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

The problem comes from an article by J.C. Simo *and*.*M* .S. Raifai :ref:`[1] <[1]>`.


Geometry
---------

The geometry can be visualized in the figure and will be used for all models.


.. image:: images/10000201000002100000022AE3CEFA7E1D6B4F0C.png
    :width: 3.0626in
    :height: 3.2134in


.. _RefImage_10000201000002100000022AE3CEFA7E1D6B4F0C.png:

Figure 1.1-1: Membrane geometry

Coordinate of Node A (48.60) and Node C (24.30).


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

The material is almost incompressible elastic, that is to say that its Poisson's ratio tends to :math:`\mathrm{0,5}`:


* Modulus of elasticity: :math:`E=70\mathit{MPa}`


* Poisson's ratio: :math:`\mathrm{\nu }=\mathrm{0,499}`

      The plasticity model is a Von Mises model with linear isotropic work hardening


* Elastic limit: :math:`\mathit{SY}=\mathrm{0,243}\mathit{MPa}`


* Work hardening module: :math:`\mathit{ET}=\mathrm{0,13474}\mathit{MPa}`


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

The left side of the membrane (:math:`\mathit{DX}=\mathit{DY}=0`) is embedded, and a vertical surface force is applied on the right side such as :math:`\mathit{FY}=\mathrm{0,1125}\mathit{kN}/\mathit{mm}\mathrm{²}`


Expansion to 3D
---------------

The 3D extension is obtained by extruding in the :math:`z` direction (:math:`1\mathit{mm}` thickness). In addition, the movements along DZ are blocked in order to be reduced to the solution in plane deformations.


.. _RefHeading__26035_1128081541: