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


.. image:: images/10000200000004530000015FCDEB098627D618FE.png
    :width: 6.4638in
    :height: 2.0484in


.. _RefImage_10000200000004530000015FCDEB098627D618FE.png:


.. _DébuBut:


Geometry
---------

 Figure 1: Reference problem (for a :math:`90°` rotation)

We consider a cubic element of matter with a side of :math:`1000\mathrm{mm}` subjected alternately to a tensile force and then to an overall rotation of :math:`45°`. It undergoes a total of 4 traction/rotation cycles.


Material data
----------------

Here we consider the elasto-plastic behavior law with isotropic von Mises type work hardening: VMIS_ISOT_LINE. The table below lists the parameters used; in order to reinforce the comparison, the parameters used result in laws of behavior that are identical in both cases (linear isotropic work hardening).


.. csv-table::

    "Young's module:", ":math:`200000\mathrm{MPa}`"
    "Poisson's Ratio", ":math:`\mathrm{0,3}`"
    "Elastic limit", ":math:`200\mathrm{MPa}`"
    "Linear work hardening module", ":math:`2000\mathrm{MPa}`"



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

In modeling :math:`A`, in :math:`\mathrm{3D}` we block the normal movements of the front and rear faces, in order to compare the results to the modeling :math:`B` :math:`\mathrm{2D}` (D_ PLAN).

In modeling :math:`C`, also in :math:`\mathrm{3D}`, the movements of the front and rear faces are left free, in order to compare the results to the modeling :math:`D` :math:`\mathrm{2D}` (C_ PLAN).

Two types of phases must be distinguished: traction phases and rotation phases.

First traction phase


.. csv-table::

    "**Entity**", "**Load Type**", "**Value**"
    "Underside", "FACE_IMPO "," :math:`\mathrm{DNOR}=0`"
    "Top side", "FACE_IMPO "," :math:`\mathrm{DNOR}=\mathrm{500mm}`"
    "Rotation axis", "DDL_IMPO "," :math:`\mathrm{DX}=0`"
    "Front panel (:math:`\mathrm{3D}`)", "FACE_IMPO "," :math:`\mathrm{DNOR}=0`"
    "Back side (:math:`\mathrm{3D}`)", "FACE_IMPO "," :math:`\mathrm{DNOR}=0`"


Next pull-ups:


.. csv-table::

    "**Entity**", "**Load Type**", "**Value**"
    "Underside", "LIAISON_OBLIQUE "," :math:`\mathrm{DZ}=0`"
    "Top side", "LIAISON_OBLIQUE "," :math:`\mathrm{DZ}=\mathrm{200mm}`"
    "Side :math:`X=0`; :math:`Z=\mathrm{1mm}` "," LIAISON_OBLIQUE "," :math:`\mathrm{DX}=0`"
    "Rotation axis", "DDL_IMPO "," :math:`\mathrm{DX}=\mathrm{0,}\mathrm{DZ}=0`"
    "Front panel (:math:`\mathrm{3D}`)", "DDL_IMPO "," :math:`\mathrm{DY}=0`"
    "Back side (:math:`\mathrm{3D}`)", "DDL_IMPO "," :math:`\mathrm{DY}=0`"


Rotation phase:

Boundary conditions


.. csv-table::

    "**Entity**", "**Load Type**", "**Value**"
    "Rotation axis", "DDL_IMPO "," :math:`\mathrm{DX}=\mathrm{0,}\mathrm{DZ}=0`"
    "Front panel (:math:`\mathrm{3D}`)", "DDL_IMPO "," :math:`\mathrm{DY}=0`"
    "Back side (:math:`\mathrm{3D}`)", "DDL_IMPO "," :math:`\mathrm{DY}=0` or free"


The rotation load is imposed via a macro named CHAR_ROTA; an overall rotation of :math:`45°` per phase is imposed, divided into 5 increments of 9°.