Reference issues
======================

Geometry
---------

Geometry is a segment with 2 nodes. The initial length of the segment is :math:`0.1\mathrm{m}`.


.. image:: images/1000020100000640000000B9A2387CB7FAA54173.png
    :width: 3.1492in
    :height: 0.3638in


.. _RefImage_1000020100000640000000B9A2387CB7FAA54173.png:


Modeling A
--------------

Discreet is a SEG2de type K_T_D_L. Its behavior is CHOC_ENDO.


Material properties
~~~~~~~~~~~~~~~~~~~~~~~~~

The table below shows the characteristics of the material. During a calculation carried out with the operator STAT_NON_LINE, depreciation is not taken into account.


.. csv-table::

    "Ux
    [m]", "Strength
    [N]", "Stiffness
    [N/m]"
    "0.00", "0.0", "2000.0"
    "0.20", "400.0", "2000.0"
    "0.50", "450.0", "2000.0"
    "0.70", "400.0", "2000.0"
    "0.95", "375.0", "2000.0"
    "1.30", "350.0", "2000.0"
    "1.60", "300.0", "2000.0"


The figure below shows the behavior corresponding to the data.


.. image:: images/1000020100000CC6000006654DFAFC3B70645267.png
    :width: 5.9055in
    :height: 2.9484in


.. _RefImage_1000020100000CC6000006654DFAFC3B70645267.png:

The following commands are used to define the material:

ldepla= nu.Array ([:ref:`0.0, 2.0, 5.0, 7.0, 9.50, 13.0, 16.0, <0.0, 2.0, 5.0, 7.0, 9.50, 13.0, 16.0,>`]) /10.0

lforce= nu.Array ([:ref:`0.0, 4.0, 4.5, 4.0, 3.75, 3.50, 3.0, <0.0, 4.0, 4.5, 4.0, 3.75, 3.50, 3.0,>`]) * 100.0

# Constant stiffness

lraid= nu.Array ([:ref:`2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, <2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0,>`]) * 1000.0

# Damping: useless in static but mandatory to give

death = nu.Array ([:ref:`0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, <0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,>`])

#

fctfx **= DEFI_FONCTION (NOM_PARA =** 'X', **ABSCISSE =** ldepla, **ORDONNEE =** lforce, **)**) **

fctrd **= DEFI_FONCTION (NOM_PARA =** 'X', **ABSCISSE =** lrepla, **ORDONNEE =** stiff, **)**) **

ctam **= DEFI_FONCTION (NOM_PARA =** 'X', **ABSCISSE =** ldepla, **ORDONNEE =** lamort, **)**) **

#

Grilleac **= DEFI_MATERIAU (**

**DIS_CHOC_ENDO** = **_F (**

**FX** = fctfx, **RIGI_NOR** **= fctrd,** AMOR_NOR **** = fctam,

**DIST_1** = 0.0, **DIST_2** ** = 0.0,

**CRIT_AMOR** **=** 'INCLUS',

**)**,

**)**

Note: it is mandatory to fill in CRIT_AMOR. When the calculation is performed in non-linear statics, whether the value is INCLUS or EXCLUS has no influence on the results [:ref:`R5.03.17 <R5.03.17>`].


B modeling
--------------

This case models behavior CHOC_ENDO with a stiffness that is variable and a function of :math:`\mathrm{Ux}`.

The discrete one is a K_T_D_L.


Material properties
~~~~~~~~~~~~~~~~~~~~~~~~~

The table below shows the characteristics of material DIS_CHOC_ENDO. For a calculation carried out with the operator STAT_NON_LINE, depreciation is not taken into account.


.. csv-table::

    "Ux
    [m]", "Strength
    [N]", "Stiffness
    [N/m]"
    "0.00", "0.0", "2000.0"
    "0.20", "400.0", "2000.0"
    "0.50", "450.0", "1800.0"
    "0.70", "400.0", "1400.0"
    "0.95", "375.0", "1400.0"
    "1.30", "350.0", "1350.0"
    "1.60", "300.0", "1330.0"


Compared to modeling :math:`A`, only the definition of stiffness changes.

# Variable stiffness

lraid= nu.Array ([:ref:`2.0, 2.0, 1.8, 1.4, 1.4, 1.35, 1.33, <2.0, 2.0, 1.8, 1.4, 1.4, 1.35, 1.33,>`]) * 1000.0

The figure below shows the behavior corresponding to the data.


.. image:: images/1000020100000CC6000006650D7BFD7DE8F89B72.png
    :width: 5.9055in
    :height: 2.9484in


.. _refImage_1000020100000 CC6000006650D7BFD7DE8F89B72 .png: