Reference problem
=====================


Geometry
---------


+-----------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+
|                                                                                                                             |Face                                                                                          |
+ .. image:: images/10000000000002DA0000024BBCB7A0517499B7B4.png                                                              + :math:`\mathit{YZ}`                                                                          +
|    :width: 3.1272in                                                                                                         |                                                                                              |
+    :height: 2.6319in                                                                                                        +                                                                                              +
|                                                                                                                             | :math:`(\mathrm{1,3}\mathrm{,5}\mathrm{,7})`                                                 |
+                                                                                                                             +                                                                                              +
|                                                                                                                             |                                                                                              |
+-----------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------+



Material properties
-----------------------


.. csv-table::

    "isotropic elasticity:", ":math:`E=206\mathrm{400.MPa}` "," :math:`\nu \mathrm{=}0.3`"
    "plasticity:
    (coefficients of the Rousselier model)", ":math:`D=2.`
    :math:`{f}_{0}\mathrm{=}{5.10}^{\mathrm{-}4}`
    :math:`{\sigma }_{1}=\mathrm{490.MPa}` ", ""


The rational traction curve is entered point by point with:

:math:`R(p)\mathrm{=}{r}_{i}+({r}_{0}\mathrm{-}{r}_{i}){e}^{\mathrm{-}\mathit{bp}}`

with :math:`p`: cumulative plastic deformation

and :math:`{r}_{i}\mathrm{=}1500\mathit{MPa}`

:math:`{r}_{0}\mathrm{=}\mathrm{520.MPa}`

:math:`b=2.4`


.. image:: images/1000038A000011C700000D06D710BB60389913EE.svg
    :width: 229
    :height: 168


.. _RefImage_1000038A000011C700000D06D710BB60389913EE.svg:


Boundary conditions and loads
-------------------------------------


.. csv-table::

    ":math:`\mathrm{N04}` "," :math:`\mathrm{dx}=\mathrm{dy}=0` ", "Face :math:`\mathit{YZ}`:", ":math:`\mathrm{FX}=\mathrm{FY}=–F(t)`"
    ":math:`\mathrm{N08}` "," :math:`\mathit{dx}\mathrm{=}\mathit{dy}\mathrm{=}\mathit{dz}\mathrm{=}0` ", "Face :math:`\mathrm{XZ}`:", ":math:`\mathrm{FX}=–F(t)`"
    ":math:`\mathrm{N02},\mathrm{N06}` "," :math:`\mathrm{dx}=0` ", "Face :math:`\mathrm{1YZ}`:", ":math:`\mathrm{FY}=F(t)`"
    "", "", "Face :math:`\mathrm{1XZ}`:", ":math:`\mathrm{FX}=F(t)`"


409.707

.. image:: images/100006AA000069BB00004FE4CCC186550A7F1C7E.svg
    :width: 229
    :height: 168


.. _RefImage_100006AA000069BB00004FE4CCC186550A7F1C7E.svg:


Initial conditions
--------------------

Zero stresses and deformations at :math:`t=0`.