Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

The reference solution was obtained with various finite element calculation codes using different explicit, semi-implicit or implicit algorithms [:ref:`2 <2>`]


Reference quantities
----------------------

:math:`\mathrm{EPXX}`: plastic deformation following :math:`X`

:math:`\mathrm{EPYY}`: plastic deformation following :math:`Y`


Reference quantity and result
---------------------------------


+------------------+---------------------+------------------------------+
|Moment :math:`(s)`|Component            |Reference                     |
+------------------+---------------------+------------------------------+
|                  |:math:`\mathrm{EPXX}`|:math:`6.125\times {10}^{-7}` |
+                  +---------------------+------------------------------+
|                  |:math:`\mathrm{EPYY}`|:math:`-4.684\times {10}^{-7}`|
+------------------+---------------------+------------------------------+
|                  |:math:`\mathrm{EPXX}`|:math:`7.056\times {10}^{-4}` |
+                  +---------------------+------------------------------+
|                  |:math:`\mathrm{EPYY}`|:math:`-5.720\times {10}^{-4}`|
+------------------+---------------------+------------------------------+
|                  |:math:`\mathrm{EPXX}`|:math:`7.061\times {10}^{-4}` |
+                  +---------------------+------------------------------+
|                  |:math:`\mathrm{EPYY}`|:math:`-5.724\times {10}^{-4}`|
+------------------+---------------------+------------------------------+
|                  |:math:`\mathrm{EPXX}`|:math:`7.061\times {10}^{-4}` |
+                  +---------------------+------------------------------+
|                  |:math:`\mathrm{EPYY}`|:math:`-5.724\times {10}^{-4}`|
+------------------+---------------------+------------------------------+
|                  |:math:`\mathrm{EPXX}`|:math:`-2.443\times {10}^{-5}`|
+                  +---------------------+------------------------------+
|                  |:math:`\mathrm{EPYY}`|:math:`1.377\times {10}^{-4}` |
+------------------+---------------------+------------------------------+
|                  |:math:`\mathrm{EPXX}`|:math:`-7.788\times {10}^{-4}`|
+                  +---------------------+------------------------------+
|                  |:math:`\mathrm{EPYY}`|:math:`8.423\times {10}^{-4}` |
+------------------+---------------------+------------------------------+
|                  |:math:`\mathrm{EPXX}`|:math:`-1.534\times {10}^{-3}`|
+                  +---------------------+------------------------------+
|                  |:math:`\mathrm{EPYY}`|:math:`1.432\times {10}^{-3}` |
+------------------+---------------------+------------------------------+


Bibliographical references
---------------------------


1. Structural Analysis Software Validation Guide: SFM, AFNOR technique, ISBN :2-12-486611-7


2. Validation of calculation codes in viscoplasticity: Report of a scientific interest group. (GIS), ONERA France, 1989