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 :math:`\text{X-FEM}` elements


* Test the non-regression of the volume forces imposed on a crack :math:`\text{X-FEM}`

*Review on linear elements*

With the CALC_G command, good precision is obtained on :math:`{K}_{I}` and :math:`{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:

.. csv-table::

    "", "TRIA3 + topological (D modeling)", "TRIA3 + geometric (C modeling)", "TRIA6 + topological (E modeling)"
    "System size", "20788 ddls", "21396 ddls", "82032 ddls"
    "CALC_G: :math:`{K}_{I}` "," 0.5% "," 0.2% "," 0.3%"
    "CALC_G: :math:`{K}_{\mathit{II}}` "," 2.0% "," 2.0% "," 2.0% "," 2.0%"
    "CALC_G: :math:`G` "," 4.0% "," 1.0% "," 0.6%"
    "POST_K1_K2_K3: :math:`{K}_{I}` "," 6.0% "," 0.2% "," 0.2%"
    "POST_K1_K2_K3: :math:`{K}_{\mathit{II}}` "," 6.0% "," 3.0% "," 1.5%"