Verification and validation
==========================

Test cases
---------

The references of the test cases and associated documentation are given in the following table.

.. list-table:: Cas-tests et documentations associées.

 *-**Test case reference**
   - **Documentation reference**
   - **Description**
 *-*ssnv160g*
   - [v6.04.160]
   - Isotropic compression test
 *-*ssnv202c*
   - [v6.04.202]
   - Oedometric compression test
 *-*wtnv122d*
   - [v7.31.122]
   - Undrained triaxial compression test 
 *-*comp012h*
   - [v6.07.112]
   - Compatibility test with command CALC_GEO_MECA
   
Examples of answers to the material point
--------------------------------------

The following three figures show some answers obtained using the executable MTest (answers to the hardware point): 

* Isotropic compression test;
* Isotropic tensile test;
* Triaxial compression tests for several confinement stresses.
 
The model parameters used in these simulations are grouped together in the table below.
 
.. list-table:: Paramètres du modèle simulé.
  
 *-**Effect**
   - **Name**
   - **Definition**
   - **Symbol**
   - **Value**
 * - Isotropic nonlinear elasticity
   - | *BulkModulus*
     | *ShearModulus*
     | *SwellingIndex*
   - | Compressibility module
     | Shear module
     | Elastic nonlinearity index
   - |:math: `K`
     |:math: `\ mu`
     |:math: `\ kappa`
   - | 160 MPa
     | 100 MPa
     | 50
 * - Initial elasticity domain
   - | *initCritPress*
     | *critstateSlope*
     | *TensileYieldStress*
   - | Initial critical pressure
     | Critical state slope
     | Isotropic tensile strength
   - |:math: `p_ {c0} `
     |:math: `M`
     |:math: `\ sigma_0`
   - | 1 MPa
     | 1
     | 10 kPa
 * - Kinematic-isotropic work hardening
   - | *IncoplastIndex*
   - | Plastic incompressibility index
   - |:math: `\ beta`
   - | 50  
   
   
.. figure:: images/compression_isotrope_MCC.svg
 :align: center
 :width: 960
 :height: 360
 
 Isotropic compression test driven by mean stress :math:`\sigma_m`. In the load phase, the response is elastic non-linear (:math:`Ip=0`) up to :math:`-\sigma_m=2p_{c0}+\sigma_0=2.01` MPa, then irreversible (:math:`Ip=1`). The work hardening is then positive. The discharge from :math:`-\sigma_m=10` MPa to zero is elastic non-linear (:math:`Ip=0`).
 
.. figure:: images/traction_isotrope_MCC.svg
 :align: center
 :width: 960
 :height: 360 
 
 Isotropic tensile test driven by vertical deformation :math:`\epsilon_{zz}`. After the elastic load phase, the stress saturates at :math:`\sigma_m=\sigma_0=10` kPa, without showing any positive or negative work hardening. It should be noted that the nonlinearity of the elasticity is imperceptible. The expression for constraint :eq:`expression_contrainte` explains it by condition :math:`\sigma_m\ll K/\kappa`, a situation encountered in this load with the parameters of the simulated model.
 
.. figure:: images/compression_triaxiale_MCC.svg
 :align: center
 :width: 960
 :height: 360 
 
 Triaxial compression tests with multiple confinement stresses :math:`-\sigma_{xx}=-\sigma_{yy}`. Equivalent stress :math:`\sigma_{eq}` has negative work hardening at the weakest confinements and positive work hardening at the strongest. In parallel, the evolution of volume plastic deformation :math:`\xi=\mathrm{tr}(\boldsymbol{\epsilon}^p)` goes from a regime of dilatance (:math:`\dot{\xi}>0`) to contraction (:math:`\dot{\xi}<0`). It should be noted that the first loading phase at equivalent stress :math:`\sigma_{eq}=0` corresponds to confinement with :math:`-\sigma_{xx}=-\sigma_{yy}=-\sigma_{zz}`.