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


Geometry
---------

Consider the geometry described in the figure where the dimensions in mm are as follows:

:math:`{d}_{1}=0.2{d}_{2}=1.2{d}_{3}=10.6r=0.75{h}_{1}=0.95{h}_{2}=4{a}_{1}=0.3{a}_{2}=0.2`


.. image:: images/10000000000004EB000002965C3F4B7AD475D58D.png
    :width: 6.3374in
    :height: 3.3319in


.. _RefImage_10000000000004EB000002965C3F4B7AD475D58D.png:

Figure 1: Problem geometry (image from [:ref:`1 <1>`])


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

The 2 materials are isotropic elastic whose properties are:


* :math:`E=68.96E8\mathrm{MPa}` :math:`\nu =0.32`


*:math:`E\text{*}=6.896E8\mathrm{MPa}` :math:`\nu \text{*}=0.32`

They are both represented in large deformations according to the model of Simo and Miehe.


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

The lower edge of the massif is embedded.

The upper edge of the stamp is subjected to an imposed displacement given by:

:math:`\begin{array}{ccc}t\in [\mathrm{0,1}]& {u}_{x}=0& {u}_{y}=t\\ t\in [\mathrm{1,2}]& {u}_{x}=10(t-1)& {u}_{y}=1\end{array}`

For contact, the punch is master and the massive slave. We consider Coulomb friction with a coefficient :math:`\mu =0.3`.


Initial conditions
--------------------

Néant