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


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

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


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

An unstructured quadratic mesh of the perforated half-plate and of the potential crack is produced.

Solid elements (:math:`\mathrm{DCB}`): 404 TRIA6

Interface elements (crack path): 19 QUAD8


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.


.. csv-table::

    "**Size tested**", "**Code_Aster**", "**Tolerance (** :math:`\text{\%}` **)**"
    ":math:`U` at the moment 50", "2.87853E-03", "0.10"
    ":math:`F` at time 50", "2.88263E+07", "0.10"
    ":math:`U` at the moment 75", "6.55609E-03", "0.10"
    ":math:`F` at time 75", "1.04922E+07", "0.10"
    ":math:`U` at time 100", "7.47879E-03", "0.10"
    ":math:`F` at time 100", "4.94452E+06", "0.10"
    ":math:`U` at time 140", "0.0157679", "0.10"
    ":math:`F` at time 140", "8.56080E+05", "0.10"