Ratings
=========




Generalities
-----------

The deformations are positive in extension and the stresses are positive for tensile states.


.. csv-table::

    "**Notion**", "**Description**"
    ":math:`{I}_{1}\text{=}\text{tr}(\sigma )` ", "First constraint invariant"
    ":math:`s\text{=}\sigma \text{-}\frac{\text{tr}(\sigma )}{3}I` ", "Constraint deviator"
    ":math:`{s}_{\text{II}}\text{=}\sqrt{s\text{.}s}` ", "Second invariant of the deviatory stress tensor"
    ":math:`e\text{=}\varepsilon -\frac{\text{tr}(\varepsilon )}{3}I` ", "Deformation deviator"
    ":math:`{\varepsilon }_{\nu }\text{=}\text{tr}(\varepsilon )` ", "Trace of deformations: volume deformation"
    ":math:`{\varepsilon }^{p}` ", "Plastic deformation tensor"
    ":math:`{\varepsilon }_{{}_{\nu }}^{p}\text{=}\text{tr}({\varepsilon }^{p})` ", "Variation in plastic volume"
    ":math:`\delta {\gamma }^{p}\text{=}\sqrt{\frac{2}{3}d{e}^{p}:d{e}^{p}}` ", "Cumulative plastic shear deformation"
    ":math:`{\mathrm{\sigma }}_{1}` ", "Major main constraint"
    ":math:`{\mathrm{\sigma }}_{3}` ", "Minor primary constraint (:math:`{\mathrm{\sigma }}_{1}<{\mathrm{\sigma }}_{2}<{\mathrm{\sigma }}_{3}`)"
    ":math:`H` ", "Hooke matrix"
    ":math:`\mu` ", "Lamé coefficient"





Model parameters
--------------------


.. csv-table::

    "**Notion**", "**Description**"
    ":math:`\mathrm{\gamma }` ", "Work hardening parameter (defined in paragraph :ref:`3.2.3 <Ref100116782>`)"
    ":math:`S` ", "Represents the state of damage and fracturing of the rock"
    ":math:`m` ", "Model smoothing parameter"
    ":math:`{\mathrm{\sigma }}_{c}` ", "Strength of healthy rock without any damage"
    ":math:`{\mathrm{\gamma }}^{\text{rup}}` ", "Work hardening parameter corresponding to material breakage"
    ":math:`{\mathrm{\gamma }}^{\text{res}}` ", "Work hardening parameter corresponding to the start of residual resistance"
    ":math:`({\mathrm{S\sigma }}_{c}^{2}{)}^{\text{rup}}` ", "Product value :math:`S{\sigma }_{c}^{2}` at breakpoint reached in :math:`{\mathrm{\gamma }}^{\text{rup}}`"
    ":math:`({\mathrm{S\sigma }}_{c}^{2}{)}^{\text{end}}` ", "Product value :math:`S{\sigma }_{c}^{2}` at damage initiation :math:`(\mathrm{\gamma }=0)`"
    ":math:`({\mathrm{m\sigma }}_{c}{)}^{\text{rup}}` ", "Product value :math:`m{\sigma }_{c}` at breakpoint reached in :math:`{\mathrm{\gamma }}^{\text{rup}}`"
    ":math:`({\mathrm{m\sigma }}_{c}{)}^{\text{end}}` ", "Product value :math:`m{\sigma }_{c}` at damage initiation :math:`(\mathrm{\gamma }=0)`"
    ":math:`E` ", "Young's module"
    ":math:`\mathrm{\nu  }` ", "Poisson's ratio"
    ":math:`\mathrm{\beta  }` ", "Characterize residual resistance"
    ":math:`{\phi }^{\text{end}}` ", "Friction angle at damage initiation :math:`(\mathrm{\gamma }=0)`: optional parameter taken to be zero by default"
    ":math:`{\phi }^{\text{rup}}` ", "Friction angle at break reached in :math:`{\mathrm{\gamma }}^{\text{rup}}`"
    ":math:`{\phi }^{\text{res}}` ", "Friction angle at residual resistance reached in :math:`{\mathrm{\gamma }}^{\text{res}}`"
    ":math:`\mathrm{\alpha }` ", "Model parameter characterizing the post-fracture behavior of the material"