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


Modeling geometry A
------------------------------

An axisymmetric bar of radius :math:`\mathrm{1mm}` and height :math:`\mathrm{10mm}` subjected to a simple tensile test (with imposed displacement) is considered. This test is chosen because it makes it possible to obtain uniform mechanical fields.


.. image:: images/100002000000013500000338742F0B1CCB770930.png
    :width: 1.4807in
    :height: 3.9366in


.. _RefImage_100002000000013500000338742F0B1CCB770930.png:

**Figure 1.1: Axisymmetric bar.**


Modeling geometry B
------------------------------

Here we consider a cube with side :math:`\mathrm{1mm}` subjected to traction.

The front face is blocked in direction :math:`\text{X}`, the left face in direction :math:`\text{Y}`, the bottom face in direction :math:`\text{Z}` and an incremental pull of :math:`\mathrm{0,001}\text{mm}` is applied to the upper face.


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

The material is perfect elastoplastic with a Young's modulus of :math:`300000\text{MPa}`, a Poisson's ratio of 0 and an elastic limit of :math:`300\text{MPa}`.


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

For modeling A, 5 traction increments of :math:`\mathrm{0,01}\text{mm}` are carried out, so that the total deformation increment is :math:`1.0\text{E-3}` and the elastic limit is reached at the first step.

For modeling B, the front face is blocked in direction :math:`\text{X}`, the left face in direction, the left face in direction :math:`\text{Y}`, and an incremental pull of :math:`\mathrm{0,001}\text{mm}` is applied to the upper face. :math:`\text{Z}`

The temperature varies linearly in the bar from :math:`\text{O°C}` to :math:`\text{5O°C}` over the 5 time steps.

In order to test the various possibilities offered by the macro-command CALC_BORDET, when possible, parameters that depend on the temperature and the plastic deformation rate are used. The list of parameters used is shown in the table below.


.. csv-table::

    "**Parameter**", "**Type**", "**Value**"
    "M", "Scalar", "22"
    "SIG_CRIT ", "Scalar", "250"
    "VOLU_REFE ", "Scalar", "1"
    "SIGM_REFE ", "Function", ":math:`200+\text{T}`"
    "SEUIL_CALC ", "Tablecloth", ":math:`\{\begin{array}{cc}10T& \text{si}{\dot{\stackrel{ˉ}{\varepsilon }}}^{p}=\mathrm{0,0005}\\ 5T& \text{si}{\dot{\stackrel{ˉ}{\varepsilon }}}^{p}=\mathrm{0,001}\end{array}`"
    "DEF_PLAS_REFE ", "Scalar", "0"


**Table** 1.1 **: Bordet parameters used**