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


Geometry
---------


.. image:: images/10000201000000E4000000E9C23475EFDC23EB54.png
    :width: 1.8472in
    :height: 1.8902in


.. _RefImage_10000201000000E4000000E9C23475EFDC23EB54.png:

height: :math:`h=1m`

width: :math:`p=1m`

Point coordinates (in meters):


.. csv-table::

    "", ":math:`A`"
    ":math:`x` ", "1."
    ":math:`y` ", "1."
    ":math:`z` ", "0."



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

Elastic properties under the keyword ELAS:

:math:`E=24.6` :math:`\mathrm{MPa}`

:math:`\mathrm{\nu }=0.47`

:math:`\mathrm{\alpha }={10}^{-5}` :math:`{K}^{-1}`

Viscoplastic properties under the keyword VISC_MAXWELL:

Infinite volume viscosity :math:`{\mathrm{\eta }}_{v}={10}^{10}` :math:`\mathit{Pa}\mathrm{.}s`

Deviatoric viscosity :math:`{\mathrm{\eta }}_{d}=1.59{10}^{7}` :math:`\mathit{Pa}\mathrm{.}s`


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

**Phase 1:**

The sample is brought to a homogeneous state of stresses: :math:`{\mathrm{\sigma }}_{\mathit{xx}}^{0}={\mathrm{\sigma }}_{\mathit{yy}}^{0}={\mathrm{\sigma }}_{\mathit{zz}}^{0}=\mathrm{0,5}\mathit{MPa}` in 1000 s, by imposing the corresponding total pressure on the front, right lateral and upper faces. The movements are blocked on the back (:math:`{u}_{x}=0`), left side (:math:`{u}_{y}=0`) and bottom (:math:`{u}_{z}=0`) faces.

**Phase 2:**

The movements are kept blocked on the rear (:math:`{u}_{x}=0`), left lateral (:math:`{u}_{y}=0`) and lower (:math:`{u}_{z}=0`) faces.

An imposed displacement is applied on the upper face in order to obtain a deformation :math:`{\mathrm{\epsilon }}_{\mathit{zz}}=-\mathrm{0,01}` (for 1000 s counted from the start of phase 2). On the front and right lateral faces, boundary conditions under total stress are maintained:

:math:`\mathrm{\sigma }\mathrm{.}n={\mathrm{\sigma }}_{0}(=0.5\mathit{MPa})`