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


Geometry
---------


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


1.

Uy = 0


.. image:: images/Shape3.gif


.. _RefSchema_Shape3.gif:

Consider a test tube :math:`\mathrm{CT25}` with a ligament length: :math:`a=27.5\mathrm{mm}` (:math:`a/W=0.55`). Along the :math:`z` axis, the thickness is :math:`e=1\mathrm{mm}`. Test piece :math:`\mathrm{CT25}` is modelled in plane deformations. For reasons of symmetry, one half of it is represented in :math:`\mathrm{2D}`.


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

Young's modulus: 214100 :math:`\mathrm{Mpa}`

Poisson's ratio: :math:`\nu =0.3`. The traction curve used is shown in the following table:


.. csv-table::

    ":math:`\epsilon` "," :math:`\sigma (\text{MPa})`"
    "0.003439678", "740.6632663"
    "0.004628373", "842.148772"
    "0.00607988", "876.3117064"
    "0.007654628", "895.2063119"
    "0.010417548", "911.0718694"
    "0.014178015", "925.022448"
    "0.017543214", "935.2135771"
    "0.021942493", "945.6948965"
    "0.027416704", "960.732311"
    "0.033866984", "975.8041996"
    "0.040205805", "988.2450325"
    "0.046616375", "1000.143035"
    "0.052903597", "1010.004051"
    "0.058235889", "1017.5664"


Table 1.1


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

The load is of the displacement type imposed at a point located in the center of the pin, which is modelled by four undeformable angular sectors. With half of the test piece modelled, a symmetry condition is applied to the ligament (:math:`y=0`).