4. B modeling#

4.1. Characteristics of modeling#

In this modeling, the simplex method is tested for crack propagation.

Level-sets are determined by solving the updating equations.

4.2. Characteristics of the mesh#

Here we use the same mesh as in modeling \(A\).

4.3. Tested sizes and results#

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

4.3.1. Results on KI:#

A relative non-regression test is carried out on \({K}_{I}\) compared to \({K}_{I\mathrm{maillage}}\) with an accuracy of \(\text{5\%}\).

Identification

Code_Aster

Reference

Difference ( \(\text{\%}\) )

CALC_G

KI_1

2.43961 10-1

2.43961 10-1

2.43961 10-1

2.03 10-4%

KI_2

0.29056

2.90147 10-1

0.1%

KI_3

0.3308

3.30840 10-1

3.910-4%

KI_4

0.3759

3.75984 10-1

0.02%

KI_5

0.43355

4.33606 10-1

7.9 10-4%

KI_6

0.497

4,96975 10-1

0.025%

KI_7

0.573

5,73785 10-1

0.12%

KI_8

0.6705

6,70222 10-1

0.03%

KI_9

0.7899

7,89716 10-1

0.03%

KI_10

0.93757

9.39463 10-1

0.2%

KI_11

1.1508

1.15201

1.15201

0.11%

KI_12

1.4472

1.45163

0.30%

KI_13

1.8923

1.91885

1.38%

4.3.2. Results on \({K}_{\mathrm{II}}\):#

For this test, we want \({K}_{\mathrm{II}}\) to be as \({K}_{\mathrm{II}}={K}_{\mathrm{IIref}}\pm {5.10}^{-2}\). (absolute test)

Identification

Code_Aster

Reference

Difference

CALC_G

KII_1

0.04277

4.27722 10-2

3.92 10-8

KII_2

-0.00019

1.21013 10-4

3.1 10-4

3.1 10-4

KII_3

0.00864

7,10255 10-3

1,54 10-3

1,54 10-3

KII_4

0.00068

1.94683 10-3

0.0013

KII_5

0.001988

1.20266 10-3

7.85 10-4

KII_6

-0.0003965

8.82542 10-4

1.27 10-3

8.82542 10-3

KII_7

-0.001049

-1.23199 10-3

1.82 10-4

-1.82 10-4

KII_8

-0.01141

-3,54655 10-3

7,86 10-3

7,86 10-3

KII_9

0.006572

-4.54122 10-3

0.0111

KII_10

0.001981

-8,18030 10-3

0.01

KII_11

-0.038036

-1.55772 10-2

0.0224

KII_12

-0.012783

-2,31849 10-2

0.0104

KII_13

-0.02314

-3,52229 10-2

0.012