B modeling
==============


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

Modeling :math:`B` is three-dimensional and static linear (3D). Its purpose is to test the orthotropy of Hujeux's law. The following mechanical properties are used:


+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+
|Elastic parameters                                                                                                      |Humid parameters (modified compared to §1.2)                              |
+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+
|:math:`{E}_{\mathrm{xx}}`                                                            |:math:`62000\mathrm{MPa}`         |:math:`n`                                            |:math:`0`           |
+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+
|:math:`{E}_{\mathrm{yy}}`                                                            |:math:`31000\mathrm{MPa}`         |:math:`d`                                            |:math:`100`         |
+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+
|:math:`{E}_{\mathrm{zz}}`                                                            |:math:`620\mathrm{MPa}`           |:math:`b`                                            |:math:`\mathrm{0,1}`|
+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+
|:math:`{\upsilon }_{\mathrm{xx}}={\upsilon }_{\mathrm{yy}}={\upsilon }_{\mathrm{zz}}`|:math:`\mathrm{0,3}`              |:math:`{r}_{\mathrm{ela}}^{I}={r}_{\mathrm{ela}}^{D}`|:math:`1`           |
+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+
|:math:`{G}_{\mathrm{xx}}`                                                            |:math:`11910\mathrm{MPa}`         |                                                     |                    |
+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+
|:math:`{G}_{\mathrm{yy}}`                                                            |:math:`23820\mathrm{MPa}`         |                                                     |                    |
+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+
|:math:`{G}_{\mathrm{zz}}`                                                            |:math:`\mathrm{238,2}\mathrm{MPa}`|                                                     |                    |
+-------------------------------------------------------------------------------------+----------------------------------+-----------------------------------------------------+--------------------+

Isotropic compression of the sample is carried out up to :math:`{p}_{f}=-300\mathrm{kPa}` in :math:`101` (time step between :math:`t=-10` and :math:`t=0`).


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

The solutions are calculated at point :math:`C` and compared to a true orthotropic linear elastic calculation performed with *Code_Aster*. They are given in terms of longitudinal :math:`{\epsilon }_{\mathrm{xx}}` and transverse :math:`{\epsilon }_{\mathrm{yy}}` deformations, and summarized in the following tables:

:math:`{ϵ}_{\mathit{xx}}`

.. csv-table::

    ":math:`{\epsilon }_{\mathrm{zz}}` ", "**Reference type**", "**Reference value**", "**Tolerance (%)**"
    "-6.40E-5"," AUTRE_ASTER ", "-2.580E-7", "1.0"
    "-1.28E-4"," AUTRE_ASTER ", "-5.170E-7", "1.0"
    "-1.92E-4"," AUTRE_ASTER ", "-7.750E-7", "1.0"
    "-2.56E-4"," AUTRE_ASTER ", "-1.033E-6", "1.0"
    "-3.20E-4"," AUTRE_ASTER ", "-1.291E-6", "1.0"


:math:`{ϵ}_{\mathit{yy}}`

.. csv-table::

    ":math:`{\epsilon }_{\mathrm{zz}}` ", "**Reference type**", "**Reference value**", "**Tolerance (%)**"
    "-6.40E-5"," AUTRE_ASTER ", "-7.10E-7", "1.0"
    "-1.28E-4"," AUTRE_ASTER ", "-1.42E-6", "1.0"
    "-1.92E-4"," AUTRE_ASTER ", "-2.13E-6", "1.0"
    "-2.56E-4"," AUTRE_ASTER ", "-2.84E-6", "1.0"
    "-3.20E-4"," AUTRE_ASTER ", "-3.55E-6", "1.0"



notes
---------

The difference between the two simulations, which model the same behavior, is very small.