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


Geometry
---------


.. image:: images/10000000000001990000015E821899A16F246D2F.jpg
    :width: 2.4327in
    :height: 2.45in


.. _RefImage_10000000000001990000015E821899A16F246D2F.jpg:


.. image:: images/10000000000001DA0000015EA06FDC41CEDCF624.jpg
    :width: 2.8854in
    :height: 2.3736in


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.. image:: images/100000000000020F000001A2B9018A120B43CB10.jpg
    :width: 3.4547in
    :height: 2.639in


.. _RefImage_100000000000020F000001A2B9018A120B43CB10.jpg:


.. csv-table::

    "**Measures**", "**Values (** :math:`\text{mm}` **)**"
    ":math:`\mathit{Lx}` ", "22.2"
    ":math:`\mathit{Ly}` ", "15"
    ":math:`\mathit{Lz}` ", "4"
    ":math:`a` ", "9"
    ":math:`a\text{'}` ", "8.94"
    ":math:`b` ", "6"
    ":math:`b\text{'}` ", "5.94"
    ":math:`p` ", "0.1"


The structure under consideration is a block with an elliptical notch. As part of this modeling and for reasons of symmetry, only a quarter of the block is taken into account.


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

Young's module: :math:`223194\text{MPa}`.

Poisson's ratio: :math:`\nu \mathrm{=}0.3`.

Tensile curve (Von Misès isotropic plasticity):


.. csv-table::

    "Deformation applied", "Stress threshold raised :math:`[\text{MPa}]`"
    "0.00379042", "846"
    "0.00579042", "849.2"
    "0.01179042", "840.9"
    "0.01479042", "842.4"
    "0.01879042", "849.7"
    "0.02179042", "855.9"
    "0.02979042", "894.2"
    "0.04679042", "951.2"
    "0.07179042", "1012.9"
    "0.10379042", "1067.1"
    "0.13479042", "1106.6"
    "0.20379042", "1165.7"
    "0.30379042", "1228.4"
    "0.40379042", "1275.3"
    "0.50379042", "1313"
    "0.60379042", "1344.8"
    "0.70379042", "1372.4"
    "0.80379042", "1396.8"
    "0.90379042", "1418.7"
    "1.0037904", "1438.7"


Table 1.1


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

The face located in :math:`x=0` has an imposed displacement along the :math:`x` axis zero.

The face located in :math:`y=\mathrm{Ly}` has an imposed displacement along the :math:`y` axis zero.

The face located in :math:`z=0` has an imposed displacement along the :math:`z` axis zero.

A force that increases linearly in time is applied to the face located at an altitude of :math:`\mathrm{Lz}`.

This strength is worth :math:`\mathrm{2000N}` at the moment :math:`\text{INST}=\mathrm{20s}`.