Reference problem
=====================

Geometry
---------

A discrete element of zero size with 2 knots.

Local coordinate system = global coordinate system.

A K_ TR_D_L stiffness matrix assigned by default:

:math:`1.6N/m` in translation, :math:`1.9N/m` in rotation.

The stiffness characteristics in the local direction :math:`y` (here equal to the global axis :math:`Y`) are modified by a behavior relationship of the type ARME in force-displacement introduced by a characteristic material.


Material properties
-----------------------

Linked to an incremental behavior ARME with 5 parameters: :math:`{d}_{e}` (keyword DLE) = (keyword) = :math:`0.048m`, :math:`{d}_{l}` (keyword DLP) = :math:`0.7m`, :math:`{K}_{\mathrm{el}}` (keyword KYE) = :math:`1.67\mathit{E4}N/m` :math:`{K}_{\mathrm{pl}}` KYP :math:`2.9\mathit{E3}N/m`, :math:`{K}_{G}` (key word KYG) = :math:`\mathrm{1 E6 }N/m`.

• :math:`{d}_{e}` limiting displacement of the elastic domain,

• :math:`{d}_{l}` limiting displacement of the plastic domain,

• :math:`{K}_{\mathrm{el}}` slope of the elastic domain,

• :math:`{K}_{\mathrm{pl}}` slope of the plastic domain,

• :math:`{K}_{G}` ultimate slope,

Behaviour of a cocking arm under longitudinal stress


.. image:: images/1000104E00001F510000112816547A497DB92680.svg
    :width: 403
    :height: 221


.. _RefImage_1000104E00001F510000112816547A497DB92680.svg:

:math:`{d}_{e}=0.048m`, :math:`{d}_{l}=0.7m`, :math:`{L}_{e}=\mathrm{800 }N`, :math:`{F}_{m}=\mathrm{2800 }N`

Unidirectional force-displacement behavior with 1 internal variable: :math:`{d}_{p}–{d}_{e}` defined by 5 parameters: :math:`{d}_{e}`, :math:`{d}_{l}`, :math:`{K}_{\mathrm{el}}`, :math:`{K}_{\mathrm{pl}}` and :math:`{K}_{G}`, assigned to a discrete element with 2 nodes.


Boundary conditions and loads
-------------------------------------

Embedding in one of the 2 knots.

Force imposed in the local direction :math:`y` (identical to global :math:`Y`) on the second node, in load increments. A unit increment equal to :math:`\mathrm{500 }N`.


Initial conditions
--------------------

Zero displacements, efforts, and internal variables.