E modeling
==============

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

In this modeling, we use the operator DYNA_NON_LINE (see [:ref:`U4.53.01 <U4.53.01>`]) with the relationship DIS_CONTACT. The integration diagram is NEWMARK.

This modeling corresponds to the direct transient response of the friction pad. It validates the orientation of the discrete as well as the initial interpenetration.

• For the first case: The normal contact direction is the global axis :math:`X` which corresponds in the test case to the global axis :math:`X`. The sliding plane is the local plane :math:`(Y,Z)`, i.e. the plane :math:`(Y,Z)` in the global coordinate system. We therefore direct the shock element to a node, with the keyword ORIENTATION from the AFFE_CARA_ELEM operator in the following way:

**ORIENTATION =_F (MAILLE =' EL1 '**, **CARA =' VECT_X_Y '**,

**VALE =(** 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 **)**, **)**) **,**) **,

The tangential shock stiffness considered is :math:`{K}_{T}=4\phantom{\rule{0ex}{0ex}}000000N/m`, the Coulomb coefficient is :math:`\mathrm{\mu }=\mathrm{0,1}`. The normal shock stiffness is :math:`20N/m`

The law of shock behavior is therefore defined as follows in DEFI_MATERIAU:

MATCH1 **= DEFI_MATERIAU (**

**DIS_CONTACT =_F (RIGI_NOR =20.0**, **RIGI_TAN =4000000.0**, **COULOMB =0.1)**, **

**)**

To be able to obtain a reaction force from the plane on the system, the system must be slightly pressed into the plane obstacle by a distance :math:`\delta n` such as: :math:`{F}_{n}={K}_{n}\cdot \delta n`.

The reaction balances the weight of the skate, so we have: :math:`{F}_{n}=\mathrm{mg}` i.e. :math:`\mathrm{\delta }n=\mathit{mg}/{K}_{n}`. The first loading steps achieve this sinking.

• For the second case: The normal direction of contact is the local axis :math:`X` which corresponds in the test case to the global axis :math:`Z`. The sliding plane is the local plane :math:`(Y,Z)`, i.e. the plane :math:`(X,Y)` in the global coordinate system. We therefore direct the shock element to a node, with the keyword ORIENTATION from the AFFE_CARA_ELEM operator in the following way:

**ORIENTATION =_F (MAILLE =' EL1 '**, **CARA =' VECT_X_Y '**,

**VALE =(** 0.0, 0.0, 1.0, 1.0, 1.0, 0.0 **)**, **)**) **,**) **,

To be able to obtain a reaction force from the plane on the system, the system must be slightly pressed into the plane obstacle by a distance :math:`\mathrm{\delta }n` such as: :math:`{F}_{n}={K}_{n}\cdot \mathrm{\delta }n`.

The reaction balances the weight of the skate, so we have: :math:`{F}_{n}=\mathit{mg}` i.e. :math:`\mathrm{\delta }n=\mathit{mg}/{K}_{n}`.

We considered a normal shock stiffness of :math:`20N/m` so we have :math:`\delta n=\mathrm{0,5}` from where :math:`\mathit{DIST}\underline{\phantom{\rule{2em}{0ex}}}1=0.5`.

MATCH2 **= DEFI_MATERIAU (**

**DIS_CONTACT =_F (RIGI_NOR =20.0**, **RIGI_TAN =4000000.0**,

**COULOMB =0.10**, **DIST_1 =0.50)**,

**)**


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

Number of knots: 1

Number of meshes and types: 1 POI1


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

Values of the movements in the direction of the oscillator for the times when the sign of the speed changes and when the mass stops.

.. csv-table::

    "**instant**", "**reference value**", "**Tolerance**"
    ":math:`\mathrm{\pi }/100` "," :math:`-6.5E-04\sqrt{2}/2` ", "1.0e-04"
    ":math:`2.0\mathrm{\pi }/100` "," :math:`4.5E-04\sqrt{2}/2` ", "1.0e-04"
    ":math:`3.0\mathrm{\pi }/100` "," :math:`-2.5E-04\sqrt{2}/2` ", "1.5e-04"
    ":math:`4.0\mathrm{\pi }/100` "," :math:`0.5E-04\sqrt{2}/2` ", "1.0e-03"



.. image:: images/1000662500006CE200004CF932937AC7DD050D77.svg
    :width: 453
    :height: 320


.. _RefImage_1000662500006CE200004CF932937AC7DD050D77.svg:

**Figure** 7.3-a **:** Mass displacement.


.. image:: images/1000614A00006CE200004CF9C651CD82A5B71A12.svg
    :width: 453
    :height: 320


.. _RefImage_1000614A00006CE200004CF9C651CD82A5B71A12.svg:

**Figure** 7.3-b **:** **Mass velocity**.