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


Geometry
---------

Consider an infinite tube with an inner radius of :math:`\mathrm{20m}` and an outer radius of :math:`\mathrm{21m}`. The length of the tube is not involved in the evaluation of the reference solution, but this length is set to :math:`\mathrm{10m}` for the physical modeling of the problem (illustration).


.. image:: images/10000000000001D30000027336934B21081ADB55.png
    :width: 1.9453in
    :height: 2.6138in


.. _RefImage_10000000000001D30000027336934B21081ADB55.png:

Illustration 1.1.1: Geometry of the concrete tube with a thickness of 1 m and an internal radius of 20 m


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

The concrete material is isotropic elastic whose properties are:


* :math:`E=31000\mathrm{MPa}`


* :math:`\nu =0.2`

The properties of clean creep concrete (model ULMV_FP) are given below:


* K_RS = :math:`2.0e11\mathrm{Pa}`,


* ETA_RS = :math:`4.0e16\mathrm{Pa.s}`,


* K_IS = :math:`5.0e10\mathrm{Pa}`,


* ETA_IS = :math:`1.0e17\mathrm{Pa.s}`,


* K_RD = :math:`5.0e11\mathrm{Pa}`,


* ETA_RD = :math:`1.0e16`,


* ETA_ID = :math:`1.0e17`.


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

On edge :math:`\mathrm{AB}`, vertical movements along the :math:`Y` axis are blocked.

On edge :math:`\mathrm{AD}`, a confinement pressure of :math:`\mathrm{1MPa}` is imposed.

On edge :math:`\mathrm{BC}`, a uniform connection is imposed for all the nodes in the :math:`X` direction.

On edge :math:`\mathrm{CD}`, a uniform connection is imposed for all the nodes in the :math:`Y` direction.

Uniform bond boundary conditions ensure that an infinite cylinder is modelled and not a finite dimensional cylinder.


Initial conditions
--------------------

nought