1. Reference problem#

1.1. Geometry#

The structure is a unit cube (\(\mathit{LX}\mathrm{=}1m\), \(\mathit{LY}\mathrm{=}1m\) and \(\mathit{LZ}\mathrm{=}1m\)), with a flat opening crack of length \(a\mathrm{=}\mathrm{0,5}m\), located halfway up [Figure 1.1-1.1-a]. The face located in plane \(x\mathrm{=}0\) is called the back face and the front face located in plane \(x\mathrm{=}\mathit{LX}\) is called the front face.

_images/10000000000001D9000001B2196D73F52C7531F4.png

Figure 1.1‑ 1.1-a : geometry of the cracked cube

1.2. Material properties#

Young’s module: \(E\mathrm{=}100\mathit{MPa}\)

Poisson’s ratio: \(\nu \mathrm{=}0\).

1.3. Boundary conditions and loads#

The load studied is a loading that stresses the crack in \(\mathit{III}\) mode (off-plane), without creating discontinuity of movement.

To do this, we impose an embedding of the nodes on the back face: \(\mathit{DX}\mathrm{=}\mathit{DY}\mathrm{=}\mathit{DZ}\mathrm{=}0\) and a displacement of the nodes on the front face in the normal direction (i.e. along the \(x\) axis) \(\mathit{DNOR}\mathrm{=}{10}^{}6m\).

1.4. Bibliography#

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