K modeling
==============


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

We use the same ingredients as the J modeling by combining ALGO_CONT = STANDARD for zone 1 with GLISSIERE with ALGO_CONT = PENALISATION for zone 2.

3D modeling (linear elements) is used.


.. image:: images/Object_74.svg
    :width: 641
    :height: 362


.. _RefImage_Object_74.svg:

The continuous contact formulation is used. This test case is used to validate the CONTACT_INIT = 'INTERPENETRE' feature. Here we use the GLISSIERE function, which makes it possible to maintain contact throughout the extrusion, mathematically. The result is physically similar to modeling without a slide, since it is a frictionless extrusion.


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


.. image:: images/Object_75.png
    :width: 4.6102in
    :height: 2.2854in


.. _RefImage_Object_75.png:

Number of knots: 3292

Number of meshes: 2150 HEXA8, 260 PENTA6, 260, 1814 QUAD4 and 68 TRIA63

Number of nodes in contact: 210


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

The reference values are considered to be those of modeling C. The following displacement :math:`Y` of the point :math:`K` of the plot 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"," 0.10%"
    "Point :math:`K`/Point :math:`C` - :math:`\mathit{DY}` ", "'ANALYTIQUE'", "20.8250"," 2.0%"
    "Point :math:`K`/Point :math:`D` - :math:`\mathit{DY}` ", "'ANALYTIQUE'", "55.8800"," 1.50%"
    "Point :math:`K`/Point :math:`E` - :math:`\mathit{DY}` ", "'ANALYTIQUE'", "140.0", "0.2%", "0, 2%"
    "Point :math:`K`/Point :math:`F` - :math:`\mathit{DY}` ", "'ANALYTIQUE'", "155.0", "0.2%"


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` and :math:`F` of the chain.


.. 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%"



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:`0\mathit{mm}` to", ":math:`20\mathit{mm}` in 4 steps"
    "* from", ":math:`20\mathit{mm}` to", ":math:`70\mathit{mm}` in 5 steps"
    "* from", ":math:`70\mathit{mm}` to", ":math:`140\mathit{mm}` in 2 steps"
    "* from", ":math:`140\mathit{mm}` to", ":math:`155\mathit{mm}` in 1 step"


In this modeling, the external forces are sufficiently important and the use of an absolute convergence criterion is not mandatory because the symmetry conditions on the plot have been slightly disturbed.