modeling.

Behaviour of DRUCK_PRAGER at parabolic negative work hardening.


.. image:: images/Shape4.gif


.. _RefSchema_Shape4.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{.}]\times [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.)`

Node groups:

 :math:`A,B`

Mails

 :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}`


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


+----------------------------------+---------+---------------------+------------------------+-----------------------------+
|Grandeur                          |Point    |:math:`\mathrm{Inst}`|Reference               |Tolerance (:math:`\text{\%}`)|
+----------------------------------+---------+---------------------+------------------------+-----------------------------+
|:math:`\mathrm{SIXX}(\mathrm{Pa})`|:math:`C`|:math:`2.0`          |:math:`-2.0\mathrm{E6}` |0.1                          |
+----------------------------------+---------+---------------------+------------------------+-----------------------------+
|:math:`\mathrm{SIYY}(\mathrm{Pa})`|:math:`C`|:math:`1.07`         |:math:`-8.69\mathrm{E6}`|0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.16`         |:math:`-1.37\mathrm{E7}`|0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.34`         |:math:`-9.90\mathrm{E6}`|0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.53`         |:math:`-9.91\mathrm{E6}`|0.1                          |
+----------------------------------+---------+---------------------+------------------------+-----------------------------+
|:math:`\mathrm{V1}`               |:math:`C`|:math:`1.07`         |:math:`0`               |0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.16`         |:math:`1.26E-3`         |0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.34`         |:math:`1.12E-2`         |0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.53`         |:math:`2.01E-2`         |0.1                          |
+----------------------------------+---------+---------------------+------------------------+-----------------------------+
|:math:`\mathrm{DY}(m)`            |:math:`C`|:math:`1.07`         |:math:`-1.05E-3`        |0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.16`         |:math:`-2.40E-3`        |0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.34`         |:math:`-5.10E-3`        |0.1                          |
+                                  +         +---------------------+------------------------+-----------------------------+
|                                  |         |:math:`1.53`         |:math:`-7.95E-3`        |0.1                          |
+----------------------------------+---------+---------------------+------------------------+-----------------------------+