7. Modeling E#
7.1. Characteristics of modeling#
Method GEOMETRIQUE is used by PROPA_FISS to update the crack position. No auxiliary grids are used.
7.2. Characteristics of the mesh#
We use the same mesh as that of modeling \(A\).
7.3. Tested sizes and results#
The values of \({K}_{I}\) and \({K}_{\mathrm{II}}\) are tested for both cracks after each propagation. To check if these values are correct, a relative tolerance equal to \(\text{5\%}\) is used for the values of \({K}_{I}\). On the other hand, to check if the value of \({K}_{\mathrm{II}}\) is zero, we use an absolute tolerance (threshold value) linked to the value of \({K}_{I}\): it is considered that \({K}_{\mathrm{II}}\) is zero if its value is less than \(\text{1\%}\) of the value of \({K}_{I}\). Indeed, in this case we can overlook the value of \({K}_{\mathrm{II}}\).
Propagation |
Crack |
\({K}_{I}\) reference [\(\mathrm{Pa}\sqrt{\mathrm{mm}}\)] |
Tolerance |
1 |
left |
3.7992E+07 |
< 5% |
righthand |
3.7992E+07 |
< 5% |
|
2 |
left |
4.1791E+07 |
< 5% |
righthand |
4.1791E+07 |
< 5% |
|
3 |
left |
4.6316E+07 |
< 5% |
righthand |
4.6316E+07 |
< 5% |
Propagation |
Crack |
\({K}_{\mathrm{II}}\) reference [\(\mathrm{Pa}\sqrt{\mathrm{mm}}\)] |
Tolerance [\(\mathrm{Pa}\sqrt{\mathrm{mm}}\)] |
1 |
left |
0 |
< \({K}_{I\mathrm{Aster}}/100\) |
righthand |
0 |
< \({K}_{I\mathrm{Aster}}/100\) |
|
2 |
left |
0 |
< \({K}_{I\mathrm{Aster}}/100\) |
righthand |
0 |
< \({K}_{I\mathrm{Aster}}/100\) |
|
3 |
left |
0 |
< \({K}_{I\mathrm{Aster}}/100\) |
righthand |
0 |
< \({K}_{I\mathrm{Aster}}/100\) |
7.4. notes#
All values tested are within the tolerances used. This means that method GEOMETRIQUE correctly calculates both the position of the two cracks and the level sets.
The error obtained on the values of \({K}_{I}\) is almost zero and the values of \({K}_{\mathrm{II}}\) are always in the order of the \(\text{0.01\%}\) values of \({K}_{I}\). The results obtained are therefore very satisfactory.