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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

We consider a cube with side :math:`\mathrm{1m}` which rests on a plane (:math:`{x}_{2}=0` on the lower face), subjected to pressure :math:`F` on the upper face and in a situation of plane deformation following :math:`{x}_{3}` (:math:`{x}_{3}=0` on the right and left faces). The cube can therefore only be stretched along axis :math:`{x}_{1}`).


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

We test on three different materials, corresponding to three common models in hyper-elasticity.


.. csv-table::

    "Behavior ELAS_HYPER ", "Mooney-Rivlin", "Neo-Hookean", "Signorin"
    "C10", "0.709", "1.2345", "0.1234"
    "C01", "2.3456", "0", "1.2345"
    "C20", "0", "0", "0", "0.456"
    "NAKED", "0.499", "0.499", "0.499"



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


.. csv-table::

    "* Lower side", ": :math:`\mathrm{DY}=0`"
    "* Top side", ": :math:`F=0.876\mathrm{Pa}`"
    "* Left and right face", ": :math:`\mathrm{DZ}=0` in 3D, nothing in D_ PLAN"


The load is increasing from :math:`F=0` to :math:`F=\mathrm{0.876Pa}`, in 20 increments.