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


Geometry
---------

A :math:`\mathrm{1cm}` long bar, cut into 4 :math:`\mathrm{2,5}\mathit{mm}` elements. It is embedded at one end and is subject to an imposed displacement :math:`U` at the other.


.. image:: images/10000200000001A2000000534BC84F64FCAC817C.png
    :width: 4.3492in
    :height: 0.8665in


.. _RefImage_10000200000001A2000000534BC84F64FCAC817C.png:

Illustration 1: Diagram of the geometry of the member under tension

The area of the cross sections is :math:`A\mathrm{=}{\mathrm{1m}}^{2}`.


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

An elastoplastic material with linear isotropic work hardening (VMIS_ISOT_LINE) is considered with the following characteristics:

:math:`\begin{array}{c}E\mathrm{=}100000\text{MPa}\\ \nu \text{=}\mathrm{0,3}\\ {E}_{T}\text{=}10000\text{MPa}\\ {\sigma }_{Y}\text{=}100\text{MPa}\end{array}`


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

Embedded in :math:`A` :math:`(\mathrm{DZ}=\mathrm{DY}=\mathrm{DX}=0)`.

To avoid rigid body movements, :math:`\mathrm{DZ}=\mathrm{DY}=0` for all knots.

A single load is applied: a traction in motion imposed from :math:`U=1\text{mm}` to node :math:`B`.