5. C modeling

5.1. Characteristics of the mesh

In this modeling, the upwind method is tested for crack propagation. Level-sets are determined by solving the updating equations by schema with finite differences.

5.2. Characteristics of the mesh

The same mesh as in modeling \(A\) (§2.1) is used here.

5.3. Tested sizes and results

For each propagation step, we test the value of the stress intensity factors \({K}_{I}\) and \({K}_{\mathit{II}}\) given by CALC_G.

5.3.1. Results on \({K}_{I}\):

A relative non-regression test is carried out on \({K}_{I}\) compared to \({K}_{I\mathit{maillage}}\) with an accuracy of \(\text{3\%}\).

Identification	Code_Aster	Reference	Difference ( \(\text{\%}\) )
CALC_G
KI_1	0.243960	2,43961 10-1	2.03E -04%
KI_2	0.290552	2.90147 10-1	0.14%
KI_3	0.330871	3,30840 10-1	9.645E -03%
KI_4	0.375936	3.75984 10-1	0.0126%
KI_5	0.433524	4.33606 10-1	0.02%
KI_6	0.496884	4.96975 10-1	0.02%
KI_7	0.572963	5.73785 10-1	0.14%
KI_8	0.673340	6.70222 10-1	0.46%
KI_9	0.788694	7.89716 10-1	0.13%
KI_10	0.94306	9.39463 10-1	0.39%
KI_11	1.151406	1.15201	1.15201	0.05%
KI_12	1.44998	1.45163	0.11%
KI_13	1.92206	1.9185	0.17%

5.3.2. Results on \({K}_{\mathit{II}}\):

For this test, we want \({K}_{\mathit{II}}\) to be as \({K}_{\mathit{II}}={K}_{\mathit{IIref}}\pm {3.10}^{-2}\). (absolute test)

Identification	Code_Aster	Reference	Difference
CALC_G
KII_1	0.0427721	4.27722 10-2	3.92E-08	4.27721
KII_2	-0.0001827	1.21013 10-4	3.04 E-04	3.04 E-04
KII_3	0.0086350	7.10255 10-3	1.53E-03	1.53E-03
KII_4	0.0006797	1.94683 10-3	1.27E-03	1.27E-03
KII_5	0.0019676	1.20266 10-3	7.64E-04	1.20266 10-3
KII_6	-0.0001195	8,82542 10-4	1.00E-03
KII_7	-0.0009619	-1.23199 10-3	2.70E-04	-1.23199 10-3
KII_8	-0.0002964	-3,54655 10-3	3.84E-03	3.84E-03
KII_9	-0.0027228	-4.54122 10-3	1.82E-03	1.82E-03
KII_10	-0.0258299	-8,18030 10-3	0.017
KII_11	-0.0041077	-1.55772 10-2	0.01146
KII_12	-0.0283523	-2,31849 10-2	-2.31849 10-2	5.17E-03
KII_13	-0.0304681	-3,52229 10-2	4.75E-03