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


Geometry
---------

The structure is a healthy rectangle in which two oblique interfaces are introduced. The interfaces are parallel and placed as shown on the []. The dimensions of the structure as well as those concerning the geometry of the interfaces are:

:math:`H=9m`;

:math:`L=4m`;

:math:`B=4m`;

:math:`h=2.125m`;

:math:`\alpha =13.49`


.. image:: images/10000000000000E100000163909A5EB5CE99F1AC.png
    :width: 2.3291in
    :height: 3.6764in


.. _RefImage_10000000000000E100000163909A5EB5CE99F1AC.png:

Figure 1.1-1: Geometry of the structure and positioning of **interfaces** s.


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

Young's module: :math:`E=100\mathrm{MPa}`

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


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

The blocking of horizontal movements is imposed at the four corners of the structure (see [:ref:`Figure 1.3-1 <Figure 1.3-1>`]). On the lower and upper edges of the rectangle, movements along the :math:`Y` axis are imposed which will close the interfaces in order to generate contact pressure. The middle block is subject to significant sliding by applying a controlled movement along the :math:`X` axis on its left edge.

The numerical values of the imposed movements are:

 :math:`{\mathrm{Depl}}_{X}=2.00m`;

 :math:`{\mathrm{Depl}}_{Y}=1.0E-2m`.

Their application is carried out according to a conventional ramp function, in 4 load steps.

The Coulomb coefficient of friction is taken to be equal to :math:`\mathrm{0,5}`.


.. image:: images/1000000000000105000001871547BC985F5A145D.png
    :width: 2.3953in
    :height: 3.7047in


.. _RefImage_1000000000000105000001871547BC985F5A145D.png:

**Figure 1.3-1: Illustration of boundary conditions and loads.**