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


Geometry
---------

The structure is a unit cube (:math:`\mathit{LX}\mathrm{=}1m`, :math:`\mathit{LY}\mathrm{=}1m` and :math:`\mathit{LZ}\mathrm{=}1m`), with a flat opening crack of length :math:`a\mathrm{=}\mathrm{0,5}m`, located halfway up [:ref:`Figure 1.1-1.1-a <Ref94087906>`]. The face located in plane :math:`x\mathrm{=}0` is called the back face and the front face located in plane :math:`x\mathrm{=}\mathit{LX}` is called the front face.


.. image:: images/10000000000001D9000001B2196D73F52C7531F4.png
    :width: 4.0126in
    :height: 3.7201in


.. _RefImage_10000000000001D9000001B2196D73F52C7531F4.png:


.. _Ref94087906:

**Figure 1.1‑** 1.1-a **: geometry of the cracked cube**


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

Young's module: :math:`E\mathrm{=}100\mathit{MPa}`

Poisson's ratio: :math:`\nu \mathrm{=}0`.


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

The load studied is a loading that stresses the crack in :math:`\mathit{III}` mode (off-plane), without creating discontinuity of movement.

To do this, we impose an embedding of the nodes on the back face: :math:`\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0` and a displacement of the nodes on the front face in the normal direction (i.e. along the :math:`x` axis) :math:`\mathit{DNOR}\mathrm{=}{10}^{}6m`.


Bibliography
--------------


1. GENIAUT S., MASSIN P.: eXtended Finite Element Method, *Code_Aster* Reference Manual, [:ref:`R7.02.12 <R7.02.12>`]