7. E modeling#

7.1. Characteristics of modeling#

This is a modeling \(X-\mathrm{FEM}\), in three dimensions, with the definition of contact on the discontinuity interface defined by a level function (level set noted \(\text{LN}\) for the normal level set) directly in the command file using the operator DEFI_FISS_XFEM [U4.82.08].

The level function equation for the interface is as follows:

\(\text{LN}=Y-12.5\)

No tangential level set is necessary since the keyword TYPE_DISCONTINUITE =” INTERFACE “is used, which allows the structure to be completely divided into two parts.

The cohesive law is introduced through the DEFI_CONT operator, by specifying ALGO_CONT =” CZM “, and the cohesive behavior law is activated using the keyword RELATION =” CZM_EXP_REG”.

Here we are testing the \(I\) and \(\mathrm{II}\) opening modes.

7.2. Characteristics of the mesh#

We discretize the structure in \(1\times 1\times 5\) finite elements HEXA8. The interface is therefore present in the central element through level sets.

_images/100000000000020D00000334F29B6B70B868AFEB.png

Figure 7.2-a : mesh with 5 HEXA8

7.3. Piloting#

Specific control of type SAUT_IMPO, we use the group of nodes located immediately above the crack.

7.4. 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

H1Z for all nodes

1.36362396705485E-07

1.0E-5

0.5

LAGS_Cpour all nodes

3.66296853301E+05

1.0E-5

0.75

H1Z for all nodes

6.818119835274E-08

1.0E-5

0.75

LAGS_Cpour all nodes

1.8314842665E+05

1.0E-5

2

H1Z for all nodes

4.0908719011645E-07

1.0E-5

2

LAGS_Cpour all nodes

1.098890559903E+06

1.0E-5

3.5

H1Z for all nodes

7.49999999999582E-04

1.0E-5

3,5

LAGS_Cpour all nodes

1.75867720687844E+05

1.0E-5

1.0E-5

4.5

H1Z for all nodes

2.49999999999582E-04

1.0E-5

4.5

LAGS_Cpour all nodes

58622.573562549

1.0E-5

5.5

H1Z for all nodes

7.49999999999582E-04

1.0E-5

5,5

LAGS_Cpour all nodes

1.75867720687844E+05

1.0E-5

7

H1Z for all nodes

1.49999999999958E-03

1.0E-5

7

LAGS_Cpour all nodes

28117.686527187

1.0E-5

9.5

H1Z for all nodes

2.49999999999582E-04

1.0E-5

9.5

LAGS_Cpour all nodes

4686.28108785798

1.0E-5

12

H1Z for all nodes

1.49999999999958E-03

1.0E-5

12

LAGS_Cpour all nodes

28117.686527187

1.0E-5

15

H1Z for all nodes

2.99999999999958E-03

1.0E-5

15

LAGS_Cpour all nodes

718.731177854856

1.0E-5

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-5

0.5

LAGS_F1pour all nodes

3.66296853301E+05

1.0E-5

0.75

H1X for all nodes

6.818119835274E-08

1.0E-5

0.75

LAGS_F1pour all nodes

1.8314842665E+05

1.0E-5

2

H1X for all nodes

4.0908719011645E-07

1.0E-5

2

LAGS_F1pour all nodes

1.098890559903E+06

1.0E-5

3.5

H1X for all nodes

7.49999999999582E-04

1.0E-5

3,5

LAGS_F1pour all nodes

1.75867720687844E+05

1.0E-5

1.0E-5

4.5

H1X for all nodes

2.49999999999582E-04

1.0E-5

4.5

LAGS_F1pour all nodes

58622.573562549

1.0E-5

5.5

H1X for all nodes

7.49999999999582E-04

1.0E-5

5,5

LAGS_F1pour all nodes

1.75867720687844E+05

1.0E-5

7

H1X for all nodes

1.49999999999958E-03

1.0E-5

7

LAGS_F1pour all nodes

28117.686527187

1.0E-5

9.5

H1X for all nodes

2.49999999999582E-04

1.0E-5

9.5

LAGS_F1pour all nodes

4686.28108785798

1.0E-5

12

H1X for all nodes

1.49999999999958E-03

1.0E-5

12

LAGS_F1pour all nodes

28117.686527187

1.0E-5

15

H1X for all nodes

2.99999999999958E-03

1.0E-5

15

LAGS_F1pour all nodes

718.731177854856

1.0E-5

7.5. 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.