2. Modeling A#

2.1. Characteristics of modeling#

Simulation at the hardware point.

2.2. Tested sizes and results#

2.2.1. Charging path 1 (ESSAI_TRIA_DR_M_D)#

The solutions are post-processed at the single point of the model and compared to references GEFDYN in terms of equivalent Von Mises stress \(Q\) and volume deformation \({\mathrm{ϵ}}_{v}\)

\(Q=\sqrt{\frac{3}{2}{\sigma }^{d}\mathrm{:}{\sigma }^{d}}\)

Identification

Reference type

Reference value

Tolerance

\({\mathrm{\epsilon }}_{\mathit{zz}}=1\text{\%}\)

“SOURCE_EXTERNE”

117640 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=2\text{\%}\)

“SOURCE_EXTERNE”

157072 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=5\text{\%}\)

“SOURCE_EXTERNE”

200850 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=10\text{\%}\)

“SOURCE_EXTERNE”

207649 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=20\text{\%}\)

“SOURCE_EXTERNE”

185854 Pa

  1. %

\({\varepsilon }_{v}\mathrm{=}\mathit{tr}(\varepsilon )\)

Identification

Reference type

Reference value

Tolerance

\({\mathrm{\epsilon }}_{\mathit{zz}}=1\text{\%}\)

“SOURCE_EXTERNE”

0.382%

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=2\text{\%}\)

“SOURCE_EXTERNE”

0.434

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=10\text{\%}\)

“SOURCE_EXTERNE”

-1.07%

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=20\text{\%}\)

“SOURCE_EXTERNE”

-3.191%

  1. %

2.2.2. Charging path 2 (ESSAI_TRIA_ND_M_D)#

The solutions are post-treated at the single point of the model and compared to references GEFDYN. in terms of equivalent Von Mises stress \(Q\) and isotropic effective pressure \(P\text{'}\).

\(Q\mathrm{=}\sqrt{\frac{3}{2}{\sigma }^{d}\mathrm{:}{\sigma }^{d}}\)

Identification

Reference type

Reference value

Tolerance

\({\mathrm{\epsilon }}_{\mathit{zz}}=0.1\text{\%}\)

“SOURCE_EXTERNE”

31547 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=0.2\text{\%}\)

“SOURCE_EXTERNE”

40129 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=0.5\text{\%}\)

“SOURCE_EXTERNE”

51937 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=1.\text{\%}\)

“SOURCE_EXTERNE”

68286 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=2.\text{\%}\)

“SOURCE_EXTERNE”

1103161 Pa

  1. %

\(P\text{'}=\frac{\mathit{tr}(\mathrm{\sigma }\text{'})}{3}\)

Identification

Reference type

Reference value

Tolerance

\({\mathrm{\epsilon }}_{\mathit{zz}}=0.1\text{\%}\)

“SOURCE_EXTERNE”

138887 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=0.2\text{\%}\)

“SOURCE_EXTERNE”

133789 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=0.5\text{\%}\)

“SOURCE_EXTERNE”

124952 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=1.\text{\%}\)

“SOURCE_EXTERNE”

136801 Pa

  1. %

\({\mathrm{\epsilon }}_{\mathit{zz}}=2.\text{\%}\)

“SOURCE_EXTERNE”

185971 Pa

  1. %

2.2.3. Charging path 3 (ESSAI_TRIA_ND_C_F)#

The solutions are post-treated at the single point of the model and compared to GEFDYN references in terms of isotropic effective pressure \(P\text{'}\)

\(P\text{'}=\frac{\mathit{tr}(\mathrm{\sigma }\text{'})}{3}\)

Identification

Reference type

Reference value

Tolerance

\(t=10.s\)

“SOURCE_EXTERNE”

  1. Not

  1. %

\(t\mathrm{=}30.s\)

“SOURCE_EXTERNE”

  1. Not

  1. %

\(t\mathrm{=}50.s\)

“SOURCE_EXTERNE”

  1. Not

  1. %

\(t\mathrm{=}70.s\)

“SOURCE_EXTERNE”

52999 Pa

  1. %

\(t=84.8s\)

“SOURCE_EXTERNE”

  1. Not

  1. %

2.2.4. Charging path 4 (ESSAI_TRIA_DR_C_D)#

A non-regression test is carried out on the equivalent stress of Von Mises \(Q\) and of volume deformation \({\mathrm{ϵ}}_{\mathit{vol}}\).

\(Q=\sqrt{\frac{3}{2}{\sigma }^{d}\mathrm{:}{\sigma }^{d}}\)

Identification

Reference type

Reference value

Tolerance

\(t=10.s\)

“NON_REGRESSION”

-15.57654 E+04 Pa

0.0001%

\(t=30.s\)

“NON_REGRESSION”

4.24744 E+04 Pa

0.0001%

\(t=50.s\)

“NON_REGRESSION”

-15.39714 E+04 Pa

0.0001%

\({ϵ}_{\mathit{vol}}\)

Identification

Reference type

Reference value

Tolerance

\(t=10.s\)

“NON_REGRESSION”

4.33281931383E-03

0.0001%

\(t=30.s\)

“NON_REGRESSION”

-5.89630135815E-04

0.0001%

\(t=50.s\)

“NON_REGRESSION”

8.75197203863E-03

0.0001%

2.2.5. Charging path 5 (ESSAI_TRIA_DR_C_D)#

A non-regression test is carried out on the equivalent stress of Von Mises \(Q\) and of volume deformation \({\mathrm{ϵ}}_{\mathit{vol}}\).

