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


Geometry
---------


.. image:: images/100000000000015000000229479178F85E54E778.png
    :width: 2.8138in
    :height: 4.872in


.. _RefImage_100000000000015000000229479178F85E54E778.png:


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


Material 1
~~~~~~~~~~

.. csv-table::

    "Young's module", ":math:`E=6\times {10}^{12}\mathit{Pa}`"
    "Poisson's Ratio", ":math:`\nu =0.2`"



Material 2
~~~~~~~~

.. csv-table::

    "Young's module", ":math:`E=1\times {10}^{11}\mathit{Pa}`"
    "Poisson's Ratio", ":math:`\nu =0.3`"



Material 3
~~~~~~~~

.. csv-table::

    "Young's module", ":math:`E=2\times {10}^{11}\mathit{Pa}`"
    "Poisson's Ratio", ":math:`\nu =0.2`"



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



Points :math:`\mathit{P8}` and :math:`\mathit{P8S}` are used to apply force :math:`{F}_{Y}`.

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

For all the calculations carried out, the same movements are imposed.

Imposed displacement:

.. csv-table::

    "Embedding on side :math:`\mathit{P8P9S}` "," :math:`\mathit{DX}=0`"
    "Embedding on side :math:`\mathit{P8SP9}` "," :math:`\mathit{DX}=0`"
    "Embedding node :math:`\mathit{P11}` "," :math:`\mathit{DY}=0`"


According to the calculations, 2 types of loading are imposed:

Imposed loading:

.. csv-table::

    "Pressure distributed over line :math:`\mathit{P0P8}` "," :math:`1.`"
    "Pressure distributed over line :math:`\mathit{P0P8S}` "," :math:`1.`"


Or:

.. csv-table::

    "Nodal force on the GROUP_NO :math:`\mathit{P8}` "," :math:`\mathit{Fy}=1.591549E-3`"
    "Nodal force on the GROUP_NO :math:`\mathit{P8S}` "," :math:`\mathit{Fy}=-1.591549E-3`"