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


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

The modeling is :math:`\mathrm{3D}` with a hydro-mechanical coupling in quasistatic non-linear mode.

In loading phase 1, the sample is brought to consolidation pressure :math:`{\sigma }_{\mathrm{xx}}^{0}={\sigma }_{\mathrm{yy}}^{0}={\sigma }_{\mathrm{zz}}^{0}={\sigma }^{0}=-30\mathrm{kPa}`

We use Hujeux's law *cyclic*.


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

Number of knots: :math:`20`

Number of meshes and type: 1 HEXA20 and 6 QUAD8


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

The solutions are calculated at point :math:`C` and compared to the results obtained with GEFDYN. They are given in terms of isotropic pressure, plastic volume deformation :math:`{\varepsilon }_{v}^{p}` and mobilization factors, and summarized in the following tables:

:math:`3\mathrm{\cdot }P\text{'}\mathrm{=}{\sigma }_{\mathit{ij}}\mathrm{\cdot }{\delta }_{\mathit{ij}}` :math:`(\mathit{kPa})`

+---------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------+--------------+
|                                                                                                         |Code_Aster (:math:`\mathit{kPa}`)|GEFDYN (:math:`\mathit{kPa}`)|Relative error|
+ .. image:: images/Object_13.svg                                                                         +                                 +                             +              +
|    :width: 91                                                                                           |                                 |                             |              |
+    :height: 24                                                                                          +                                 +                             +              +
|                                                                                                         |                                 |                             |              |
+ (:math:`\mathit{kPa}`)                                                                                  +                                 +                             +              +
|                                                                                                         |                                 |                             |              |
+---------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------+--------------+
|-15                                                                                                      |-80.223                          |-80.194                      |0.038%        |
+---------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------+--------------+
|15                                                                                                       |-73.988                          |-74.078                      |-0.122%       |
+---------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------+--------------+
|-15                                                                                                      |-66.055                          |-66.250                      |-0.295%       |
+---------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------+--------------+
|15                                                                                                       |-52.625                          |-52.999                      |-0.707%       |
+---------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------+--------------+
|-15                                                                                                      |-45,539                          |-45.672                      |-0.292%       |
+---------------------------------------------------------------------------------------------------------+---------------------------------+-----------------------------+--------------+


:math:`{\varepsilon }_{v}^{p}\mathrm{=}\mathit{trace}({\varepsilon }^{p})`

+---------------------------------------------------------------------------------------------------------+----------+--------+--------------+
|                                                                                                         |Code_Aster|GEFDYN  |Relative error|
+ .. image:: images/Object_15.svg                                                                         +          +        +              +
|    :width: 91                                                                                           |          |        |              |
+    :height: 24                                                                                          +          +        +              +
|                                                                                                         |          |        |              |
+ (:math:`\mathit{kPa}`)                                                                                  +          +        +              +
|                                                                                                         |          |        |              |
+---------------------------------------------------------------------------------------------------------+----------+--------+--------------+
|-15                                                                                                      |-2.62e-5  |-2.63e-5|-0.225%       |
+---------------------------------------------------------------------------------------------------------+----------+--------+--------------+
|                                                                                                         |-2.80e-5  |-2.78e-5|0.854%        |
+ .. image:: images/Object_16.svg                                                                         +          +        +              +
|    :width: 91                                                                                           |          |        |              |
+    :height: 24                                                                                          +          +        +              +
|                                                                                                         |          |        |              |
+                                                                                                         +          +        +              +
|                                                                                                         |          |        |              |
+---------------------------------------------------------------------------------------------------------+----------+--------+--------------+
|                                                                                                         |-4.48e-5  |-4.43e-5|1.076%        |
+ .. image:: images/Object_17.svg                                                                         +          +        +              +
|    :width: 91                                                                                           |          |        |              |
+    :height: 24                                                                                          +          +        +              +
|                                                                                                         |          |        |              |
+                                                                                                         +          +        +              +
|                                                                                                         |          |        |              |
+---------------------------------------------------------------------------------------------------------+----------+--------+--------------+
|                                                                                                         |-7.11e-5  |-7.05e-5|0.842%        |
+ .. image:: images/Object_18.svg                                                                         +          +        +              +
|    :width: 91                                                                                           |          |        |              |
+    :height: 24                                                                                          +          +        +              +
|                                                                                                         |          |        |              |
+                                                                                                         +          +        +              +
|                                                                                                         |          |        |              |
+---------------------------------------------------------------------------------------------------------+----------+--------+--------------+
|                                                                                                         |-1.13e-4  |-1.11e-4|1.412%        |
+ .. image:: images/Object_19.svg                                                                         +          +        +              +
|    :width: 91                                                                                           |          |        |              |
+    :height: 24                                                                                          +          +        +              +
|                                                                                                         |          |        |              |
+                                                                                                         +          +        +              +
|                                                                                                         |          |        |              |
+---------------------------------------------------------------------------------------------------------+----------+--------+--------------+
|                                                                                                         |-1.85e-4  |-1.85e-4|0.261%        |
+ .. image:: images/Object_20.svg                                                                         +          +        +              +
|    :width: 91                                                                                           |          |        |              |
+    :height: 24                                                                                          +          +        +              +
|                                                                                                         |          |        |              |
+                                                                                                         +          +        +              +
|                                                                                                         |          |        |              |
+---------------------------------------------------------------------------------------------------------+----------+--------+--------------+