\(Q\mathrm{=}\sqrt{\frac{3}{2}{\sigma }^{d}\mathrm{:}{\sigma }^{d}}\)

Identification

Reference type

Reference value

Tolerance

\(t=20.s\)

“NON_REGRESSION”

-15.58495 E+04 Pa

0.0001%

\(t=40.s\)

“NON_REGRESSION”

3.66029 E+04 Pa

0.0001%

\(t=50.s\)

“NON_REGRESSION”

-14.29862 E+04 Pa

0.0001%

\({ϵ}_{\mathit{vol}}\)

Identification

Reference type

Reference value

Tolerance

\(t=20.s\)

“NON_REGRESSION”

4.33090139425 E-3

0.0001%

\(t=40.s\)

“NON_REGRESSION”

3.24057746269 E-3

0.0001%

\(t=50.s\)

“NON_REGRESSION”

9.73288861173 E-3

0.0001%

2.2.6. Charging path 6 (ESSAI_CISA_DR_C_D)#

A non-regression test is carried out on the constraint \({\mathrm{\sigma }}_{\mathit{xy}}\) at various times during the loading.

\({\sigma }_{\mathit{xy}}\)

Identification

Reference type

Reference value

Tolerance

\(t=10.s\)

“NON_REGRESSION”

-1.002427E+04 Pa

0.0001%

\(t=30.s\)

“NON_REGRESSION”

1.00516E+04 Pa

0.0001%

\(t=50.s\)

“NON_REGRESSION”

-1.000155E+04 Pa

0.0001%

2.2.7. Charging path 7 (ESSAI_OEDO_DR_C_F)#

A non-regression test is carried out on the volume deformation \({ϵ}_{\mathit{vol}}\) and the stress \({\sigma }_{\mathit{xx}}\) at various times of loading.

\({ϵ}_{\mathit{vol}}\)

Identification

Reference type

Reference value

Tolerance

\(t=10.s\)

“NON_REGRESSION”

8.48266637218E-04

0.0001%

\(t=50.s\)

“NON_REGRESSION”

1.6871423233218E-03

0.0001%

\(t=90.s\)

“NON_REGRESSION”

2.14894009601E-03

0.0001%

\({\sigma }_{\mathit{xx}}\)

Identification

Reference type

Reference value

Tolerance

\(t\mathrm{=}10.s\)

“NON_REGRESSION”

49721.6863437 Pa

0.0001%

\(t=50.s\)

“NON_REGRESSION”

53981.1605469 Pa

0.0001%

\(t=90.s\)

“NON_REGRESSION”

56319.3772981 Pa

0.0001%

2.2.8. Charging path 8 (ESSAI_ISOT_DR_C_F)#

The solutions are post-treated at the single point of the model and the values of the volume deformation \({\mathrm{ϵ}}_{\mathit{vol}}\) are compared with the results of the ssnv204a test case at different times of loading.

\({\mathrm{ϵ}}_{\mathit{vol}}\)

Identification

Reference type

Reference value

Tolerance

\(t=10.s\)

“AUTRE_ASTER”

0.01356660

0.1%

\(t=30.s\)

“AUTRE_ASTER”

0.00091215

0.1%

\(t=50.s\)

“AUTRE_ASTER”

0.01591635

0.1%

2.2.9. Charging path 9 (ESSAI_TRIA_ND_C_D)#

A non-regression test is carried out on the average effective stress \(P\text{'}\), the equivalent Von Mises stress \(Q\) and the plastic volume deformation \({\mathrm{ϵ}}_{\mathit{vol}}^{\mathit{plas}}\).

\(P\text{'}=\frac{\mathit{trace}\left(\mathrm{\sigma }\text{'}\right)}{3}\)

Identification

Reference type

Reference value

Tolerance

\(t=20.s\)

“NON_REGRESSION”

10064.1486965Pa

0.0001%

\(t=110.s\)

“NON_REGRESSION”

25713.2501603Pa

0.0001%

\(Q\mathrm{=}\sqrt{\frac{3}{2}{\sigma }^{d}\mathrm{:}{\sigma }^{d}}\)

Identification

Reference type

Reference value

Tolerance

\(t=20.s\)

“NON_REGRESSION”

-7514.28427045Pa

0.0001%

\(t=110.s\)

“NON_REGRESSION”

-29890.4822779

0.0001%

\({\mathrm{ϵ}}_{\mathit{vol}}^{\mathit{plas}}\)

Identification

Reference type

Reference value

Tolerance

\(t=20.s\)

“NON_REGRESSION”

-0.000189977948884

0.0001%

\(t=110.s\)

“NON_REGRESSION”

-0.000555199619402

0.0001%

2.3. notes#

The reference values GEFDYN are already used in three existing tests, which correspond to the first three loading paths:

  • path 1: ssnv197 [V6.04.197], modeling A

  • path 2: wtnv133 [V7.31.133], modeling A

  • path 3: wtnv134 [V7.31.134], B modeling