13. Summaries of results

The conclusions of this test case are as follows:

• The definition and calculation of local \(G\) on closed crack bottoms is validated. In particular, the independence of local \(G\) with respect to the angle is checked for axisymmetric crack and loading. There is a difference of less than \(\text{2\%}\) across the entire crack background for a DISCRETISATION “LINEAIRE”.

• The POST_K1_K2_K3 command, which makes it possible to calculate the stress intensity factors by exploiting the jump in movements on the lips of the crack, is also validated. This method, less accurate than CALC_G/CALC_G_XFEM, makes it possible to obtain here (with an appropriate mesh: middle nodes of the edges touching the bottom of the crack moved to a quarter of these edges) values of \(\mathrm{K1}\) and \(\mathrm{K3}\) within \(\text{2 \%}\) of the reference.

Three interpolation methods are used and give similar results. Method 3 is interesting because it provides a single value of the stress intensity factors and not a maximum value and a minimum value.

The use of POST_K1_K2_K3 to study a crack caused by loosening knots is tested and gives satisfactory results.

• We validate the calculation of the bilinear form of \(G\) and the CALC_K_G option of CALC_G_XEM.

• The \(\text{X-FEM}\) method makes it possible to evaluate the stress intensity factors \(K\) on a non-cracked mesh with an error less than \(\text{20\%}\) with CALC_G_XFEM. With the POST_K1_K2_K3 operator, the precision increases considerably, reaching a departure from the analytical solution of \(\text{2\%}\).

• We validate the calculations for elements 3D_ INCO_UPG, 3D_ INCO_UP, AXIS_INCO_UPG and AXIS_INCO_UP