6. D modeling#

6.1. Characteristics of modeling#

The modeling characteristics are the same as for modeling \(A\).

6.2. Characteristics of the mesh#

The mesh is here refined compared to that of modeling \(C\). We discretize the structure in \(2\times (11\times 55)\) finite elements TRIA3. The interface is therefore present within the central elements through level sets.

_images/100000000000013400000346E13F42160EE84D6F.png

Figure 6.2-a : D modeling mesh

6.3. Piloting#

A specific control \(\mathrm{XFEM}\) SAUT_LONG_ARCsur is used to control all the edges intersected by the crack.

6.4. Tested sizes and results#

Fashion \(I\) :

The values of contact Lagrangians LAGS_C are tested at all the nodes of the mesh crossed by the interface after convergence of the iterations of each STAT_NON_LINE operator, these values being uniform on the interface. To test all the values at once, we test the minimum and the maximum number of contact Lagrangians.

No

Identification

Reference

Tolerance (%)

0.5

H1Y for all nodes

1.36362396705485E-07

1.0E-6

0.5

LAGS_Cpour all nodes

3.66296853301E+05

1.0E-6

0.75

H1Y for all nodes

6.818119835274E-08

1.0E-6

0.75

LAGS_Cpour all nodes

1.8314842665E+05

1.0E-6

2

H1Y for all nodes

4.0908719011645E-07

1.0E-6

2

LAGS_Cpour all nodes

1.098890559903E+06

1.0E-6

3.5

H1Y for all nodes

7.49999999999582E-04

1.0E-6

3,5

LAGS_Cpour all nodes

1.75867720687844E+05

1.0E-6

4.5

H1Y for all nodes

2.49999999999582E-04

1.0E-6

4.5

LAGS_Cpour all nodes

58622.573562549

1.0E-6

5.5

H1Y for all nodes

7.49999999999582E-04

1.0E-6

5,5

LAGS_Cpour all nodes

1.75867720687844E+05

1.0E-6

7

H1Y for all nodes

1.49999999999958E-03

1.0E-6

7

LAGS_Cpour all nodes

28117.686527187

1.0E-6

9.5

H1Y for all nodes

2.49999999999582E-04

1.0E-6

9.5

LAGS_Cpour all nodes

4686.28108785798

1.0E-6

12

H1Y for all nodes

1.49999999999958E-03

1.0E-6

12

LAGS_Cpour all nodes

28117.686527187

1.0E-6

15

H1Y for all nodes

2.99999999999958E-03

1.0E-6

15

LAGS_Cpour all nodes

718.731177854856

1.0E-6

Fashion \(\mathrm{II}\):

The values of the Lagrangian friction values LAGS_F1 are tested at all the nodes of the mesh crossed by the interface after convergence of the iterations of each STAT_NON_LINE operator, these values being uniform on the interface. To test all the values at once, we test the minimum and the maximum of the Lagrangian friction values.

No

Identification

Reference

Tolerance (%)

0.5

H1X for all nodes

1.36362396705485E-07

1.0E-6

0.5

LAGS_F1pour all nodes

3.66296853301E+05

1.0E-6

0.75

H1X for all nodes

6.818119835274E-08

1.0E-6

0.75

LAGS_F1pour all nodes

1.8314842665E+05

1.0E-6

2

H1X for all nodes

4.0908719011645E-07

1.0E-6

2

LAGS_F1pour all nodes

1.098890559903E+06

1.0E-6

3.5

H1X for all nodes

7.49999999999582E-04

1.0E-6

3,5

LAGS_F1pour all nodes

1.75867720687844E+05

1.0E-6

4.5

H1X for all nodes

2.49999999999582E-04

1.0E-6

4.5

LAGS_F1pour all nodes

58622.573562549

1.0E-6

5.5

H1X for all nodes

7.49999999999582E-04

1.0E-6

5,5

LAGS_F1pour all nodes

1.75867720687844E+05

1.0E-6

7

H1X for all nodes

1.49999999999958E-03

1.0E-6

7

LAGS_F1pour all nodes

28117.686527187

1.0E-6

9.5

H1X for all nodes

2.49999999999582E-04

1.0E-6

9.5

LAGS_F1pour all nodes

4686.28108785798

1.0E-6

12

H1X for all nodes

1.49999999999958E-03

1.0E-6

12

LAGS_F1pour all nodes

28117.686527187

1.0E-6

15

H1X for all nodes

2.99999999999958E-03

1.0E-6

15

LAGS_F1pour all nodes

718.731177854856

1.0E-6

6.5. Comments#

The contact and friction values of the Lagrangians are calculated explicitly as a function of the displacement jump that is controlled. It is therefore natural to have almost zero errors.