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


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

.. figure:: images/Object_26.svg
 :align: center
 :width: 480
 :height: 360

 3D modeling.


.. list-table:: Caractéristiques du maillage.

 * - Number of knots
   - 20
 * - Number of meshes
   - | 1 of the HEXA 20 type
     | 6 of the QUAD 8 type

.. list-table:: Mailles définies.

 *-* DROITE *
   - NO3, NO5, NO8, N10, N10, NO12,, NO15, NO17, NO20
 *-* GAUCHE *
   - NO1, NO4, NO6, NO9, NO11,,, NO13, NO16, NO18
 *-* DEVANT *
   - NO6, NO7, NO8, NO11, NO12,,, NO18, NO19, NO20
 *-* DERRIERE *
   - NO1, NO2, NO3, NO9, NO10,,, NO13, NO14, NO15
 *-* BAS *
   - NO13, NO14, NO15, NO16, NO17,,, NO18, NO19, NO20
 *-* HAUT *
   - NO1, NO2, NO3, NO4, NO5,,, NO6, NO7, NO8

The symmetry boundary conditions are:

*On the stitches* DEVANT *and* DERRIERE *: :math:`DX=0`.
*On the stitches* GAUCHE *and* DROITE *: :math:`DY=0`.
*On the mesh* BAS *: :math:`DZ=0`.

During the isotropic compression phase, the same normal stress is imposed on the three meshes *HAUT*, *DROITE* and * *DEVANT*. During the triaxial compression phase, this normal stress remains imposed on *DROITE* and *DEVANT*. Simultaneously, vertical displacement is imposed increasing in compression on the *HAUT* mesh.

It should be noted that during these two charges, neither the capillary pressure nor the gas pressure varies. They remain equal to :math:`\mathrm{PRE1}={200}` kPa and :math:`\mathrm{PRE2}={1}` Pa respectively.

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

The solutions are calculated at points NO8 to :math:`t=1` and :math:`t=2` each corresponding to the times at which the two loads are completed. They are given in terms of radial deformation :math:`\varepsilon_{xx}` and net axial stress :math:`\sigma_{zz}''` in :numref:`v7.31.123-resultats_grandeurs`.

.. _v7.31.123-resultats_grandeurs:

.. list-table:: Résultats.

 *-**Moment**
   - **Size**
   - **Reference type**
   - **Value**
 * - :math:`t=1` (first load)
   - |:math: `\ varepsilon_ {xx}`
     |:math: `\ sigma_ {zz} "`
   - | NON_REGRESSION
     | NON_REGRESSION
   - |:math: `-0.02042190167564005`
     |:math: `-200000` Pa
 * - :math:`t=2` (second load)
   - |:math: `\ varepsilon_ {xx}`
     |:math: `\ sigma_ {zz} "`
   - | NON_REGRESSION
     | NON_REGRESSION
   - |:math: `-0.001372567575432986909`
     |:math: `-433762.5637656013` By

The :numref:`v7.31.123-reponse_modelisation_A` shows the answers obtained.

.. _v7.31.123-reponse_modelisation_A:

.. figure:: images/reponse_modelisation_A.svg
 :align: center
 :width: 800
 
 Changes in radial deformation :math:`\varepsilon_{xx}` and net axial stress :math:`\sigma_{zz}''` with axial deformation :math:`\varepsilon_{zz}` during both isotropic and triaxial compression loads.