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


Geometry
---------

It is an elliptical crack immersed in a medium that is supposed to be infinite. We only model one eighth of a parallelepiped:


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

:math:`E=210\mathrm{000.MPa}`

:math:`\nu \mathrm{=}0.3`


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

Symmetry with respect to the 3 main planes:

:math:`{U}_{x}=0.` in the :math:`X=0` plan.

:math:`{U}_{Y}=0.` in the :math:`Y=0` plan.

:math:`{U}_{Z}=0.` in the :math:`Z=0.` plane out of the crack

The loading conditions are either:

:math:`P=1\mathrm{MPa}` in plane :math:`Z=1250\mathrm{mm}` (modeling :math:`A`)

either:

:math:`\mathrm{FZ}={8.10}^{-4}N/{\mathrm{mm}}^{3}` on all volume elements (loading equivalent to the previous one) (models :math:`F` and :math:`G`).