1. Reference problem#

1.1. 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:

_images/Object_1.svg

The dimensions of the crack are as follows:

\(\mathrm{OP}=\text{OR}=1.0\)

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

\(\mathrm{OB}=\mathrm{OD}=\mathrm{OC}=30.0\)

1.2. Material properties#

Thermal conductivity:

\(\lambda =1.\)

Coefficient of thermal expansion:

\(\alpha \mathrm{=}{10}^{\mathrm{-}6}\mathrm{/}°C\)

Young’s module:

\(E={2.10}^{5}\mathrm{MPa}\)

Poisson’s ratio:

\(\nu =0.3\)

1.3. Boundary conditions and loads#

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

  • \(\mathrm{DX}=0\) out of \(\mathrm{ODHE}\);

  • \(\mathrm{DY}=0\) out of \(\mathrm{OEFB}\);

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

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

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

  • \(\mathrm{TEMP}=-1\) out of \(\mathrm{OPQR}\).