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


Geometry
---------

The structure is a healthy square in which two interfaces are introduced, shown in red in Figure 1.1-a. The two interfaces intersect. The dimensions of the structure as well as the position of the interfaces are given in this figure.


.. image:: images/Object_1.png
    :width: 2.3929in
    :height: 2.2098in


.. _RefSchema_Object_1.png:

Figure 1.1-a: Structure geometry, interface position, and area numbering used to test the difference between calculated and analytical displacements.


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

The material has an isotropic elastic behavior whose properties are:

Young's module: :math:`100\mathit{MPa}`

Poisson's ratio: :math:`0.3`


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

In the non-contact case (models A to D), moving conditions are applied on the left and right edges of the structure, so that each of the 4 zones has a different displacement from the others according to :math:`X`. This load is shown in FIG. 1.3-a. We block the movements in :math:`Y` (and in :math:`Z` for the :math:`3D` models) on these same edges. Rigid mode movements are then obtained for the 4 blocks.


.. image:: images/Object_2.png
    :width: 4.3173in
    :height: 2.2756in


.. _RefSchema_Object_2.png:

Figure 1.3-a: Illustration of boundary conditions and loads, non-contact cases.

In the case of contact (E to H models), roller conditions are imposed on the left and bottom edges and the stepped pressure in FIG. 1.3-b is applied to the right and top edges. This load is represented in FIG. 1.3-c. Each block is then compressed uniformly according to :math:`X` and :math:`Y`. For :math:`\mathrm{3D}` models, a roller condition is imposed in :math:`Z=0`.


.. image:: images/Object_37.png
    :width: 3.5673in
    :height: 2.5173in


.. _RefSchema_Object_37.png:

Figure 1.3-b: Pressure imposed along :math:`X` on the top edge and according to :math:`Y` on the right edge, **(in** :math:`\mathit{MPa}` **) .**


.. image:: images/Object_34.png
    :width: 4.3673in
    :height: 3.5256in


.. _RefSchema_Object_34.png:

Figure 1.3-c: Illustration of boundary conditions and loads, contact cases.