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


Geometry and boundary conditions
------------------------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

**Figure** 1.1-a **: geometry of the studied structure**

The structure studied is a hollow sphere under pressure :math:`p=\mathrm{1MPa}`. The symmetry properties of the problem will be used.

The inner radius is :math:`{R}_{\text{int}}=100\mathrm{mm}` and the outer radius is :math:`{R}_{\text{ext}}=200\mathrm{mm}`).


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


.. csv-table::

    "**Law of behavior**", "**Elastic behavior**", "**Plastic behavior**", "**Damaging behavior**", "**Damaging behavior**
    **(weakened zone)**"
    "VMIS_ISOT_LINE "," :math:`E\mathrm{=}200.000\mathit{MPa}`
    :math:`\nu \mathrm{=}\mathrm{0,3}` "," :math:`{\sigma }_{y}\mathrm{=}300\mathit{MPa}`
    :math:`{E}_{T}\mathrm{=}0` "," :math:`{\sigma }_{y}\mathrm{=}5\mathit{MPa}`
    :math:`{E}_{T}\mathrm{=}\mathrm{-}10000\mathit{MPa}`"