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


Geometry
---------

height: :math:`h\mathrm{=}1m`

width: :math:`l\mathrm{=}1m`

thickness: :math:`e\mathrm{=}1m`

.. image:: images/1000682400002C6B0000221CF920E400191AE434.svg
    :width: 286
    :height: 228


.. _RefImage_1000682400002C6B0000221CF920E400191AE434.svg:

Point coordinates (in meters):


.. csv-table::

    "", ":math:`A` "," :math:`B` "," :math:`C` "," :math:`D`"
    ":math:`x` ", "0. ", "0. ", "0.5", "1."
    ":math:`y` ", "0. ", "1. ", "0.5", "1."
    ":math:`z` ", "0. ", "0. ", "0.5", "0."



Property of materials
----------------------

:math:`E\mathrm{=}1500.00{10}^{3}\mathit{kPa}`

:math:`\nu \mathrm{=}0.27`


.. image:: images/Object_1.svg
    :width: 286
    :height: 228


.. _RefImage_Object_1.svg:


Initial conditions, boundary conditions, and loading
----------------------------------------

**Phase 1:**

The sample is brought to a homogeneous state:

.. image:: images/Object_2.svg
    :width: 286
    :height: 228


.. _RefImage_Object_2.svg:

, by imposing the corresponding confinement pressure on the front, right lateral and upper faces. The movements are blocked on the back (:math:`{u}_{x}\mathrm{=}0`), left side (:math:`{u}_{y}\mathrm{=}0`) and bottom (:math:`{u}_{z}\mathrm{=}0`) faces.

**Phase 2:**

The movements are maintained blocked on the rear (:math:`{u}_{x}\mathrm{=}0`), left lateral (:math:`{u}_{y}\mathrm{=}0`) and lower (:math:`{u}_{z}\mathrm{=}0`) faces, as well as the confinement pressure on the front and right lateral faces. An imposed displacement is applied on the upper face:

.. image:: images/Object_9.svg
    :width: 286
    :height: 228


.. _RefImage_Object_9.svg:

, so as to obtain a deformation :math:`{\varepsilon }_{\mathit{zz}}\mathrm{=}\mathrm{-}20\text{\%}` (counted from the start of phase 2).