7. Modeling E

7.1. Characteristics of modeling

We test the criteria in formulas, “MATAKE_MODI_AV”, “”, “DANG_VAN_MODI_AV”, “FATESOCI_MODI_AV” (find the results of the test cases SSLV135B)

7.2. Characteristics of the mesh

Meshing is not required.

7.3. Tested sizes and results

For the criteria “MATAKE_MODI_AV” and the associated formula criterion (SSLV135B)

For results with option COURBE_GRD_VIE =” WOHLER “and for option COURBE_GRD_VIE =” FORM_VIE “and FORMULE_VIE =” WHOL “:

Identification	Reference type	Reference value
component \(x\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	-0.38268343236509 0.38268343236509
component \(y\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	0.92718385456679 0.92387953251129
component \(z\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	0.0000000000000E+00
\(\text{ENDO}({n}_{1})\)	“AUTRE_ASTER”	7.0532362250863E-04

In the table above, components \(x\) and \(y\) of \({n}_{1}\) and \({n}_{2}\) have two values because there are two vectors that correspond to the same damage value \(\text{ENDO}({n}_{1})\) = \(\text{ENDO}({n}_{2})\).

For results with option COURBE_GRD_VIE = “FORM_VIE” and FORMULE_VIE = WHOL_F:

Identification	Reference type	Reference value
component \(x\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	-0.38268343236509 0.38268343236509
component \(y\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	0.92718385456679 0.92387953251129
component \(z\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	0.0000000000000E+00
\(\text{ENDO}({n}_{1})\)	“AUTRE_ASTER”	3.3180845213285E-04

In the table above, components \(x\) and \(y\) of \({n}_{1}\) and \({n}_{2}\) have two values because there are two vectors that correspond to the same damage value \(\text{ENDO}({n}_{1})\) = \(\text{ENDO}({n}_{2})\).

For the criteria “DANG_VAN_MODI_AV” and the associated formula criterion (SSLV135B)

For results with option COURBE_GRD_VIE =” WOHLER “and for option COURBE_GRD_VIE =” FORM_VIE” and FORMULE_VIE = WHOL:

Identification	Reference type	Reference value
component \(x\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	-7.0710678118655E-01 7.0710678118655E-01
component \(y\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	7.0710678118655E-01	“”	7.0710678118655E-01
component \(z\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	0.0000000000000E+00
\(\text{ENDO}({n}_{1})\)	“AUTRE_ASTER”	1.3419917535855E-04	1.3419917535855E-04

In the table above, components \(x\) and \(y\) of \({n}_{1}\) and \({n}_{2}\) have two values because there are two vectors that correspond to the same damage value \(\text{ENDO}({n}_{1})\) = \(\text{ENDO}({n}_{2})\).

For results with option COURBE_GRD_VIE = “FORM_VIE” and FORMULE_VIE = WHOL_F:

Identification	Reference type	Reference value
component \(x\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	-7.0710678118655E-01 7.0710678118655E-01
component \(y\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	7.0710678118655E-01	“”	7.0710678118655E-01
component \(z\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	0
\(\text{ENDO}({n}_{1})\)	“AUTRE_ASTER”	8.7633062468223E-05

In the table above, components \(x\) and \(y\) of \({n}_{1}\) and \({n}_{2}\) have two values because there are two vectors that correspond to the same damage value \(\text{ENDO}({n}_{1})\) = \(\text{ENDO}({n}_{2})\).

For the criteria “FATESOCI_MODI_AV” and the associated formula criterion (SSLV135B)

For results with option COURBE_GRD_VIE =” WOHLER “, COURBE_GRD_VIE =” FORM_VIE” and FORMULE_VIE = MANCO1:

Identification	Reference type	Reference value
component \(x\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	-4.3837114678908E-01 4.3837114678908E-01
component \(y\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	0.90258528434986
component \(z\) of \({n}_{1}\) and \({n}_{2}\)	“AUTRE_ASTER”	0
\(\text{ENDO}({n}_{1})\)	“AUTRE_ASTER”	0.43649132038876

In the table above, the \(x\) component of \({n}_{1}\) and \({n}_{2}\) has two values because there are two vectors that correspond to the same damage value \(\text{ENDO}({n}_{1})\) = \(\text{ENDO}({n}_{2})\).