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


Geometry
---------

Consider a rectangle of length :math:`325m` and width :math:`10m` in plane :math:`(\mathrm{0,}X,Y)`.


.. image:: images/1000000000000375000000DF5ECDBD3794327099.png
    :width: 6.3374in
    :height: 1.5965in


.. _RefImage_1000000000000375000000DF5ECDBD3794327099.png:

The thickness of the membrane is entered in AFFE_CARA_ELEM via the keyword EPAIS and is equal to :math:`e={\mathrm{2,2783.10}}^{-5}m`. This thickness is chosen so as to obtain a mass equal to that used in test case SSNL114, at an identical density.


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

The material is hyperelastic, almost incompressible, isotropic, whose properties are:


* :math:`E=57000\mathit{MPa}`


* :math:`\mathrm{\nu }=0.49`


* :math:`\mathrm{\rho }=2\mathrm{844,23}\mathit{kg}/{m}^{3}`

We use Saint Venant Kirchhoff's law of behavior.


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

On edges :math:`\mathit{AB}` and :math:`\mathit{CD}`: :math:`\mathit{DX}=0`, :math:`\mathit{DZ}=0`.

On edge :math:`\mathit{AD}`: :math:`\mathit{DY}=0`.

Gravity is applied to the entire model, it is worth :math:`g=\mathrm{9,81}m/{s}^{2}` and is oriented according to (0,0, -1) in the :math:`(X,Y,Z)` coordinate system.

The non-following pressure is applied to the entire model, it is worth :math:`p\text{}=\text{}\mathrm{\rho }\ast e\ast g\text{}\approx \text{}\mathrm{0,6357}\mathit{Pa}` and is oriented according to :math:`(\mathrm{0,0,}-1)` in the coordinate system :math:`(X,Y,Z)`.

The two loads are treated separately.


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

An initial voltage of :math:`10\mathit{MPa}` is entered in AFFE_CARA_ELEM using the N_ INIT keyword. This tension disappears after the first Newton increment.