2. Principle of the test#

In DEFI_FISS_XFEM you can define the crack on a grid using one of the following methods:

  1. by giving the grid mesh to be used by MODELE_GRILLE,

  2. by giving a crack with a grid already associated with FISS_GRILLE.

The second method was designed for cases where lobster is used to refine the mesh of the structure. In this case, the grid associated with the crack given by FISS_GRILLE is also associated with the new crack and the level sets already defined are kept the same. The information concerning the location of the calculation domain and the use of an auxiliary grid is kept for the new crack, which allows it to be propagated correctly by PROPA_FISS. On the other hand, the level sets on the mesh are calculated by interpolation by Homard and they are passed directly to DEFI_FISS_XFEM by DEFI_FISS/CHAMP_NO_LS *.

To verify the correct functioning of the two methods, the crack \(\mathit{FISS0}\) in the figure will be propagated by PROPA_FISS in three steps:

  1. we propagate \(\mathit{FISS0}\), crack with an associated auxiliary grid, which was defined using the MODELE_GRILLE operand in DEFI_FISS_XFEM. We get \(\mathit{FISS1}\).

  2. we refine the \(\mathit{FISS1}\) mesh by Homard. Then we will define the same crack on the refined mesh while keeping the auxiliary grid (operand FISS_GRILLE from DEFI_FISS_XFEM). We get \(\mathit{FISS1raff}\), which coincides with \(\mathit{FISS1}\) except where the mesh is more refined.

  3. we spread \(\mathit{FISS1raff}\) and we get \(\mathit{FISS2}\).

The same values for the angle of propagation and the advance of the crack are imposed at each point at the bottom of the crack. These values are kept constant between the two propagations. The propagated funds are therefore always straight and their position in the structure is known a prima facie. If both methods work correctly, the position of \(\mathit{FISS2}\) should coincide with the expected position.

2.1. Calculation method#

For each point on the bottom, at each propagation step, the same propagation angle \(\beta\) and the same advance \(\Delta a\) of the crack are imposed. We can therefore calculate the coordinates of each bottom point after each propagation step (figures and):

\({Y}_{i}={Y}_{i-1}+\Delta a\cdot \mathrm{cos}(i\cdot \beta )\)

\({Z}_{i}={Z}_{i-1}+\Delta a\cdot \mathrm{sen}(i\cdot \beta )\)

where \((\mathrm{0,}{Y}_{i},{Z}_{i})\) and \((\mathrm{4,}{Y}_{i},{Z}_{i})\) are the end points of the segment that coincides with the bottom of crack \(\mathit{FISSi}\). At the beginning, for crack \(\mathit{FISS0}\) (figure):

\({Y}_{0}=1\)

\({Z}_{0}\mathrm{=}0\)

2.2. Reference quantities and results#

The coordinates of the end points expected for background \(\mathit{FISS2}\) are therefore as follows:

\({X}_{2}\mathrm{=}\mathrm{[}\mathrm{0,4}\mathrm{]}\)

\({Y}_{2}=2.189\mathrm{mm}\)

\({Z}_{2}\mathrm{=}0.156\mathit{mm}\)

To check the effective position of background \(\mathit{FISS2}\) in the finite element model, we use the values of the level sets at the points of intersection between the segment defined by the two end points above and the faces of the elements of the mesh. If the position of the bottom after propagation is calculated correctly, the value of the two level sets should be equal to zero for all intersection points found because, by definition, the crack background is formed by all the points where the tangent and normal level sets equal zero.

The intersection points and the value of the level sets at these points can be calculated using the post-processing command MACR_LIGN_COUPE.