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


Geometry
---------

We consider a notched plate with a height of :math:`10\mathit{dm}`. With a width :math:`3\mathit{dm}` and a notch radius :math:`1\mathit{dm}`.


.. image:: images/10000000000001B00000027DE55D1F6471B68862.png
    :width: 2.1984in
    :height: 3.5055in


.. _RefImage_10000000000001B00000027DE55D1F6471B68862.png:

**Figure 1:** **Representation of the problem**


Common properties of the material
-------------------------------

The material in question is assimilated to concrete (we work on a decimeter scale):

Elastic characteristics:

 :math:`E\mathrm{=}3.E10\text{Pa}\mathrm{=}3.E8{\text{N/dm}}^{2}`

 :math:`\nu =0.2`

Tensile elasticity limit of the law of damage:

 :math:`\mathit{SY}\mathrm{=}3.E4{\text{N/dm}}^{2}\mathrm{=}3.E6\text{Pa}`

Energy release rate per crack surface (Griffith constant):

 :math:`{G}_{f}\mathrm{=}10\text{N/dm}\mathrm{=}100{\text{J/m}}^{2}`


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

**Block**: :math:`\mathrm{DX}=0` on a group of nodes located in the middle of the axis (:math:`x=0.`), in order to ensure the maintenance of the structure.

**Load**: Imposed or controlled displacement (varies according to the modeling) in the direction of traction.