C modeling
==============


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

The simulation is carried out axisymmetrically. The interface elements allow the crack to be represented along :math:`{\Gamma }_{i}`. Their modeling is AXIS_INTERFACE_S and their cohesive behavior is CZM_TAC_MIX. The other elements of the mesh are QUAD8 with ELAS elastic behavior in AXIS modeling.


Material parameters
-------------------

The values of the Young's modulus, the Poisson's ratio, the critical stress and the toughness of the material are taken as follows:


.. image:: images/Object_49.svg
    :width: 360
    :height: 25


.. _RefImage_Object_49.svg:

Moreover, the Lagrangian penalty parameter is taken to be equal to PENA_LAGR =1000.

(NB: these are "test" values that do not correspond to any particular material.)


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

The mesh is identical to modeling A with two differences: all the cells are quadratic (QUAD8) and the cohesive element layer is composed of elements with a small thickness, oriented with the ORIE_FISSURE command.


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

To test the numerical solution, we use the equation [:ref:`éq 2-1 <éq 2-1>`]. We denote :math:`{F}^{R}` as the resultant of the force along :math:`{\Gamma }_{i}` multiplied by :math:`2\pi`.


+------------------------------------------------------------------------------------------------+------------+-------------------+----------------------------------------+
|**Size tested**                                                                                 |**Theory**  |**Aster_code**     |**Difference (** :math:`\text{\%}` **)**|
+------------------------------------------------------------------------------------------------+------------+-------------------+----------------------------------------+
|                                                                                                |1.576931E-01|1.5769307873679E-01|-1.35E-05                               |
+ .. image:: images/Object_53.svg                                                                +            +                   +                                        +
|    :width: 360                                                                                 |            |                   |                                        |
+    :height: 25                                                                                 +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+ right now: 3                                                                                   +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+------------------------------------------------------------------------------------------------+------------+-------------------+----------------------------------------+
|                                                                                                |1.25499E+01 |1.2549900398014E+01|3.17E-06                                |
+ .. image:: images/Object_54.svg                                                                +            +                   +                                        +
|    :width: 360                                                                                 |            |                   |                                        |
+    :height: 25                                                                                 +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+ right now: 3                                                                                   +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+------------------------------------------------------------------------------------------------+------------+-------------------+----------------------------------------+
|                                                                                                |2.656474E-01|2.6564739519277E-01|-1.81E-06                               |
+ .. image:: images/Object_55.svg                                                                +            +                   +                                        +
|    :width: 360                                                                                 |            |                   |                                        |
+    :height: 25                                                                                 +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+ right now: 6                                                                                   +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+------------------------------------------------------------------------------------------------+------------+-------------------+----------------------------------------+
|                                                                                                |9.486833E+00|9.4868329805100E+00|-2.05E-07                               |
+ .. image:: images/Object_56.svg                                                                +            +                   +                                        +
|    :width: 360                                                                                 |            |                   |                                        |
+    :height: 25                                                                                 +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+ right now: 6                                                                                   +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+------------------------------------------------------------------------------------------------+------------+-------------------+----------------------------------------+
|                                                                                                |3.63577E-01 |3.6357700583331D-01|1.60E-06                                |
+ .. image:: images/Object_57.svg                                                                +            +                   +                                        +
|    :width: 360                                                                                 |            |                   |                                        |
+    :height: 25                                                                                 +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+ right now: 8                                                                                   +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+------------------------------------------------------------------------------------------------+------------+-------------------+----------------------------------------+
|                                                                                                |6.7082E+00  |6.7082039325061D+00|5.86E-05                                |
+ .. image:: images/Object_58.svg                                                                +            +                   +                                        +
|    :width: 360                                                                                 |            |                   |                                        |
+    :height: 25                                                                                 +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+ right now: 8                                                                                   +            +                   +                                        +
|                                                                                                |            |                   |                                        |
+------------------------------------------------------------------------------------------------+------------+-------------------+----------------------------------------+