6. D modeling

6.1. Characteristics of modeling

This is a 3D model using quadratic XFEM elements. The column on which the modeling is performed is divided into 5 HEXA20. The interface is unmeshed and cuts the column in \(Z={L}_{d}=\frac{\mathit{LZ}}{2}\). The interface is thus in accordance with the middle nodes of the central element. We have 3 XFEM elements and 2 classic elements.

6.2. Characteristics of the mesh

The mesh is identical to that of the c-modeling except that it is quadratic. It is composed of 5 HEXA20.

6.3. Tested sizes and results

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

Quantities tested	Reference type	Reference value	Tolerance (%)
DZ (below) MIN	“ANALYTIQUE”	-2.5E-02	0.001
DZ (above) MAX	“ANALYTIQUE”	2.5E-02	0.001

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

Quantities tested	Reference type	Reference value	Tolerance (%)
DX (underside [BCFG])	“ANALYTIQUE”	6.25E-02	0.001
DX (above face [BCFG])	“ANALYTIQUE”	-6.25E-02	0.001

The displacement field is presented in the direction \(z\) (Figure) and \(x\) (Figure).

Figure 6.3-a : Field of movement by direction (Oz)

Figure 6.3-b : Field of movement according to direction (Ox)