3. Modeling A

3.1. Characteristics of modeling

Interfaces and cracks are defined by level sets.

The initial mesh is refined 3 times in a row, using the distance indicator provided by RAFF_XFEM. Each time, 20% of the stitches with the most « errors » are refined.

3.2. Characteristics of the mesh

The initial mesh is healthy: it consists of \(20\mathrm{\times }20\) linear quadrangles.

Figure 3.2-1 : initial healthy mesh

3.3. Tested sizes and results

We test the value of the error indicator at the output of RAFF_XFEM at points \({P}_{1}\), \({P}_{2}\), \({P}_{3}\) and \({P}_{4}\), for each refined mesh.

Identification	Reference	Reference type	\(\text{\%}\) tolerance
\(I({P}_{1})\)	-0.270156	“ANALYTIQUE”	0.1%
\(I({P}_{2})\)	-0.270156	“ANALYTIQUE”	0.1%
\(I({P}_{3})\)	-0.269258	“ANALYTIQUE”	0.1%
\(I({P}_{4})\)	-0.320156	“ANALYTIQUE”	0.1%

For information, the mesh obtained after refinement is shown on the. We can see that for interfaces, it is not only the meshes close to the interfaces that are refined, but all the meshes contained in the inclusion. This is due to the way in which Homard manages the conformal connection of the cut quadrangles. This phenomenon does not occur with triangles. This is why in the rest of the models, we will prefer to start from an initial mesh of triangles.

Figure 3.3-1: refined healthy mesh