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




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

Compression - traction with the law parameter GLRC_DM: ALPHA_C =100.

:math:`\mathrm{A6}`

.. image:: images/1000000000000320000001E18AA1E5624797F771.jpg
    :width: 4.0665in
    :height: 2.4382in


.. _RefImage_1000000000000320000001E18AA1E5624797F771.jpg:

Figure 13.1-a: mesh and boundary conditions.

Modeling: DKTG

Boundary conditions:


* Embedding in :math:`{A}_{1}`;


* :math:`\mathrm{DX}=0.0` and :math:`\mathrm{DRY}=0.0` on the :math:`{A}_{1}-{A}_{3}` edge;


* :math:`\mathrm{DX}={U}_{0}\times f(t)` on the :math:`{A}_{2}-{A}_{4}` edge;

where :math:`{U}_{0}=2.0\times {10}^{-3}m` and :math:`f(t)` represent the amplitude of cyclic loading as a function of the (pseudo-time) parameter :math:`t`. To properly verify the model, a loading cycle is considered as follows:


.. image:: images/10000000000001F800000120B23CA7090775C644.png
    :width: 4.9583in
    :height: 2.6638in


.. _RefImage_10000000000001F800000120B23CA7090775C644.png:

Figure 13.1-b: Load function :math:`f(t)`.



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

Number of knots: 9 Number of stitches: 8 TRIA3; 8 SEG2.



Tested values and results
----------------------------

The average reaction forces along the axis :math:`\mathrm{Ox}` and the average displacements along the axis :math:`\mathrm{Oy}` *en* :math:`\mathrm{A2}-\mathrm{A4}` obtained by multi-layer modeling (reference) and by that based on the model GLRC_DM are compared, in terms of relative differences; the tolerance is taken as an absolute value on these relative differences; the tolerance is taken as an absolute value on these relative differences:


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    "Dissipation at :math:`t=\mathrm{0,05}` "," ANALYTIQUE ", "0", "5 10-2"
    "Dissipation at :math:`t=\mathrm{0,75}` "," NON_REGRESSION ", "254.9756", "5 10-2"
    "Dissipation at :math:`t=1` "," NON_REGRESSION ", "346.5721", "5 10-2"
    "COMPRESSION :math:`t=\mathrm{0,25}` ", "", "", ""
    "*Relative difference in forces* :math:`\mathrm{FX}` "," NON_REGRESSION "," ", "4.046337 105", "5 10-2"
    "*Relative difference in displacement* :math:`\mathrm{DY}` "," ANALYTIQUE "," ", "0", "5 10-2"
    "COMPRESSION :math:`t=\mathrm{1,0}` ", "", "", ""
    "*Relative difference in forces* :math:`\mathrm{FX}` "," NON_REGRESSION "," ", "5.204660 105", "5 10-2"
    "*Relative difference in movement* :math:`\mathrm{DY}` "," ANALYTIQUE "," ", "0", "0.1"
    "COMPRESSION :math:`t=\mathrm{1,5}` ", "", "", ""
    "*Relative difference in forces* :math:`\mathrm{FX}` "," NON_REGRESSION "," ", "-2.687820 106", "5 10-2"
    "*Relative difference in movement* :math:`\mathrm{DY}` "," ANALYTIQUE "," ", "0", "0.1"
    "TRACTION :math:`t=\mathrm{3,0}` ", "", "", ""
    "*Relative difference in forces* :math:`\mathrm{FX}` "," NON_REGRESSION "," ", "-4.175743 106", "5 10-2"
    "*Relative difference in movement* :math:`\mathrm{DY}` "," ANALYTIQUE "," ", "0", "0.1"
    "TRACTION :math:`t=\mathrm{3,5}` ", "", "", ""
    "*Relative difference in forces* :math:`\mathrm{FX}` "," NON_REGRESSION "," ", "-2.087571 106", "5 10-2"
    "*Relative difference in movement* :math:`\mathrm{DY}` "," ANALYTIQUE "," ", "0", "0.1"


.. _RefNumPara__30393464:


.. _refnumpara__30393464: