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


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

The idea is to perform a numerical simulation corresponding to the problem presented in the previous part and to compare the results obtained. The discontinuous elements make it possible to represent the crack along :math:`{\Gamma }_{0}`. The latter have PLAN_ELDI modeling and CZM_EXP behavior. The other elements of the mesh are QUAD4 elastics in D_ PLAN modeling.

The values of the parameters of the Airy function for the construction of the analytical solution are taken arbitrarily:

:math:`\alpha =0{\text{MPa.mm}}^{-1},\beta =1/4\pi {\text{MPa.mm}}^{-1},\gamma =1/2\text{MPa}\text{et}\eta =0\text{MPa}`


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

The plate is meshed structured in quadrangles with 20 meshes in the width and 50 in the height. Elements are arranged at discontinuity along side :math:`{\Gamma }_{0}` with the normal directed following :math:`-X`. This is achieved using the CREA_FISS keyword from CREA_MAILLAGE (see documentation [:ref:`U4.23.02 <U4.23.02>`]).


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


.. csv-table::

    "**Size tested**", "**Type**", "**Reference**", "**Tolerance (** :math:`\text{\%}` **)**"
    "Threshold variable: :math:`\mathrm{VI1}`
    On the element :math:`\mathrm{MJ15}` ", "'ANALYTIQUE'", "0.49315", "0.10"
    "Threshold variable: :math:`\mathrm{VI1}`
    On element :math:`\mathrm{MJ45}` ", "'ANALYTIQUE'", "1.075", "0.10"
    "Normal stress: :math:`\mathrm{VI6}`
    On element :math:`\mathrm{MJ30}` ", "'ANALYTIQUE'", "0.4489", "0.10"