3. Modeling A#

3.1. Characteristics of modeling#

Method UPWIND is used by PROPA_FISS to solve the crack propagation equations.

No auxiliary grids are used. This is possible because the mesh of the structure is very regular.

3.2. Characteristics of the mesh#

The structure is modelled by a mesh composed of 1440 elements QUAD4 (see).

_images/1000020100000180000002E3EB49BD20839025B0.png

Figure 3.2-a : structure mesh

The mesh is very coarse to reduce the calculation time. It is more refined in the crack propagation zone. In this area the dimension of the elements is \(25\times 25\mathrm{mm}\). The largest element used has a dimension equal to \(25\times 100\mathrm{mm}\).

3.3. Tested sizes and results#

The values of \({K}_{I}\) and \({K}_{\mathrm{II}}\) for the two depths of the crack are tested after each propagation. To check if these values are correct, a relative tolerance equal to 5% is used for the values of \({K}_{I}\). On the other hand, to check whether the value of \({K}_{\mathit{II}}\) is zero, an absolute tolerance (threshold value) linked to the value of \({K}_{I}\) is used: it is considered that \({K}_{\mathit{II}}\) is zero if its value is less than 1% of the value of \({K}_{I}\). Indeed, in this case we can overlook the value of \({K}_{\mathit{II}}\).

We test the maximum value of \({K}_{I}\) and \({K}_{\mathit{II}}\) between the two bottoms of the crack.

Propagation

\({K}_{I}\) reference [\(\mathit{Pa}\sqrt{\mathit{mm}}\)]

Tolerance [%]

1

2.2997E+07

5.0

2

2.5878E+07

5.0

3

2.8894E+07

5.0

Propagation

Max \({K}_{\mathit{II}}\) [\(\mathit{Pa}\sqrt{\mathit{mm}}\)]

\({K}_{I}\) reference [\(\mathit{Pa}\sqrt{\mathit{mm}}\)]

\({K}_{\mathit{II}}\) threshold [\(\mathit{Pa}\sqrt{\mathit{mm}}\)]

1

7.4881E+03

2.2997E+07

2.2997E+05

2

4.0283E+03

2.5878E+07

2.5878E+05

3

2.0639E+04

2.8894E+07

2.8894E+05

3.4. notes#

All values tested are within the tolerances used. This means that method UPWIND correctly calculates both the position of the two bottoms of the crack 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 0.1% of the values of \({K}_{I}\). The results obtained are therefore very satisfactory.