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


Geometry
---------

Structure :math:`\mathrm{2d}` is a unit square (:math:`\mathrm{LX}=1m`, :math:`\mathrm{LY}=1m`), with a right crack leading to the right, located halfway up. [:ref:`Figure 1.1-1 <Ref94087906>`]. We call the left line the line in :math:`x=0`, the right line the line in :math:`x=\mathrm{LX}`, and the bottom line the line in :math:`y=0`.


.. image:: images/10000000000001B80000018CEBBE8AB3F1FBC801.png
    :width: 3.6346in
    :height: 3.3134in


.. _RefImage_10000000000001B80000018CEBBE8AB3F1FBC801.png:


.. _Ref94087906:

**Figure** 1.1-1 **: geometry of the cracked square plate**


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

Young's module: :math:`E\mathrm{=}205000\mathit{MPa}`

Poisson's ratio: :math:`\nu \mathrm{=}0.3`

Coefficient of thermal expansion: :math:`\alpha \mathrm{=}\mathrm{1,282}{10}^{\mathrm{-}5}`

Thermal conductivity: :math:`\lambda \mathrm{=}1{\mathit{W.m}}^{\text{-1}}\mathrm{.}{K}^{\text{-1}}`

Calorific volume capacity: :math:`\rho {C}_{p}\mathrm{=}0\mathit{J.m}\mathrm{-}{\mathrm{3.K}}^{\mathrm{-}1}`


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


For the thermal part
~~~~~~~~~~~~~~~~~~~~~~~~~~

Thermal loading consists in applying an imposed temperature :math:`T=20°C` on the nodes on the left line and an imposed temperature :math:`T=220°C` on the nodes on the right line. The temperature gradient is uniform and opens the crack in mixed mode.


For the mechanical part
~~~~~~~~~~~~~~~~~~~~~~~~~~

The nodes in the lower line are embedded.


Bibliography
-------------



.. _Ref112833703:


.. _Ref112833260:

1. GENIAUT S., MASSIN P.: eXtended Finite Element Method, *Code_Code_Aster* Reference Manual, [:ref:`R7.02.12 <R7.02.12>`]


2. GALENNE E., PROIX J.M.: Calculation of stress intensity factors, [:ref:`R7.02.08 <R7.02.08>`].