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


Geometry
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We consider a notched test piece 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:** **Problem Representation**


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

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

Elastic characteristics:

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

 :math:`\nu =0.2`

Tensile elasticity limit of the law of damage:

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

Energy release rate per crack surface (Griffith constant):

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

Density:

 :math:`\mathit{Rho}=2300\mathit{Kg}/{m}^{3}=2.3\mathit{Kg}/{\mathit{dm}}^{3}`


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

**Block**: :math:`\mathrm{DX}=0` on the nodes that belong to the axis of symmetry (:math:`x=0.`), in order to ensure the maintenance of the structure (in red in Figure 1).

**Loading**: A movement is imposed on the upper and lower parts of the notched test piece (in green in FIG. 1).