12. J modeling#

12.1. Characteristics of modeling#

The modeling characteristics are the same as for modeling \(A\), except that we change the position of the level set in order to position it at the interface between two elements.

The equation for the level function for the interface is as follows:

\(\text{LN}=Y-2\)

12.2. Characteristics of the mesh#

We discretize the structure in \(2\times 5\) finite elements TRIA3. The interface is therefore present between two elements through level sets.

_images/10000000000000F1000003241A3D4ED9F6D803E0.png

Figure 12.2-a : J modeling mesh

12.3. Piloting#

A specific XFEM SAUT_IMPO control is used on all intersected edges.

12.4. 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

12.5. 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.