3. Modeling A

3.1. Characteristics of modeling

This is a D_ PLAN_HM modeling using quadratic HM- XFEM elements. The bar on which the modeling is performed is divided into 5 QUAD8. The interface is unmeshed and cuts off the central element. So we have 3 HM- XFEM elements and 2 classical HM 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 consists of 5 quadratic quadratic quadratic cells (QUAD8).

3.3. Tested sizes and results

The results (resolution with STAT_NON_LINE) are summarized in the table below for each of the 8 calculation moments. To test all the nodes of the bar at the same time, we calculate MIN and MAX.

Quantities tested	Reference type	Reference value	Tolerance (%)
LAGS_C MIN (instant 1)	“ANALYTIQUE”	-0.116 MPa	0.0001
LAGS_C MAX (instant 1)	“ANALYTIQUE”	-0.116 MPa	0.0001
LAGS_F1 MIN (instant 1)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MAX (instant 1)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MIN (instant 2)	“ANALYTIQUE”	0.116 MPa	0.0001
LAGS_C MAX (instant 2)	“ANALYTIQUE”	0.116 MPa	0.0001
LAGS_F1 MIN (instant 2)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MAX (instant 2)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MIN (instant 3)	“ANALYTIQUE”	1.0173120729 MPa	0.0001
LAGS_C MAX (instant 3)	“ANALYTIQUE”	1.0173120729 MPa	0.0001
LAGS_F1 MIN (instant 3)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MAX (instant 3)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MIN (instant 4)	“ANALYTIQUE”	0.50865603645 MPa	0.0001
LAGS_C MAX (instant 4)	“ANALYTIQUE”	0.50865603645 MPa	0.0001
LAGS_F1 MIN (instant 4)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MAX (instant 4)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MIN (instant 5)	“ANALYTIQUE”	“”	0.69758542141 MPa	0.0001
LAGS_C MAX (instant 5)	“ANALYTIQUE”	“”	0.69758542141 MPa	0.0001
LAGS_F1 MIN (instant 5)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MAX (instant 5)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MIN (instant 6)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MAX (instant 6)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MIN (instant 6)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MAX (instant 6)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MIN (instant 7)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MAX (instant 7)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MIN (instant 7)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MAX (instant 7)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_C MIN (instant 8)	“ANALYTIQUE”	-0.116 MPa	0.0001
LAGS_C MAX (instant 8)	“ANALYTIQUE”	-0.116 MPa	0.0001
LAGS_F1 MIN (instant 8)	“ANALYTIQUE”	0 MPa	0.0001
LAGS_F1 MAX (instant 8)	“ANALYTIQUE”	0 MPa	0.0001