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


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

The modeling is carried out in plane deformations with 3644 elements TRI3 for the mass and 201 elements QU4 for the discontinuity. The cohesive law passed is CZM_EXP_REG. Mechanical loading is slow: loading speed :math:`{q}_{t}` is :math:`\mathrm{0,002}\mu {\mathrm{m.s}}^{-1}`.

Discretization in time: 29 time steps from :math:`10s`.


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

The results of numerical modeling are compared with those obtained experimentally by Slowik and Saouma.

The figure shows the force applied by the wedge as a function of CMOD and the figure shows the pressure profiles in the crack.


.. image:: images/10000000000004D40000035FEF52C97B30D96A05.jpg
    :width: 5.3102in
    :height: 3.45in


.. _RefImage_10000000000004D40000035FEF52C97B30D96A05.jpg:

**Figure** 3.2-a **: Force-CMOD curve obtained numerically and comparison with the experimental results of Slowik and Saouma**


.. image:: images/10000000000004D700000367CE24BDEFCA582B75.jpg
    :width: 4.8035in
    :height: 4.0173in


.. _RefImage_10000000000004D700000367CE24BDEFCA582B75.jpg:

**Figure** 3.2-b **: Pressure profiles in the crack at different times. Numeric curves are thick curves. The experimental measurements (Slowik and Saouma) are represented by solid triangles.**

The force-CMOD curve obtained numerically is very close to the experimental curve. In addition, trends in the evolution of pressure in the crack are also well reproduced.

It should also be noted that these results are very similar to those obtained numerically by Segura and Carol.

A comparison test with the experiment is carried out on the component according to :math:`x` of the force applied in :math:`B\text{'}` (option FORC_NODA) as well as on the pressure at a point of the crack.


.. csv-table::

    "**Point**", "**Time (** :math:`s` **)**", ":math:`\mathrm{Fx}` **(** :math:`\mathrm{kN}/{\mathrm{mm}}^{\mathrm{²}}` **)**
    **reference**", ":math:`\mathrm{Fx}` **(** :math:`\mathrm{kN}/{\mathrm{mm}}^{\mathrm{²}}` **)**
    **Aster**", "**Difference (** :math:`\text{\%}` **)**"
    ":math:`B\text{'}` ", "100", "-12.65", "-12.65", "-13.08", "3.4"
    ":math:`B\text{'}` ", "150", "-6.41", "-6.41", "-6.46", "0.76"
    ":math:`B\text{'}` ", "250", "-0.765", "-0.765", "-0.792", "3.5"



.. csv-table::

    ":math:`X` **(** :math:`\mathrm{mm}` **)**", ":math:`Y` **(** :math:`\mathrm{mm}` **)**", "**Time (** :math:`s` **)**", ":math:`\mathrm{PRE1}` **(** :math:`\mathrm{Mpa}` **)**", "**(** **)**
    **reference**", ":math:`\mathrm{PRE1}` **(** :math:`\mathrm{MPa}` **)**
    **Aster**", "**Difference (** :math:`\text{\%}` **)**"
    "0", "-41", "140", "140", "0.155", "0.155", "0.149", "3.8"
    "0", "-41", "190", "0.190", "0.190", "0.188", "0.86"
    "0", "-41", "240", "240", "0.200", "0.202", "0.81"


The following non-regression tests are added:


.. csv-table::

    ":math:`X` **(** :math:`\mathrm{mm}` **)**", ":math:`Y` **(** :math:`\mathrm{mm}` **)**", "**Time (** :math:`s` **)**", ":math:`\mathrm{PRE1}` **(** :math:`\mathrm{Mpa}` **)**", "**(** **)**
    **Aster**"
    "0", "-41", "140", "0.1491"
    "0", "-41", "190", "0.1884"
    "0", "-41", "240", "0.2016"