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


Geometry
---------


.. image:: images/100000000000026E00000286373CDD98E6398708.png
    :width: 4.1811in
    :height: 3.8091in


.. _RefImage_100000000000026E00000286373CDD98E6398708.png:

Figure 1.1 Problem geometry

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


.. csv-table::

    "Young's module", ":math:`E=2\times {10}^{11}\mathit{Pa}`"
    "Poisson's Ratio", ":math:`\nu =0.3`"



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

Point :math:`\mathit{PB}` is for applying force :math:`{F}_{Y}`.

The position of point :math:`\mathit{PB}` is different depending on the models, and is managed by the parameter :math:`C`.

The distance :math:`a` separating the points :math:`\mathit{P8}` and :math:`\mathit{P0}` is a constant parameter (:math:`a=\mathrm{0,1}`).

In the various models, the :math:`c/a` ratio is modified.

The lip of the crack is line :math:`\mathit{P8P0}`. So :math:`\mathit{P0}` is the crack front.

For all models (A, B, C and D):

Imposed displacement:

.. csv-table::

    "Embedding on side :math:`\mathit{P8P9}` "," :math:`\mathit{DX}=0`"
    "Embedding on side :math:`\mathit{P0P11}` "," :math:`\mathit{DY}=0`"


Imposed loading:


.. math::
: label: EQ-None

    \ textrm {Nodal force on the point}
    \ mathit {PB}


Only the position of point :math:`\mathit{PB}`, and the resulting mesh, are different between the models (the size of the radius of the mesh radiating at the bottom of the crack is different depending on the models).