Settings
==========

Classification
--------------

Seven parameters are necessary to define the modified Cam-Clay model, which are classified below.

.. list-table:: Paramètres.

 *-**Effect**
   - **Name**
   - **Definition**
   - **Unit**
   - **Interval**
   - **Symbol**
 * - Isotropic nonlinear elasticity
   - | *BulkModulus*
     | *ShearModulus*
     | *SwellingIndex*
   - | Compressibility module
     | Shear module
     | Elastic nonlinearity index
   - | [Not]
     | [Not]
     | [-]
   - |:math: `\ mathbb {R} ^ {+*}`
     |:math: `\ mathbb {R} ^ {+*}`
     |:math: `\ mathbb {R} ^ {+}`
   - |:math: `K`
     |:math: `\ mu`
     |:math: `\ kappa`
 * - Initial elasticity domain
   - | *initCritPress*
     | *critstateSlope*
     | *TensileYieldStress*
   - | Initial critical pressure
     | Critical state slope
     | Isotropic tensile strength
   - | [Not]
     | [-]
     | [Not]
   - |:math: `\ mathbb {R} ^ {+*}`
     |:math: `\ mathbb {R} ^ {+*}`
     |:math: `\ mathbb {R} ^ {+}`
   - |:math: `p_ {c0} `
     |:math: `M`
     |:math: `\ sigma_0`
 * - Kinematic-isotropic work hardening
   - | *IncoplastIndex*
   - | Plastic incompressibility index
   - | [Not]
   - |:math: `\ mathbb {R} ^ {+}`
   - |:math: `\ beta`


Equivalence to parameters [r7.01.14]
-------------------------------------

The following table shows the equivalence of the seven parameters of the modified Cam-Clay model presented here to those necessary to define the model CAM_CLAY [r7.01.14] [:ref:`r7.01.14 <R7.01.14>`] _.

 **Note:**

 The following table proposes an identification of the elastic behavior of the modified Cam-Clay model shown here in model CAM_CLAY [:ref:`r7.01.14 <R7.01.14>`] _. However, this is not an exact step. In the latter, the elasticity adopted is linear in terms of deviatoric behavior and assumes a non-zero hydrostatic stress state (:math:`\boldsymbol{\sigma}=-\widetilde{P}_0\boldsymbol{I}`) with zero elastic deformation. The reader is invited to go through [:ref:`r7.01.14 <R7.01.14>`] _ to get more details on the elasticity being formulated in equation 3.5-6.

.. list-table:: Équivalence aux paramètres du modèle CAM_CLAY [r7.01.14]. Pour lever toute confusion, ces derniers sont sur-indexés par le symbole :math:`\widetilde{\cdot}` pour les différencier de ceux définis dans ce document.

 *-**Relationship to parameters [r7.01.14] **
   - **Reference [r7.01.14]**
 * - :math:`K\approx\widetilde{k}_0\widetilde{P}_0+\widetilde{K}_{cam}`
   - equation 3.3-3
 * - :math:`\mu\approx\widetilde{\mu}`
   - equation 3.3-1
 * - :math:`\kappa=\widetilde{k}_0`
   - equation 3.3-3
 * - :math:`p_{c0}=\widetilde{P}_{cr}^0`
   - equation 3.3-4
 * - :math:`M=\widetilde{M}`
   - equation 3.2-1
 * - :math:`\sigma_0=-\widetilde{P}_{trac}`
   - equation 3.2-1
 * - :math:`\beta=\widetilde{k}`
   - equation 3.3-4