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


Geometry
---------

We consider a cube with side :math:`3\,{mm}`.


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

The material is elasto-plastic with linear isotropic work hardening (VMIS_ISOT_LINE) whose
properties are:


* Modulus of elasticity: :math:`E=210000\,{MPa}`


* Poisson's ratio: :math:`\nu =0.3`


* Linear work hardening module: :math:`H=100\,{MPa}`


* Elastic limit: :math:`{\sigma }_{y}=100\,{MPa}`


* Thermal conductivity: a function of the temperature in the figure


* Volume heat: a function of the temperature in the figure


.. figure:: images/100002010000022E0000019D72B15F1859CF2C82.png
    :width: 3.4429in
    :height: 2.4791in

    Thermal conductivity


.. figure:: images/100002010000022E0000019DB10A84CBD51D37C6.png
    :width: 3.3516in
    :height: 2.4807in

    Volume heat


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

Thermal calculation
~~~~~~~~~~~~~~~~~

A radiation condition is imposed on five sides of the cube (see figure).
:ref:`v1.01.395-fig-rayonnement`) with:


* Boltzman constant: :math:`{5,67}\times {10}^{-14} J \, {{mm}}^{-2} \, {K}^{4}`;


* emissivity: :math:`0,75`


* outside temperature: :math:`20°C`


.. figure:: images/1000000000000423000002E37275065166D3E4F0.png
 :name: v1.01.395-fig-radiation
    :width: 2.8772 in
    :height: 2.0075 in

    Surface for radiation condition

An exchange condition on the top side (see figure :ref:`v1.01.395-fig-echange`) with:


* Exchange coefficient: :math:`{1,0} \, W\,{{mm}}^{-2}\,{K}^{-1}`


* Outside temperature: a function of the weather in figure :ref:`v1.01.395-fig-temperatureExte`


.. figure:: images/1000000000000423000002E3A26C9C3EE7CC0521.png
 :name: v1.01.395-fig-exchange
    :width: 2.6547 in
    :height: 1.852 in

    Surface for the exchange condition


.. figure:: images/100002010000022E0000019DD02210247C1E7701.png
 :name: v1.01.395-FIG-temperatureExte
    :width: 2.8917 in
    :height: 2.1402 in

    Outside temperature

An exchange condition on the other sides (see figure) with:


* Exchange coefficient: :math:`{1,5}\times {10}^{-5}\, W \, \,{{mm}}^{-2}\,{K}^{-1}`


* Outside temperature: :math:`20°C`


Mechanical calculation
~~~~~~~~~~~~~~~~~

On the lower surface (see figure 6 :ref:`v1.01.395-fig-surfaceEncastrement`), we impose
:math:`DX=DY=DZ=0`.

On five sides of the cube (see figure), pressure :math:`p=1000\,{MPa}` is imposed


.. figure:: images/1000000000000432000002E3D257BB742C66BCDF.png
    :width: 2.7563in
    :height: 1.898in
: name: v1.01.395 - FIG-Surface mounting

    Surface for embedding


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

Nil. -