4. B modeling

4.1. Characteristics of modeling

This modeling is strictly identical to the previous one. In order to test that the HM-XFEM model is functional with TRIA6, we choose to subdivide the 5 QUAD8 from the previous modeling, each into 2 TRIA6. This makes a total of 10 quadratic triangular elements. As before, the triangular elements contained in the extreme quadrangles are not enriched. On the contrario those contained in the 3 central quadrangles are enriched by the Heaviside function.

4.2. Characteristics of the mesh

The mesh consists of 10 quadratic triangular cells (TRIA6).

4.3. Tested sizes and results

The results (resolution with STAT_NON_LINE) are summarized in the table below according to the \(y\) direction. The tolerance is set to \({10}^{\text{-6}}\). To test all the nodes of the bar at the same time, we calculate MIN and MAX.

Quantities tested	Reference type	Reference value	Tolerance (%)
DY (below) MIN	“ANALYTIQUE”	-4.323558729E-03	0.0001
DY (below) MAX	“ANALYTIQUE”	-4.323558729E-03	0.0001
DY (above) MIN	“ANALYTIQUE”	4.297130927-03	0.0001
DY (above) MAX	“ANALYTIQUE”	4.297130927-03	0.0001

The results (resolution with STAT_NON_LINE) are summarized in the table below according to the \(x\) direction. To test all the nodes of the bar at the same time, we calculate MIN and MAX.

Quantities tested	Reference type	Reference value	Tolerance (%)
DX (below) MIN	“ANALYTIQUE”	0	0.0001
DX (below) MAX	“ANALYTIQUE”	0	0.0001
DX (above) MIN	“ANALYTIQUE”	0	0.0001
DX (above) MAX	“ANALYTIQUE”	0	0.0001

We can then observe, as in the case of modeling A, a clear discontinuity in the field of displacement linked to the presence of the interface crossing the massif. This suggests that the Heaviside function has taken into account the enrichment of the displacement field approximation.

Figure 4.3-a : Field of movement by direction (Oy)

A second modeling is then carried out which uses the same parameters as the previous one, but this time by conducting the calculation XFEM (which is then a pure mechanical calculation) with the operator MECA_STATIQUE instead of the operator STAT_NON_LINE in the case HM-XFEM. The results obtained are strictly identical to the previous ones.