.. _R5.03.17-DIS_CHOC_TRAC:

Behavior DIS_CHOC_TRAC
====

Definition
----
Behavior DIS_CHOC_TRAC is an elastic nonlinear behavior that applies to the local DX degree of freedom of discrete elements with two nodes (mesh SEG2)

The non-linear behavior is given when defining material DIS_CHOC_ELAS by a :math:`F=\mathit{fonction}(\mathrm{\Delta }U)` curve:

*   :math:`\mathrm{\Delta }U` represents the relative movement of the 2 nodes in the element's local coordinate system.

*   :math:`F` represents the effort expressed in the element's local coordinate system.


Data setting
----

Nonlinear function
~~~~
A necessary data is the function describing the non-linear behavior. This function must meet the following criteria:

*   It is a function in the sense of code_aster: defined with the operator DEFI_FONCTION,

*   The interpolations on the x-axis and the y-axis are linear,

*   The name of the abscissa when defining the function is DX,

*   Extending to the left is excluded,

*   The extension to the right of the function is either excluded or linear,

*   The function must be defined by at least 2 points.

*   The first point is :math:`(\mathrm{0.0,}0.0)` and must be given,

*   The function must be strictly increasing,

The first two points of the function are used to define the elastic slope to the behavior. The x-axis and ordinate units should be consistent with those of the problem:

*   the abscissa must be homogeneous when displaced,

*   the ordinate (value of the function) must be homogeneous to an effort.


Definition of contact distance
~~~~

++--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
||In the case of a discrete with 2 knots: :math:`\mathit{DistanceContact}=\mathit{LongueurDiscret}–\mathit{dist}1–\mathit{dist}2` The contact distance is positive in the direction of the local axis :math:`\mathit{Xloc}`.|
++--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

In the case of a discrete with 2 knots (based on a SEG2).

Let's say two structures :math:`{\Omega }_{1}` and :math:`{\mathrm{\Omega }}_{2}`. Note :math:`{d}_{N}` the normal distance between structures, :math:`{F}_{N}^{1/2}` the normal reaction force of :math:`{\mathrm{\Omega }}_{1}` over :math:`{\mathrm{\Omega }}_{2}`.

In the coordinate system local to the element, the normal distance :math:`{d}_{N}` is expressed as:

:math:`{d}_{N}=(({X}_{\mathit{loc}2}^{0}+{u}_{2})–({X}_{\mathit{loc}1}^{0}+{u}_{1}))–{\mathit{dist}}_{1}-{\mathit{dist}}_{2}`.

There will be "shock" when :math:`{d}_{N}\le 0`

The depression of the discrete will therefore be :math:`\Vert {d}_{n}\Vert` and the effort will follow the given behavior curve.

.. figure:: images/10000000000001F50000014C54BEAE24BC73A291.png
   :width: 50%
   :align: center

   Function: Contact force vs indentation