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


.. image:: images/10000000000002010000017DB9CCB0EABE4E7C63.png
    :width: 4.2756in
    :height: 2.9346in


.. _RefImage_10000000000002010000017DB9CCB0EABE4E7C63.png:


Geometry
---------

The problem is axisymmetric (with axis :math:`Y`). The punch consists of a single triangular element. It is assumed to be in initial contact with the massif at point :math:`A`, this point is therefore topologically confused between the punch and the massif.


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

The block consists of an elasto-plastic material with linear isotropic work hardening:


.. csv-table::

    ":math:`E=\mathrm{2,0}\times {10}^{5}\mathrm{MPa}`"
    ":math:`\nu =\mathrm{0,3}`"
    ":math:`{\sigma }_{y}=300\mathrm{MPa}`"
    ":math:`{E}_{T}=5000`"


The punch is assumed to be rigid and is approximated by an elastic material with a large Young's modulus:


.. csv-table::

    ":math:`E=\mathrm{2,0}\times {10}^{9}\mathrm{MPa}`"
    ":math:`\nu =\mathrm{0,3}`"



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

The base of the massif is embedded and its left side is imposed at :math:`\mathrm{DX}=0`. Horizontal displacement is set to 0. The vertical displacement of the punch is imposed to :math:`{u}_{A}=–\mathrm{0,4}\mathrm{mm}`, then increased by :math:`\mathrm{0,008}\mathrm{mm}` (elastic return) according to the following graph:


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif: