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


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


Geometry
---------



The cube is in space :math:`[0.\mathrm{,1}\mathrm{.}]\times [0.\mathrm{,1}\mathrm{.}]\times [0.\mathrm{,1}\mathrm{.}]`.

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

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

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



Cube geometry

 :math:`L=1`


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


*
    *
        * Elastic


            * :math:`E=200.0\times {10}^{3}\mathrm{Pa}` Young's module


            * :math:`\nu =0.3` Poisson's ratio


        * Lemaitre (modeling A)


            * :math:`n=10.8`; :math:`\frac{1}{K}=6.9\times {10}^{-4}`; :math:`\frac{1}{m}=0.102`




*
    *
        * Taheri (B modeling)


            * :math:`{R}_{0}=0.001`


            * :math:`\alpha =0.`


            * :math:`m=1.`


            * :math:`A=0.`


            * :math:`b=0.`


            * :math:`{C}_{1}=0.`


            * :math:`{C}_{\infty }=0.`


            * :math:`S=900.`


*
    *
        * Taheri (C modeling)


            * :math:`{R}_{0}=72.`


            * :math:`\mathrm{\alpha }=0.3`


            * :math:`m=0.1`


            * :math:`A=312.`


            * :math:`b=30.`


            * :math:`{C}_{1}=0.`


            * :math:`{C}_{\mathrm{\infty }}=0.065`


            * :math:`S=450.`


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


A and B models
~~~~~~~~~~~~~~~~~~~~~~

Imposed displacement :math:`(m)`:


* side :math:`\mathit{ABCD}`: :math:`\mathit{DZ}=0`


* side :math:`\mathit{AEHD}`: :math:`\mathit{DY}=0`


* side :math:`\mathit{BFGC}`: :math:`\mathit{DY}=0.5`


* side :math:`\mathit{ABFE}`: :math:`\mathit{DX}=0`

The displacement :math:`\mathit{DY}` imposed on face :math:`\mathit{BFGC}` varies progressively according to the function shown in the figure below.


.. image:: images/Shape2.gif


.. _RefSchema_Shape2.gif:


C modeling
~~~~~~~~~~~~~~~

Imposed displacement :math:`(m)`:


* side :math:`\mathit{ABCD}`: :math:`\mathit{DZ}=0`


* side :math:`\mathit{AEHD}`: :math:`\mathit{DY}=0`


* side :math:`\mathit{ABFE}`: :math:`\mathit{DX}=0`

Pressure imposed :math:`(\mathit{Pa})`:


* side :math:`\mathit{BFGC}`: :math:`\mathit{PRES}=-520`

The multiplier function of the pressure imposed on face :math:`\mathit{BFGC}` as a function of time is represented in the figure below.


.. image:: images/Shape3.gif


.. _RefSchema_Shape3.gif: