8. F modeling#
8.1. Characteristics of modeling#
This modeling is identical to the C modeling except for the calculation domain which is not located around the bottom of the crack. The level sets are therefore updated throughout the model.
8.2. Characteristics of the mesh#
The same mesh as that of the C modeling is used.
8.3. Tested sizes and results#
The intersection points between the edge that gives the theoretical position of the background and the faces of the elements of the mesh are calculated using MACR_LIGN_COUPE (see). For each of these points, we calculate the normal (\(\mathrm{LSN}\)) and tangent (\(\mathrm{LST}\)) level set value using the POST_RELEVE_T operator and we check that the maximum and minimum values are almost zero:
Propag. \(i\) |
Max \({\mathit{LSN}}_{i}\) |
Min \({\mathit{LSN}}_{i}\) |
Max \({\mathit{LST}}_{i}\) |
Min \({\mathit{LST}}_{i}\) |
|
1 |
-4.430E-15 |
-4.654E-15 |
3.010E-15 |
2.7616E-15 |
2.7616E-15 |
2 |
-0.00067 |
-0.00067 |
-0.00067 |
2.0122E-16 |
-1.3114E-15 |
3 |
0.00046 |
0.00046 |
-0.00046 |
-0.00041 |
-0.00041 |
The values obtained are calculated from the values at the nodes of the mesh using the shape functions of the elements. It is therefore expected that these values will be affected by an error that depends on the size of the elements in the mesh. Indeed, the precision of representation of the level sets is itself linked to the size of the elements. Consequently, a tolerance is used to check whether the calculated level sets are almost zero. Assuming that the mesh is coarse, a tolerance equal to 15% of the length of the largest edge of the mesh in the propagation zone is assigned:
Tolerance used = \(0.15\mathrm{\times }0.33\mathrm{=}0.05m\)
8.4. notes#
All tested values respect the tolerance used. This means that the position of the crack bottom calculated by the simplex method is correct.
Finally, it should be noted that after the three simulated propagations, the crack deviated from \(90\). On the other hand, the total advance is small. So a very severe mixed mode propagation was simulated. The conditions used are more severe than the conditions normally found for real structures. However, the simplex method correctly calculated the position of the crack and its robustness was therefore verified.