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


Geometry
---------

We consider two cubes :math:`A` and :math:`B` with side :math:`a\mathrm{=}2\mathit{mmm}`. The two cubes are initially in contact (no step between :math:`A` and :math:`B`).


.. image:: images/Shape1.gif


.. _RefSchema_Shape1.gif:

Here is the position of the reference points (:math:`\mathit{mm}`):


.. csv-table::

    "*Cube*", "*Point*", ":math:`x` "," :math:`y` "," :math:`z`"
    ":math:`A` "," :math:`\mathit{NH1}` ", "2", "0", "2"
    ":math:`A` "," :math:`\mathit{NH2}` ", "2", "2", "2", "2"
    ":math:`A` "," :math:`\mathit{NH3}` ", "0", "2", "2"
    ":math:`A` "," :math:`\mathit{NH4}` ", "0", "0", "2"
    ":math:`A` "," :math:`\mathit{NH5}` ", "2", "0", "4"
    ":math:`A` "," :math:`\mathit{NH6}` ", "2", "2", "4"
    ":math:`A` "," :math:`\mathit{NH7}` ", "0", "0", "2", "4"
    ":math:`A` "," :math:`\mathit{NH8}` ", "0", "0", "4"
    ":math:`A` "," :math:`\mathit{NH9}` ", "2", "2", "1", "2"
    ":math:`A` "," :math:`\mathit{NH10}` ", "1", "2", "2"
    ":math:`A` "," :math:`\mathit{NH11}` ", "0", "1", "2"
    ":math:`A` "," :math:`\mathit{NH12}` ", "1", "0", "2"
    ":math:`A` "," :math:`\mathit{NH17}` ", "2", "2", "1", "4"
    ":math:`A` "," :math:`\mathit{NH18}` ", "1", "2", "4"
    ":math:`A` "," :math:`\mathit{NH19}` ", "0", "0", "1", "4"
    ":math:`A` "," :math:`\mathit{NH20}` ", "1", "0", "4"
    ":math:`A` "," :math:`\mathit{NH26}` ", "1", "1", "4"
    ":math:`A` "," :math:`\mathit{NH21}` ", "1", "1", "2"
    ":math:`B` "," :math:`\mathit{NB1}` ", "2", "0", "0"
    ":math:`B` "," :math:`\mathit{NB2}` ", "2", "2", "0"
    ":math:`B` "," :math:`\mathit{NB3}` ", "0", "0", "2", "0"
    ":math:`B` "," :math:`\mathit{NB4}` ", "0", "0", "0"
    ":math:`B` "," :math:`\mathit{NB5}` ", "2", "0", "2"
    ":math:`B` "," :math:`\mathit{NB6}` ", "2", "2", "2", "2"
    ":math:`B` "," :math:`\mathit{NB7}` ", "0", "2", "2"
    ":math:`B` "," :math:`\mathit{NB8}` ", "0", "0", "2"
    ":math:`B` "," :math:`\mathit{NB17}` ", "2", "2", "1", "2"
    ":math:`B` "," :math:`\mathit{NB18}` ", "1", "2", "2", "2"
    ":math:`B` "," :math:`\mathit{NB19}` ", "0", "1", "2"
    ":math:`B` "," :math:`\mathit{NB20}` ", "1", "0", "2"
    ":math:`B` "," :math:`\mathit{NB26}` ", "1", "1", "2"
    ":math:`B` "," :math:`\mathit{NB9}` ", "2", "2", "1", "0"
    ":math:`B` "," :math:`\mathit{NB10}` ", "1", "2", "0"
    ":math:`B` "," :math:`\mathit{NB11}` ", "0", "0", "1", "0"
    ":math:`B` "," :math:`\mathit{NB12}` ", "1", "0", "0"
    ":math:`B` "," :math:`\mathit{NB21}` ", "1", "1", "0"



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

The two cubes are elastic with:


* Poisson's ratio: :math:`0`


* Young's module: :math:`200\mathit{GPa}`


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

We impose a :math:`\mathit{DZ}\mathrm{=}\mathrm{-}\mathrm{0.2mm}` displacement on the :math:`A` cube. The two cubes are in contact without friction.