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


Geometry
---------

It is a rectangular plate with a thickness of 1mm, with a hole and modelled with DKT DKT. Only a quarter of the plate is modelled thanks to symmetries. Dimensions are given in millimeters.


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:


.. _RefNumPara__4726_27327633:


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

**Symmetry conditions**

The plate is stuck at :math:`\mathrm{Ox}` along side :math:`\mathit{AG}\mathrm{:}\mathit{DY}=0.0,\mathit{DZ}=0.0,\mathit{DRY}=0.0`.

It is stuck at :math:`\mathrm{Oy}` along side :math:`\mathit{BD}\mathrm{:}\mathit{DX}=0.0,\mathit{DZ}=0.0,\mathit{DRX}=0.0`.

**Loading under imposed constraint**

It is subject to traction :math:`p(t)` following :math:`\mathrm{Oy}` distributed on the side :math:`\mathrm{FG}`.

:math:`p(t=0)=0`, :math:`p(t=1000)=1000`.

We stop at the very beginning of plasticity at the edge of the hole, i.e. at 110s.


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

The behavior is Von Mises elastoplastic, with isotropic work hardening.

The elastic characteristics are:


* Young's module :math:`E=200000\mathrm{MPa}`;


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


* Elastic limit: :math:`200\mathrm{MPa}`;

Work hardening is deduced from the traction curve defined by the following data (constant straight extension PROL_DROITE =' CONSTANT '):


.. image:: images/100000000000034A0000025352CD0E317977B432.png
    :width: 4.2091in
    :height: 2.9744in


.. _RefImage_100000000000034A0000025352CD0E317977B432.png:


.. csv-table::

    "**Epsilon**", "**Sigma (** :math:`\mathit{Mpa}` **)**", "", "**Epsilon**", "**Sigma (** :math:`\mathit{Mpa}` **)**"
    "1.00000E-03", "2.00000E+02", "", "1.06000E-01", "2.69626E+02", "2.00000E+02"
    "6.00000E-03", "2.15275E+02", "", "1.11000E-01", "2.69709E+02"
    "1.10000E-02", "2.27253E+02", "", "1.16000E-01", "2.69773E+02", "2.69773E+02"
    "1.60000E-02", "2.36630E+02", "", "1.21000E-01", "2.69823E+02", "2.69823E+02"
    "2.10000E-02", "2.43964E+02", "", "1.26000E-01", "2.69862E+02"
    "2.60000E-02", "2.49694E+02", "", "1.31000E-01", "2.69893E+02"
    "3.10000E-02", "2.54168E+02", "", "1.36000E-01", "2.69917E+02", "2.69917E+02"
    "3.60000E-02", "2.57659E+02", "", "1.41000E-01", "2.69935E+02", "2.69935E+02"
    "4.10000E-02", "2.60382E+02", "", "1.46000E-01", "2.69949E+02", "2.69949E+02"
    "4.60000E-02", "2.62506E+02", "", "1.51000E-01", "2.69961E+02"
    "5.10000E-02", "2.64161E+02", "", "1.56000E-01", "2.69969E+02"
    "5.60000E-02", "2.65451E+02", "", "1.61000E-01", "2.69976E+02"
    "6.10000E-02", "2.66457E+02", "", "1.66000E-01", "2.69981E+02"
    "6.60000E-02", "2.67240E+02", "", "1.71000E-01", "2.69986E+02", "2.69986E+02"
    "7.10000E-02", "2.67850E+02", "", "1.76000E-01", "2.69989E+02"
    "7.60000E-02", "2.68325E+02", "", "1.81000E-01", "2.69991E+02", "2.69991E+02"
    "8.10000E-02", "2.68696E+02", "", "1.86000E-01", "2.69993E+02"
    "8.60000E-02", "2.68984E+02", "", "1.91000E-01", "2.69994E+02"
    "9.10000E-02", "2.69209E+02", "", "1.96000E-01", "2.69996E+02", "2.69209E+02"
    "9.60000E-02", "2.69384E+02", "", "2.00000E-01", "2.69996E+02"
    "1.01000E-01", "2.69520E+02", "", "", ""


**Table** 1.3-1