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


Geometry
---------

Consider a hollow sphere with external radius :math:`1m` and internal radius :math:`0.2m`.


.. image:: images/10000000000002540000023498B8D9326FB01D3F.png
    :width: 2.3626in
    :height: 2.2362in


.. _RefImage_10000000000002540000023498B8D9326FB01D3F.png:

**Figure** 1.1-a **: Section of the sphere under study**


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

The material has an elastoplastic behavior that is perfectly plastic. Its load surface is defined by the von Mises criterion. The material properties are:


* :math:`E=200000\mathit{MPa}`


* :math:`\nu =0.3`


* :math:`{\sigma }_{y}\mathrm{=}150\mathit{MPa}`


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

Internal pressure is applied until the entire plasticization of the sphere is achieved. The outer surface is free of effort.


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

Néant