8. Summaries of results#
The objectives of this test have been achieved:
Validate on a simple case the calculation of stress intensity factors in mixed mode for linear and quadratic \(\text{X-FEM}\) elements
Test the non-regression of the volume forces imposed on a crack \(\text{X-FEM}\)
Review on linear elements
With the CALC_G command, good precision is obtained on \({K}_{I}\) and \({K}_{\mathit{II}}\) (2 to 3%) with linear elements (triangles or quadrangles), regardless of the type of enrichment at the bottom of the crack (topological or geometric).
On the other hand, with the POST_K1_K2_K3 command, activating geometric enrichment significantly improves the solution compared to the topological enrichment by default (5 to 6% → 2 to 3%).
It is therefore recommended to use enrichment by default (topological) and post-processing with CALC_G. If for some reason you want to post-process with POST_K1_K2_K3, then it’s best to activate geometric enrichment.
Report on the quadratic elements
Quadratic elements (with topological enrichment) make it possible to find results as accurate as linear elements with geometric enrichment, but for a much larger size of the system to be solved.
Comparison of the relative errors for the 30° inclined crack:
TRIA3 + topological (D modeling) |
TRIA3 + geometric (C modeling) |
TRIA6 + topological (E modeling) |
||
System size |
20788 ddls |
21396 ddls |
82032 ddls |
|
CALC_G: \({K}_{I}\) |
|
|
|
|
CALC_G: \({K}_{\mathit{II}}\) |
|
|
|
|
CALC_G: \(G\) |
|
|
|
|
POST_K1_K2_K3: \({K}_{I}\) |
|
|
|
|
POST_K1_K2_K3: \({K}_{\mathit{II}}\) |
|
|
|