3. Modeling A

3.1. Characteristics of modeling

This is a D_ PLAN modeling using linear XFEM elements.

The interface is unmeshed and cuts off the center element in \(Y={L}_{d}=\frac{13\ast \mathit{LY}}{25}\). So we have 3 XFEM elements and 2 classic elements. As indicated in the Figure, the 3 elements XFEM are subdivided into sub-triangles (to perform the Gauss-Legendre integration on either side of the lips of the interface, but these triangular sub-elements are not mesh elements).

Figure 3.1-a : Characteristics of modelling

3.2. Characteristics of the mesh

The mesh composed of 5 QUAD4 is shown in Figure.

Figure 3.2-a : 2D mesh

3.3. Tested sizes and results

The results (resolution with STAT_NON_LINE) are summarized in the table below for the \(y\) direction. We are testing the following \(y\) movement of the interface nodes.

Quantities tested	Reference type	Reference value	Tolerance (%)
DY (below) MIN	“ANALYTIQUE”	-2.6E-02	0.001
DY (above) MAX	“ANALYTIQUE”	2.4E-02	0.001

We also test the displacement along \(x\) of the two interface nodes located on the [BC] side and respectively on the lower and upper lip of the crack.

Quantities tested	Reference type	Reference value	Tolerance (%)
DX (below [BC])	“ANALYTIQUE”	2.6E-02	0.001
DX (above [BC] side)	“ANALYTIQUE”	-2.4E-02	0.001

The displacement fields are presented in the direction \(y\) (Figure) and \(x\) (Figure).

Figure 3.3-a : Field of movement by direction (Oy)

Figure 3.3-b : Field of movement according to direction (Ox)