1. Introduction#

A significant advantage of the X- FEM method being the possibility of studying several crack geometries on the same mesh, it is easy to study the evolution of the crack over time. The operator PROPA_FISS [U4.82.11] calculates the crack resulting from fatigue propagation according to a local Paris law.

From the data of a crack at a given moment and the corresponding stress intensity coefficients (Operator CALC_G [U4.82.03]), the operator calculates the level-sets after the crack has advanced, then the fiss_xfem data structure is enriched in the same way as with the DEFI_FISS_XFEM [U4.82.08] operator.

An introduction to the Level Set Method is given in [R7.02.12] .The crack propagation phase simply results in the propagation of level-sets

At present, we can calculate the new level-sets after advanced by three different approaches: by updating the level-sets using a fast marching method, by updating after a direct geometric calculation or by updating from a reconstructed propagated mesh (the crack mesh is reconstructed from the propagation data and the level-sets are calculated in a second time by distance from the mesh). The different stages of crack propagation X- FEM in*Code_Aster* change depending on the approach used.

However, the step of calculating the rate of advance of the crack bottom is common to all methods (cf. [§ 2]). We define the level-sets translating the new crack geometry and we ensure that they keep definitions close to signed distance functions (cf. [§ 4]). The propagation of a level set thus requires the following three successive steps (bib 2):

  • extension of the speed known on the iso-zero to the entire domain,

  • propagation of the level-set from this speed field,

  • reset the level-set function in order to maintain a signed distance function.

On the contrary, in the case where direct calculation is used, the new values of the two level-sets are recalculated immediately (cf. [§ 6]).