3. Modeling A#
3.1. Characteristics of modeling#
This is a modeling XFEM, in plane constraints, the discontinuity interface being defined by a level function (level set noted \(\text{LN}\) for the normal level set) directly in the command file using the DEFI_FISS_XFEM [U4.82.08] operator.
The level function equation for the interface is as follows:
\(\text{LN}=Y-2.5\)
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 operator DEFI_CONT, 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.
3.2. Characteristics of the mesh#
We discretize the structure in \(1\times 5\) finite elements QUAD4. The interface is therefore present in the central element through level sets.
Figure 3.2-a : Model A mesh
3.3. Piloting#
A specific control \(X-\mathrm{FEM}\) SAUT_IMPO is used on all the edges intersected by the crack.
3.4. 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 |
0.51.0E-6 |
|
3.66296853301E+05 |
1.0E-6 |
0.75 |
H1Y for all nodes |
6.818119835274E-08 |
1.0E-6 |
0.75 |
|
1.8314842665E+05 |
1.0E-6 |
2 |
H1Y for all nodes |
4.0908719011645E-07 |
1.0E-6 |
2 |
|
1.098890559903E+06 |
1.0E-6 |
3.5 |
H1Y for all nodes |
7.49999999999582E-04 |
1.0E-6 |
3,5 |
|
1.75867720687844E+05 |
1.0E-6 |
4.5 |
H1Y for all nodes |
2.49999999999582E-04 |
1.0E-6 |
4.5 |
|
58622.573562549 |
1.0E-6 |
5.5 |
H1Y for all nodes |
7.49999999999582E-04 |
1.0E-6 |
5,5 |
|
1.75867720687844E+05 |
1.0E-6 |
7 |
H1Y for all nodes |
1.49999999999958E-03 |
1.0E-6 |
7 |
|
28117.686527187 |
1.0E-6 |
9.5 |
H1Y for all nodes |
2.49999999999582E-04 |
1.0E-6 |
9.5 |
|
4686.28108785798 |
1.0E-6 |
12 |
H1Y for all nodes |
1.49999999999958E-03 |
1.0E-6 |
12 |
|
28117.686527187 |
1.0E-6 |
15 |
H1Y for all nodes |
2.99999999999958E-03 |
1.0E-6 |
15 |
|
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 |
|
3.66296853301E+05 |
1.0E-6 |
0.75 |
H1X for all nodes |
6.818119835274E-08 |
1.0E-6 |
0.75 |
|
1.8314842665E+05 |
1.0E-6 |
2 |
H1X for all nodes |
4.0908719011645E-07 |
1.0E-6 |
2 |
|
1.098890559903E+06 |
1.0E-6 |
3.5 |
H1X for all nodes |
7.49999999999582E-04 |
1.0E-6 |
3,5 |
|
1.75867720687844E+05 |
1.0E-6 |
4.5 |
H1X for all nodes |
2.49999999999582E-04 |
1.0E-6 |
4.5 |
|
58622.573562549 |
1.0E-6 |
5.5 |
H1X for all nodes |
7.49999999999582E-04 |
1.0E-6 |
5,5 |
|
1.75867720687844E+05 |
1.0E-6 |
7 |
H1X for all nodes |
1.49999999999958E-03 |
1.0E-6 |
7 |
|
28117.686527187 |
1.0E-6 |
9.5 |
H1X for all nodes |
2.49999999999582E-04 |
1.0E-6 |
9.5 |
|
4686.28108785798 |
1.0E-6 |
12 |
H1X for all nodes |
1.49999999999958E-03 |
1.0E-6 |
12 |
|
28117.686527187 |
1.0E-6 |
15 |
H1X for all nodes |
2.99999999999958E-03 |
1.0E-6 |
15 |
|
718.731177854856 |
1.0E-6 |
3.5. 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.