Reference problem
=====================


Geometry
----------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

**Figure 1.1-a: Geometry and boundary conditions**


Material properties
----------------------

**Cube:* elastic

:math:`E=\mathrm{2,1}\cdot {10}^{6}` :math:`\mathit{MPa}`, :math:`\nu \mathrm{=}0`

**Joint element**:


* law of behavior ELAS with the following parameters:

:math:`E=\mathrm{2,1}\cdot {10}^{6}` :math:`\mathit{MPa}`, :math:`\nu \mathrm{=}0`


* law of behavior JOINT_BA with the following parameters:


*
    * Initial settings:


.. csv-table::

    "penetration coefficient:", ":math:`\mathit{Hpen}\mathrm{=}\mathrm{0.64mm}` ", "(keyword: HPEN)"
    "", "", ""
    "stiffness module:", ":math:`{G}_{\mathit{lia}}\mathrm{=}6.65\mathrm{\times }{10}^{+\mathrm{3MPa}}` ", "(keyword: GTT)"



*
    * Tangential damage parameters:


.. csv-table::

    "elastic deformation threshold:", ":math:`{\varepsilon }_{\gamma }^{0}\mathrm{=}5\mathrm{\times }{10}^{\mathrm{-}4}` ", "(keyword: GAMD0)"
    "", "", ""
    "damage coefficient region 1:", ":math:`{\mathit{Ad}}_{1}\mathrm{=}1.0` ", "(keyword: AD1)"
    "", "", ""
    "damage coefficient region 1:", ":math:`{\mathit{Bd}}_{1}\mathrm{=}0.5` ", "(keyword: BD1)"
    "", "", ""
    "threshold of major landslides:", ":math:`{\varepsilon }_{\gamma }^{2}\mathrm{=}9.6\mathrm{\times }10\mathrm{-}1` ", "(keyword: GAMD2)"
    "", "", ""
    "damage coefficient region 2:", ":math:`{\mathit{Ad}}_{2}\mathrm{=}6\mathrm{\times }{10}^{\mathrm{-}5}{\mathit{MPa}}^{\mathrm{-}1}` ", "(keyword: AD2)"
    "", "", ""
    "damage coefficient region 2:", ":math:`{\mathit{Bd}}_{2}\mathrm{=}1.0` ", "(keyword: BD2)"



*
    * Parameters for crack friction and confinement:


.. csv-table::

    "friction:", ":math:`\gamma \mathrm{=}10.0\mathit{MPa}` ", "(keyword: VIFROT)"
    "", "", ""
    "kinematic work hardening:", ":math:`\alpha \mathrm{=}4\mathrm{\times }{10}^{\mathrm{-}1}{\mathit{MPa}}^{\mathrm{-}1}` ", "(keyword: FA)"
    "", "", ""
    "lockdown:", ":math:`c\mathrm{=}1.0` ", "(keyword: FC)"



*
    * Normal damage parameters:


.. csv-table::

    "critical normal deformation (opening):", ":math:`{\varepsilon }_{N}^{0}\mathrm{=}9\mathrm{\times }{10}^{\mathrm{-}1}` ", "(keyword: EPSTR0)"
    "", "", ""
    "normal damage coefficient:", ":math:`{\mathit{Ad}}_{N}\mathrm{=}1\mathrm{\times }{10}^{\mathrm{-}9}{\mathit{MPa}}^{\mathrm{-}1}` ", "(keyword: ADN)"
    "", "", ""
    "normal damage coefficient:", ":math:`{\mathit{Bd}}_{N}\mathrm{=}1.5` ", "(keyword: BDN)"



Boundary conditions and loads
-------------------------------------

No imposed displacements on the left side of the joint element.

Mechanical loading is imposed in the form of movements imposed on the right side of the cube in increments of :math:`0.01\mathrm{\times }U` at each time step, from 0 to 300.


note
--------

The law of behavior of the joint element is given locally (frame :math:`(n,t)`), the system calculations are performed in the global coordinate system :math:`(x,y)`. The base change was taken into account in the calculations. The test case was developed with a rotation of :math:`30°` in order to validate this basic change.