Modeling A
==============


Characteristics of modeling
-----------------------------------

We use a AXIS model (linear elements).


.. image:: images/Object_2.svg
    :width: 484
    :height: 259


.. _RefImage_Object_2.svg:



The discrete contact formulation is used (active stress method).


Characteristics of the mesh
----------------------------


.. image:: images/Object_3.png
    :width: 5.5201in
    :height: 1.5209in


.. _RefImage_Object_3.png:

Number of knots: 333

Number of meshes: 510 TRIA3 and 152 SEG2

Number of nodes in contact: 20


Tested sizes and results
------------------------------

The following displacement :math:`Y` of the point :math:`K` of the piece of paper with respect to the surface :math:`\mathrm{ABCDEFG}` of the die is tested.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "Point :math:`K`/Point :math:`B` - :math:`\mathrm{DY}` ", "'ANALYTIQUE'", "5.0000"," 0.1%"
    "Point :math:`K`/Point :math:`C` - :math:`\mathrm{DY}` ", "'ANALYTIQUE'", "20.8250"," 0.1%"
    "Point :math:`K`/Point :math:`D` - :math:`\mathrm{DY}` ", "'ANALYTIQUE'", "55.8800"," 0.2%"
    "Point :math:`K`/Point :math:`E` - :math:`\mathrm{DY}` ", "'ANALYTIQUE'", "78.6900"," 0.1%"
    "Point :math:`K`/Point :math:`F` - :math:`\mathrm{DY}` ", "'ANALYTIQUE'", "144.8950"," 0.1%"
    "Point :math:`K`/Point :math:`G` - :math:`\mathrm{DY}` ", "'ANALYTIQUE'", "155.0960"," 0.1%"


Checking mode RESOLUTION =' NON ':


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "Point :math:`K`/Point :math:`G` - :math:`\mathrm{DY}` ", "'ANALYTIQUE'", "155.0960"," 0.1%"
    "Game :math:`\mathrm{LC}` ", "'ANALYTIQUE'", "-5.0000"," 0.1%"
    "Game :math:`LE` ", "'ANALYTIQUE'", "-2.0000"," 0.1%"



notes
---------

The calculation is carried out by imposing a displacement on the back side of the block :math:`\text{(MN)}`. The displacement is imposed as follows:


.. csv-table::

    "* from", "0.mm to", "5.mm in 5 steps"
    "* from", "5.mm to", "20.mm in 5 steps"
    "* from", "20.mm to", "50.mm in 5 steps"
    "* from", "50.mm to", "70.mm in 5 steps"
    "* from", "70.mm to", "140.mm in 5 steps"
    "* from", "140.mm to", "155.mm in 5 steps"


The calculations do not converge with the default keywords used for convergence in STAT_NON_LINE, because the default value of RESI_GLOB_RELA = 1.E-6 is too restrictive (the forces to which the piece is subjected are initially relatively weak). To overcome this problem, use the keyword RESI_GLOB_MAXI = 1.E-6.