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


Geometry
---------

We consider a circular crack immersed in a thermo-elastic medium. Taking into account the symmetries of the problem, only one eighth of the structure is represented:


.. image:: images/Object_1.svg
    :width: 339
    :height: 294


.. _RefImage_Object_1.svg:

The dimensions of the crack are as follows:

:math:`\mathrm{OP}=\text{OR}=1.0`

The medium is modelled by a parallelepiped with the following dimensions:

:math:`\mathrm{OB}=\mathrm{OD}=\mathrm{OC}=30.0`


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


.. csv-table::

    "Thermal conductivity:", ":math:`\lambda =1.`"
    "Coefficient of thermal expansion:", ":math:`\alpha \mathrm{=}{10}^{\mathrm{-}6}\mathrm{/}°C`"
    "", ""
    "Young's module:", ":math:`E={2.10}^{5}\mathrm{MPa}`"
    "Poisson's ratio:", ":math:`\nu =0.3`"



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


* Mechanics: imposed movements (DDL_IMPO) on the following groups of cells:


* :math:`\mathrm{DX}=0` out of :math:`\mathrm{ODHE}`;


* :math:`\mathrm{DY}=0` out of :math:`\mathrm{OEFB}`;


* :math:`\mathrm{DZ}=0` on :math:`\mathrm{PBCDRQ}` (i.e. underside of the parallelepiped, without the crack lip).


* Thermal: temperature imposed (TEMP_IMPO) on the following groups of meshes:


* :math:`\mathrm{TEMP}=0` on :math:`\mathrm{BCGH}`, :math:`\mathrm{CDHG}` and :math:`\mathrm{EFGH}` (outer faces of the parallelepiped);


* :math:`\mathrm{TEMP}=-1` out of :math:`\mathrm{OPQR}`.