7. H modeling#
Method X- FEM with CALC_G_XFEM and POST_K1_K2_K3.
7.1. Characteristics of modeling#
This modeling makes it possible to test the calculation of \(\mathrm{K1}\) using POST_K1_K2_K3 and CALC_G_XFEM (option CALC_K_G) on a non-meshed crack (method \(\text{X-FEM}\)).
Only traction loading is taken into account. Symmetry conditions are imposed on the two lateral faces. In addition, we must not forget to impose the symmetry conditions on the lips of the crack through the jump degrees of freedom (H1X, H1Y, and H1Z).
7.2. Characteristics of the mesh#
Number of knots: 6100
Number of meshes and type: 1500 PENTA6 and 4600 HEXA8 (linear mesh)
7.3. Tested sizes and results#
The values tested are the stress intensity factors \(\mathit{K1}\) along the crack bottom, calculated either by POST_K1_K2_K3 (method 3), or by CALC_G_XFEM. The test is carried out at 3 points at the bottom of the crack: points 1 (first point), 10 and 24 (last point).
The mean squared error corresponds to the following quantity:
\(\varepsilon \mathrm{=}\sqrt{\frac{{\mathrm{\int }}_{\Gamma }{({K}_{I}^{\mathit{ref}}\mathrm{-}{K}_{I}^{\mathit{Aster}})}^{2}\mathit{ds}}{{\mathrm{\int }}_{\Gamma }{({K}_{I}^{\mathit{ref}})}^{2}\mathit{ds}}}\)
Identification |
Reference |
Reference type |
\(\text{\%}\) tolerance |
CALC_G_ XFEM |
|||
\(\mathit{K1}\) - point 1 |
1.595e6 |
|
12.00 |
\(\mathit{K1}\) - dot 10 |
1.595e6 |
|
3.00 |
\(\mathit{K1}\) - dot 24 |
1.595e6 |
|
18.00 |
Mean square error |
9.90 |
||
POST_K1_K2_K3 |
|||
\(\mathit{K1}\) - point 1 |
1.595e6 |
|
2.00 |
\(\mathit{K1}\) - dot 10 |
1.595e6 |
|
2.00 |
\(\mathit{K1}\) - dot 24 |
1.595e6 |
|
2.00 |
Mean square error |
1.15 |
||
7.4. notes#
The precision of the results obtained on a non-meshed crack (method \(\text{X-FEM}\)) and the POST_K1_K2_K3 post-treatment is very satisfactory, comparable to the precision with a FEM meshed crack. However, the results are degraded with CALC_G_XFEM as is generally the case with curved fronts (test SSVL154 as well). The use of this operator is not recommended for non-straight fronts with the \(\text{X-FEM}\) method, given the fairly modest precision of this operator (18%).
For the operator CALC_G_XFEM, smoothing types LAGRANGE do not make it possible to obtain easily usable results; smoothing of type LEGENDRE is therefore preferred.
It should be noted that the mesh used is linear; the use of a finer mesh makes it possible to improve the precision of the result, but at the expense of calculation times.