:math:`({r}_{\mathit{iso}}^{c}+{r}_{\mathit{ela}}^{s})`

+---------------------------------------------------------------------------------------------------------+----------+-------+--------------+
|                                                                                                         |Code_Aster|GEFDYN |Relative error|
+ .. image:: images/Object_22.svg                                                                         +          +       +              +
|    :width: 91                                                                                           |          |       |              |
+    :height: 24                                                                                          +          +       +              +
|                                                                                                         |          |       |              |
+ (:math:`\mathit{kPa}`)                                                                                  +          +       +              +
|                                                                                                         |          |       |              |
+---------------------------------------------------------------------------------------------------------+----------+-------+--------------+
|                                                                                                         |0.00140   |0.00138|1.329%        |
+ .. image:: images/Object_23.svg                                                                         +          +       +              +
|    :width: 91                                                                                           |          |       |              |
+    :height: 24                                                                                          +          +       +              +
|                                                                                                         |          |       |              |
+                                                                                                         +          +       +              +
|                                                                                                         |          |       |              |
+---------------------------------------------------------------------------------------------------------+----------+-------+--------------+
|                                                                                                         |0.00220   |0.00217|1.406%        |
+ .. image:: images/Object_24.svg                                                                         +          +       +              +
|    :width: 91                                                                                           |          |       |              |
+    :height: 24                                                                                          +          +       +              +
|                                                                                                         |          |       |              |
+                                                                                                         +          +       +              +
|                                                                                                         |          |       |              |
+---------------------------------------------------------------------------------------------------------+----------+-------+--------------+
|                                                                                                         |0.00341   |0.00337|1.246%        |
+ .. image:: images/Object_25.svg                                                                         +          +       +              +
|    :width: 91                                                                                           |          |       |              |
+    :height: 24                                                                                          +          +       +              +
|                                                                                                         |          |       |              |
+                                                                                                         +          +       +              +
|                                                                                                         |          |       |              |
+---------------------------------------------------------------------------------------------------------+----------+-------+--------------+
|                                                                                                         |0.00518   |0.00510|1.663%        |
+ .. image:: images/Object_26.svg                                                                         +          +       +              +
|    :width: 91                                                                                           |          |       |              |
+    :height: 24                                                                                          +          +       +              +
|                                                                                                         |          |       |              |
+                                                                                                         +          +       +              +
|                                                                                                         |          |       |              |
+---------------------------------------------------------------------------------------------------------+----------+-------+--------------+
|                                                                                                         |0.00195   |0.00189|2.947%        |
+ .. image:: images/Object_27.svg                                                                         +          +       +              +
|    :width: 91                                                                                           |          |       |              |
+    :height: 24                                                                                          +          +       +              +
|                                                                                                         |          |       |              |
+                                                                                                         +          +       +              +
|                                                                                                         |          |       |              |
+---------------------------------------------------------------------------------------------------------+----------+-------+--------------+


:math:`({r}_{\mathit{dev}}^{m}+{r}_{\mathit{ela}}^{d})`

+---------------------------------------------------------------------------------------------------------+----------+------+--------------+
|                                                                                                         |Code_Aster|GEFDYN|Relative error|
+ .. image:: images/Object_29.svg                                                                         +          +      +              +
|    :width: 91                                                                                           |          |      |              |
+    :height: 24                                                                                          +          +      +              +
|                                                                                                         |          |      |              |
+ (:math:`\mathit{kPa}`)                                                                                  +          +      +              +
|                                                                                                         |          |      |              |
+---------------------------------------------------------------------------------------------------------+----------+------+--------------+
|15                                                                                                       |0.326     |0.326 |-0.088%       |
+---------------------------------------------------------------------------------------------------------+----------+------+--------------+
|-15                                                                                                      |0.395     |0.394 |0.172%        |
+---------------------------------------------------------------------------------------------------------+----------+------+--------------+
|15                                                                                                       |0.395     |0.394 |0.172%        |
+---------------------------------------------------------------------------------------------------------+----------+------+--------------+
|-15                                                                                                      |0.579     |0.578 |0.255%        |
+---------------------------------------------------------------------------------------------------------+----------+------+--------------+



notes
---------

The comparison between Code_Aster and GEFDYNest solutions is relatively good. The differences are explained by the integration method chosen for GEFDYNqui is explicit. You would have to increase the load split to obtain values closer to those of Code_Aster.