Fissure opening
====================

The crack opening is found by displacement difference :math:`\mathit{DN}` in the direction normal to the crack path, between two points :math:`{P}_{g},{P}_{d}` on this normal.

It is then necessary to determine:


* the normal line to the crack path (taking into account the fact that the crack is known discretely by points),


* the speed of movements on this line, in particular the component of movement in the same direction,


* the coordinates of the two points :math:`{P}_{g},{P}_{d}` to operate the difference in displacement :math:`\mathit{DN}`.

The **normal** is determined on each node in the crack as the bisector of the angle formed by the two normals to the segments that have the node in common (see).

Once normal :math:`n` has been determined on a node in the crack path, a change of frame of reference is made in the field of movements, from the global coordinate system to the :math:`(n\mathrm{,}t)` coordinate system (:math:`t` is the tangent vector), in particular the component :math:`\mathit{DN}` is calculated.

Points :math:`{P}_{g},{P}_{d}` are those for which the following relationship is satisfied: :math:`X\ge` BORNE_MAX (BORNE_MAX is a parameter to be entered as an operand under the keyword RECHERCHE). The projection of field :math:`X\ge` onto the line normal to the path is therefore necessary for the determination of :math:`{P}_{g},{P}_{d}` (see).

Normally for damage laws, the value :math:`X\mathrm{=}d\mathrm{=}0.8` is sufficient to capture the movement jump (see [:external:ref:`V1.01.264 <V1.01.264>`]).


.. image:: images/10000201000002BA000001EAB99F97BCF0A53EA0.png
    :width: 4.0429in
    :height: 2.9043in


.. _RefImage_10000201000002BA000001EAB99F97BCF0A53EA0.png:

Figure 4: Average normal to the crack path for the calculation of the crack opening.


.. image:: images/10000201000002BD0000018E876E85C049660835.png
    :width: 4.0646in
    :height: 2.3201in


.. _RefImage_10000201000002BD0000018E876E85C049660835.png:

Figure 5: Projection of the DN displacement and the X field onto the normal to the crack path (normalized values); determination of :math:`{P}_{g},{P}_{d}`.