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


Geometry
---------

We consider a square plate with a side of 50 mm, the top of which is hollowed out by a disk with a radius of 40 mm whose center is located 80 mm from the bottom of the plate. The geometry is shown in the figure below. The top of the plate (line :math:`\mathit{CD}`) is in contact with the corrosive medium.


.. image:: images/1000020100000391000002BD306CB4D798CEB53D.png
    :width: 4.5181in
    :height: 3.4689in


.. _RefImage_1000020100000391000002BD306CB4D798CEB53D.png:

The case is treated axisymmetrically, which is equivalent to considering a cylinder whose upper face is hollowed out by a sphere.


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

The material is Alloy 600 at 350° C. Its behavior is considered to be visco-elastic, non-linear, isotropic.

The elastic properties are:


* :math:`E=200000\mathit{MPa}`


* :math:`\nu =\mathrm{0,3}`

The visco-elastic behavior is modelled by a Lemaitre law, whose parameters are:


* :math:`n=\mathrm{3,77}`


* :math:`m=\mathrm{4,26}`


* :math:`K(T)=\mathrm{17,67.}\mathrm{exp}(\frac{47500}{\mathrm{8,31}(T+\mathrm{273,15})})` with :math:`T` in °C. For :math:`T=350°C`, :math:`K=170182`

The parameters to be entered in the operator DEFI_MATERIAU under the keyword factor LEMAITRE [:external:ref:`U4.43.01 <U4.43.01>`] are :math:`n`, :math:`1/m` and :math:`1/K`.


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

Since the case is axisymmetric, the movement along the :math:`x` axis on the :math:`\mathit{AC}` side is blocked. In order to block rigid modes, the movement along the :math:`y` axis of the point :math:`A` is blocked.

The loading consists in applying to side :math:`\mathit{BD}` a movement of :math:`\mathrm{0,1}\mathit{mm}` along the axis :math:`x`, progressively up to :math:`t=1h`, then the loading is kept constant until :math:`t=1000h`.