D modeling
==============


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

We use a AXIS model (linear elements).


.. image:: images/Object_8.svg
    :width: 484
    :height: 259


.. _RefImage_Object_8.svg:

The continuous contact formulation is used.


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


.. image:: images/Object_9.png
    :width: 5.5201in
    :height: 1.5209in


.. _RefImage_Object_9.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"," 0.2%"
    "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%"


We test the number of iterations of Newton when the point :math:`K` of the plot is in front of the points :math:`B`, :math:`C`, :math:`D`, :math:`E`, :math:`F` and :math:`G` of the string.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "ITER_GLOB/Point :math:`B` ", "'NON_REGRESSION'", "1", "0.00%"
    "ITER_GLOB/Point :math:`C` ", "'NON_REGRESSION'", "1", "0.00%"
    "ITER_GLOB/Point :math:`D` ", "'NON_REGRESSION'", "1", "0.00%"
    "ITER_GLOB/Point :math:`E` ", "'NON_REGRESSION'", "1", "0.00%"
    "ITER_GLOB/Point :math:`F` ", "'NON_REGRESSION'", "1", "0.00%"
    "ITER_GLOB/Point :math:`G` ", "'NON_REGRESSION'", "1", "0.00%"


We test the state of the contact (field CONT_NOEU) when the point :math:`K` of the piece is in front of the points between :math:`E` and :math:`F` and all the :math:`\mathrm{5mm}`.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "CONT/Point :math:`E` ", "'NON_REGRESSION'", "0"," 0.00%"
    "CONT/Point :math:`E` + :math:`\mathrm{5mm}` ", "'NON_REGRESSION'", "0"," 0.00%"
    "CONT/Point :math:`E` + :math:`\mathrm{10mm}` ", "'NON_REGRESSION'", "2"," 0.00%"
    "CONT/Point :math:`E` + :math:`\mathrm{15mm}` ", "'NON_REGRESSION'", "2"," 0.00%"
    "CONT/Point :math:`F` ", "'NON_REGRESSION'", "2"," 0.00%"


     The first two points are not in contact.


notes
---------

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


.. csv-table::

    "* from", ":math:`\mathrm{0.mm}` to", ":math:`\mathrm{5.mm}` in 5 steps"
    "* from", ":math:`\mathrm{5.mm}` to", ":math:`\mathrm{20.mm}` in 5 steps"
    "* from", ":math:`\mathrm{20.mm}` to", ":math:`\mathrm{50.mm}` in 5 steps"
    "* from", ":math:`\mathrm{50.mm}` to", ":math:`\mathrm{70.mm}` in 5 steps"
    "* from", ":math:`\mathrm{70.mm}` to", ":math:`\mathrm{140.mm}` in 5 steps"
    "* from", ":math:`\mathrm{140.mm}` to", ":math:`\mathrm{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.