1. Reference problem#

1.1. Geometry#

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

_images/10000000000001B80000018CEBBE8AB3F1FBC801.png

Figure 1.1-1 : geometry of the cracked square plate

1.2. Material properties#

Young’s module: \(E\mathrm{=}205000\mathit{MPa}\)

Poisson’s ratio: \(\nu \mathrm{=}0.3\)

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

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

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

1.3. Boundary conditions and loads#

1.3.1. For the thermal part#

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

1.3.2. For the mechanical part#

The nodes in the lower line are embedded.

1.4. Bibliography#

  1. GENIAUT S., MASSIN P.: eXtended Finite Element Method, Code_Code_Aster Reference Manual, [R7.02.12]

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