Modeling A
==============


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

Method SIMPLEXE is used by PROPA_FISS to solve the crack propagation equations.


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

The structure is modelled by a mesh composed of 2500 elements QUAD4 (see).

The crack is not meshed. It is modelled by the :math:`\text{XFEM}` method and initially defined by two level-sets:

:math:`\mathit{LST}=y-{a}_{0}`

:math:`\mathit{LSN}=x-D`


.. image:: images/1000000000000251000003499B48FBB9E940EF92.gif
    :width: 3.4646in
    :height: 3.2319in


.. _RefImage_1000000000000251000003499B48FBB9E940EF92.gif:

**Figure** 3.2-a **: structure mesh**


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

We test the values of :math:`{K}_{I}` at each propagation step.

.. csv-table::

    "**Size**", "**Propagation**", "**Reference Type**", "**Reference Value (** :math:`\mathit{Pa}\sqrt{\mathit{mm}}` **)**", "**Tolerance**"
    **(%)**"
    ":math:`{K}_{I}` ", "1", "'ANALYTIQUE'", "''", "32030644,1127", "5.0"
    ":math:`{K}_{I}` ", "2", "'ANALYTIQUE'", "''", "52126639,0648", "5.0"
    ":math:`{K}_{I}` ", "3", "'ANALYTIQUE'", "''", "78186891,9838", "5.0"


The mechanical residual error indicator 'ERME_ELEM' is also tested on the last propagation step (in non-regression only) in order to validate the use of this indicator on 2D models with rotations.