Reference issues
======================


Geometry of the "rectangle" crack
----------------------------------------------

Consider a cube with a side of :math:`1m`. This cube has a rectangle-shaped crack with rounded corners. The crack is located in the plane of normal :math:`y` halfway between the front and back side of the cube (see). The crack is actually a half-rectangle. The length of the complete rectangle is :math:`\mathrm{2a}` and the width is :math:`\mathrm{2b}`. In addition, the corners of the rectangle are rounded, with a radius :math:`r`. So the center of the full rectangle is the coordinate point :math:`(\mathrm{0,5};\mathrm{0,5};1)`. The center of the coordinate system is point :math:`\mathrm{P4}`. In the following, we'll take :math:`a=\mathrm{0,3}`, :math:`b=\mathrm{0,15}` and :math:`r=\mathrm{0,05}`.


.. image:: images/100000000000059A000001FDAA7527F4FBFC5E0B.png
    :width: 5.972in
    :height: 2.122in


.. _RefImage_100000000000059A000001FDAA7527F4FBFC5E0B.png:

**Figure** 1.1-1 **: diagram of the cube cracked by the "rectangle" crack**

Geometry of the "cylinder" crack
--------------------------------------------

We consider the same cube as before, but including a crack in the form of a cylinder. The cylinder axis is parallel to the :math:`y` axis and passes through the point :math:`C` with coordinates :math:`(1;\mathrm{0,5};1)`. The radius of the cylinder is :math:`r\mathrm{=}\mathrm{0,5}`. The crack front is therefore a quarter of a circle. The lips of the crack are located in half-space :math:`y\mathrm{\le }\mathrm{0,5}` (see).


.. image:: images/100000000000034500000162C5ABC89D8BD3F376.png
    :width: 4.0161in
    :height: 1.698in


.. _RefImage_100000000000034500000162C5ABC89D8BD3F376.png:

Figure 1.2-1: diagram of the cube cracked by the "cylinder" crack