8. F modeling#

8.1. Characteristics of modeling#

This is the same modeling as modeling A, but contact loading conditions are applied. The junctions are built with X- FEM and the level functions in the same way as for A-modeling.

8.2. Characteristics of the mesh#

The mesh, identical to that of modeling A, is represented in FIG. 3.2-a.

8.3. Tested features#

We test the functionalities already presented for modeling A. We also test the contact X- FEM in the case of junctions with X- FEM via the operator DEFI_CONTACT.

8.4. Tested sizes and results#

The movements at the level of the crack lips are tested after having carried out the post-treatment operations relating to \(\text{X-FEM}\) (POST_MAIL_XFEM and POST_CHAM_XFEM). The DX displacement should follow function \({u}_{X}\) in equation 2.2-2. The displacement DY should follow function \({\mathit{Depl}}_{Y}\) in equation 2.2-3. The deformation shown in FIG. 8.4-a is obtained.

Identification		Reference	% tolerance	7.0
DEPZON_1	DX- \({u}_{x}\)	MIN	0	7.0
	DX- \({u}_{x}\)	MAX	0	7.0
	DY- \({u}_{y}\)	MIN	0	7.0
	DY- \({u}_{y}\)	MAX	0	7.0
DEPZON_2	DX- \({u}_{x}\)	MIN	0	7.0
	DX- \({u}_{x}\)	MAX	0	7.0
	DY- \({u}_{y}\)	MIN	0	7.0
	DY- \({u}_{y}\)	MAX	0	7.0
DEPZON_3	DX- \({u}_{x}\)	MIN	0	7.0
	DX- \({u}_{x}\)	MAX	0	7.0
	DY- \({u}_{y}\)	MIN	0	7.0
	DY- \({u}_{y}\)	MAX	0	7.0
DEPZON_4	DX- \({u}_{x}\)	MIN	0	7.0
	DX- \({u}_{x}\)	MAX	0	7.0
	DY- \({u}_{y}\)	MIN	0	7.0
	DY- \({u}_{y}\)	MAX	0	7.0

Table 8.4-1

The deformation is shown in Figure 8.4-a. The color code represents the movement field.

Figure 8.4-a: Deformed structure (Exaggeration 10).

We test the value of \({E}^{e}\) produced by the POST_ERREUR operator (expressed in \(\text{J}\times {\text{m}}^{-1}\)).

Identification	Reference type	Reference value
Ee	“ANALYTIQUE”	1,768106

We test the value of \({\Vert u\Vert }_{{L}^{2}}\) produced by the POST_ERREUR operator.

8.5. notes#

A high error is obtained. Indeed, the implementation of the redistribution of contact facets has not been implemented. Contact forces on these facets are not taken into account in the calculation. The affected area concerns in particular the junction points (which are not tested) as well as the elements containing them. Note that the results are significantly improved when the mesh is refined.