4. C modeling#
4.1. Characteristics of modeling#
The simulation is carried out axisymmetrically. The interface elements allow the crack to be represented along \({\Gamma }_{i}\). Their modeling is AXIS_INTERFACE_S and their cohesive behavior is CZM_TAC_MIX. The other elements of the mesh are QUAD8 with ELAS elastic behavior in AXIS modeling.
4.2. Material parameters#
The values of the Young’s modulus, the Poisson’s ratio, the critical stress and the toughness of the material are taken as follows:
Moreover, the Lagrangian penalty parameter is taken to be equal to PENA_LAGR =1000.
(NB: these are « test » values that do not correspond to any particular material.)
4.3. Characteristics of the mesh#
The mesh is identical to modeling A with two differences: all the cells are quadratic (QUAD8) and the cohesive element layer is composed of elements with a small thickness, oriented with the ORIE_FISSURE command.
4.4. Tested sizes and results#
To test the numerical solution, we use the equation [éq 2-1]. We denote \({F}^{R}\) as the resultant of the force along \({\Gamma }_{i}\) multiplied by \(2\pi\).
Size tested |
Theory |
Aster_code |
Difference ( \(\text{\%}\) ) |
right now: 3 |
1.576931E-01 |
1.5769307873679E-01 |
-1.35E-05 |
right now: 3 |
1.25499E+01 |
1.2549900398014E+01 |
3.17E-06 |
right now: 6 |
2.656474E-01 |
2.6564739519277E-01 |
-1.81E-06 |
right now: 6 |
9.486833E+00 |
9.4868329805100E+00 |
-2.05E-07 |
right now: 8 |
3.63577E-01 |
3.6357700583331D-01 |
1.60E-06 |
right now: 8 |
6.7082E+00 |
6.7082039325061D+00 |
5.86E-05 |