10. L modeling#
10.1. Characteristics of modeling#
This modeling is intended to validate the propagation of the potential crack surface for a calculation of propagation with cohesive elements.
The geometric method is used by PROPA_FISS to calculate the new position of the crack, with the PROPA_COHESIF operation. The calculation domain is not located and no auxiliary grid is used.
Three calls to operator PROPA_FISS are made to simulate crack propagation by cohesive elements, starting from the initial crack already present in the structure. At each call the advance and the direction of propagation of each point of the crack bottom are imposed:
Advance from the bottom point: \(\Delta a=2m\)
Propagation angle: \(\beta =30°\) for the first two calls to PROPA_FISS, \(\beta =70°\) for the last
10.2. Characteristics of the mesh#
A structured mesh is used for which the initial crack is meshed. The structure is modelled by a mesh composed of 8120 HEXA8 elements.
10.3. Tested sizes and results#
The intersection points between the line 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 (\(\mathit{LSN}\)) and tangent (\(\mathit{LST}\)) 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 |
-4.87110352E-14 |
-1.0999534E-13 |
-9.31824062E-14 |
-6.34770014E-14 |
-6.34770014E-14 |
2 |
-4.87110352E-14 |
-1.0999534E-13 |
-9.31824062E-14 |
-6.34770014E-14 |
-6.34770014E-14 |
3 |
8.07479083E-14 |
-1.80688797E-14 |
-2.95111157E-14 |
-4.96512553E-14 |
-4.96512553E-14 |
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. Considering 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 = \(0.15\times 0.25=0.0375m\)
10.4. notes#
All tested values respect the tolerance used. This means that the position of the crack bottom calculated by the geometric method is correct. The remarks are therefore the same as for modeling I.