D modeling
==============


Characteristics of modeling D
-------------------------------------

The simulation of the propagation of cracks by brittle fracture is carried out with modeling PLAN_JOINT and the law of behavior CZM_EXP_REG for cohesive meshes. The solid elements, in plane deformations D_ PLAN, are elastic.


Characteristics of the mesh
----------------------------

A linear unstructured mesh of the perforated half-plate and of the potential crack is produced.

Volume elements (DCB): 804 TRIA3

Joint elements (crack path): 19 QUAD4


Tested sizes and results
------------------------------

Non-regression tests are performed on the overall response: :math:`{F}^{i}` resulting from the force imposed on the upper face versus :math:`U` displacement of the node :math:`P` at the top of the hole.


+----------------------------------------------------------------------------------------------------+--------------+---------------------------------------+
|**Size tested**                                                                                     |**Aster_code**|**Tolerance (** :math:`\text{\%}` **)**|
+----------------------------------------------------------------------------------------------------+--------------+---------------------------------------+
|                                                                                                    |3.32215D-03   |0.10                                   |
+ .. image:: images/Object_62.svg                                                                    +              +                                       +
|    :width: 17                                                                                      |              |                                       |
+    :height: 18                                                                                     +              +                                       +
|                                                                                                    |              |                                       |
+ at moment 50                                                                                       +              +                                       +
|                                                                                                    |              |                                       |
+----------------------------------------------------------------------------------------------------+--------------+---------------------------------------+
|                                                                                                    |4.21054D+07   |0.10                                   |
+ .. image:: images/Object_63.svg                                                                    +              +                                       +
|    :width: 17                                                                                      |              |                                       |
+    :height: 18                                                                                     +              +                                       +
|                                                                                                    |              |                                       |
+ at moment 50                                                                                       +              +                                       +
|                                                                                                    |              |                                       |
+----------------------------------------------------------------------------------------------------+--------------+---------------------------------------+
|                                                                                                    |2.52359D-03   |0.10                                   |
+ .. image:: images/Object_64.svg                                                                    +              +                                       +
|    :width: 17                                                                                      |              |                                       |
+    :height: 18                                                                                     +              +                                       +
|                                                                                                    |              |                                       |
+ at the moment 100                                                                                  +              +                                       +
|                                                                                                    |              |                                       |
+----------------------------------------------------------------------------------------------------+--------------+---------------------------------------+
|                                                                                                    |5.3546D+06    |0.10                                   |
+ .. image:: images/Object_65.svg                                                                    +              +                                       +
|    :width: 17                                                                                      |              |                                       |
+    :height: 18                                                                                     +              +                                       +
|                                                                                                    |              |                                       |
+ at the moment 100                                                                                  +              +                                       +
|                                                                                                    |              |                                       |
+----------------------------------------------------------------------------------------------------+--------------+---------------------------------------+
|                                                                                                    |7.09118D-03   |0.10                                   |
+ .. image:: images/Object_66.svg                                                                    +              +                                       +
|    :width: 17                                                                                      |              |                                       |
+    :height: 18                                                                                     +              +                                       +
|                                                                                                    |              |                                       |
+ at the moment 150                                                                                  +              +                                       +
|                                                                                                    |              |                                       |
+----------------------------------------------------------------------------------------------------+--------------+---------------------------------------+
|                                                                                                    |6.75039D+06   |0.10                                   |
+ .. image:: images/Object_67.svg                                                                    +              +                                       +
|    :width: 17                                                                                      |              |                                       |
+    :height: 18                                                                                     +              +                                       +
|                                                                                                    |              |                                       |
+ at the moment 150                                                                                  +              +                                       +
|                                                                                                    |              |                                       |
+----------------------------------------------------------------------------------------------------+--------------+---------------------------------------+


We can see that the criminalization of cohesive law introduces a slight difference between the results. If we compare the results of modeling D to those of B in this way, we have the force-displacement curve of the figure.


.. image:: images/100000000000023E000001330BF9F91F452C7B80.png
    :width: 17
    :height: 17


.. _RefImage_100000000000023E000001330BF9F91F452C7B80.png:

**Figure** 5.3-a **: comparison of joint elements with elements with internal discontinuity.**