3. B modeling#
3.1. 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_JOINT and their cohesive behavior is CZM_LIN_REG. The other elements of the mesh are QUAD4 with ELAS elastic behavior in AXIS modeling.
3.2. 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 parameter for regularizing the cohesive law is taken to be equal to PENA_ADHERENCE = 0.00001. (NB: these are « test » values that do not correspond to any particular material.)
3.3. Characteristics of the mesh#
The mesh is identical to the previous one except that the layer of cohesive elements is composed of elements with a small thickness, oriented with the command ORIE_FISSURE.
3.4. Tested sizes and results#
To test the numerical solution, we use the equation [éq 2-1]. We note
the resultant of the force along \({\Gamma }_{i}\) multiplied by \(2\pi\).
Size tested |
Theory |
Aster_code |
Difference ( \(\text{\%}\) ) |
right now: 3 |
2.298338E-01 |
2.2983379490657E-01 |
-2.22E-06 |
right now: 3 |
1.049985E+01 |
1.0499850000001E+01 |
1.05E-11 |
right now: 6 |
3.884798E-01 |
3.8847977822122E-01 |
-5.61E-06 |
right now: 6 |
5.99982E+00 |
5.9998200000014E+00 |
2.27E-11 |
right now: 8 |
5.2809E-01 |
5.2809010497189E-01 |
1.99E-05 |
right now: 8 |
2.03974E+00 |
2.0397408000020E+00 |
3.92E-05 |