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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:






* Size of the square: :math:`\mathrm{1m}\mathrm{\times }\mathrm{1m}`.


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

Elastic


*
    * :math:`E=5800.0\mathrm{E6}\mathrm{Pa}` Young's module


    * :math:`\nu =0.3` Poisson's Ratio

DRUCK_PRAGER with linear negative work hardening


*
    * :math:`\alpha \mathrm{=}0.33` Pressure Dependence Coefficient


    * :math:`{p}_{\mathrm{ultm}}=0.01` Ultimate cumulative plastic deformation


    * :math:`{\sigma }^{Y}=2.57\mathrm{E6}\mathrm{Pa}` Plastic constraint


    * :math:`h=-2.\mathrm{E8}\mathrm{Pa}` Work hardening module



DRUCK_PRAGER with parabolic negative work hardening


*
    * :math:`\alpha =0.33` Pressure Dependence Coefficient


    * :math:`{p}_{\mathrm{ultm}}=0.01` Ultimate cumulative plastic deformation


    * :math:`{\sigma }^{Y}=2.57\mathrm{E6}\mathrm{Pa}` Plastic constraint


    * :math:`{\sigma }_{\mathrm{ultm}}^{Y}=0.57\mathrm{E6}\mathrm{Pa}` Ultimate constraint


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

The boundary conditions and loads applied are as follows:

Imposed loads: loads are constant :math:`t\mathrm{\in }\text{]}\mathrm{1,2}\mathrm{.}\text{]}`


* Side :math:`\mathrm{BC}` :math:`p={2.10}^{6}\mathrm{Pa}`


*
    *
        *

**Travel imposed on:**


* Side :math:`\mathrm{AB}` :math:`\mathrm{DY}=0.`


* Side :math:`\mathrm{DA}` :math:`\mathrm{DX}=0.`


* The movements vary over :math:`\mathrm{CD}` gradually, over the interval :math:`t\mathrm{\in }\text{]}\mathrm{1,2}\mathrm{.}\text{]}`, following a ramp, as in the figure below: :math:`t=1.` :math:`\mathrm{DY}=0.`

 :math:`t=2.` :math:`\mathrm{DY}=-0.015`


.. image:: images/Shape2.gif


.. _RefSchema_Shape2.gif:


Initial conditions
--------------------


*
    *
        * Initial conditions :math:`(\mathrm{Pa})`


.. csv-table::

    ":math:`\mathrm{SIXX}` "," :math:`\mathrm{SIYY}` "," :math:`\mathrm{SIZZ}` "," "," :math:`\mathrm{SIXY}` "," :math:`\mathrm{SIXZ}` "," :math:`\mathrm{SIYZ}`"
    "-2. E6", "-2. E6", "-2. E6", "0.0", "0.0", "0.0", "0.0"



*
    *


.. csv-table::

    ":math:`\mathrm{SIP}` "," :math:`\mathrm{M11}` "," :math:`\mathrm{FH11X}` "," :math:`\mathrm{FH11Y}`"
    "0.0", "0.0", "0.0", "0.0"