3. Modeling A#

3.1. Characteristics of modeling#

In this modeling, the mesh method is tested for crack propagation. Level-sets are determined by orthogonal projection onto the segments making up the crack.

3.2. Characteristics of the mesh#

The structure is modelled by a regular mesh composed of \(90\times 30\) QUAD4, respectively along the axes \(x\), \(y\). The crack is not meshed.

_images/10000000000004590000033074BD265CFFB3F105.png

Figure 3.2-a : mesh of the cracked plate

3.3. 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.

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

A relative non-regression test is carried out on \({K}_{I}\) with an accuracy of \({2.10}^{-3}\).

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

For this test, we want \({K}_{\mathrm{II}}\) to be as \({K}_{\mathrm{II}}={K}_{\mathrm{IIref}}\pm {10}^{-2}\).

Identification

Code_Aster

Reference

Difference

CALC_G

KII_1

4,27722 10-2

4,27722 10-2

KII_2

1.21013 10-4

1.21013 10-4

KII_3

7,10255 10-3

7,10255 10-3

KII_4

1.94683 10-3

1.94683 10-3

KII_5

1.20266 10-3

1.20266 10-3

KII_6

8,82542 10-4

8,82542 10-4

KII_7

-1,23199 10-3

-1,23199 10-3

KII_8

-3,54655 10-3

-3,54655 10-3

KII_9

-4.54122 10-3

-4.54122 10-3

KII_10

-8,18030 10-3

-8,18030 10-3

KII_11

-1.55772 10-2

-1.55772 10-2

KII_12

-2,31849 10-2

-2,31849 10-2

KII_13

-3,52229 10-2

-3,52229 10-2

3.4. Additional results#

_images/1000020000000213000000CCCA8374103A6CB74B.png

Figure 3.4-a : Comparison of the path obtained with the mesh method to the paths of the study by Mariani and Perego

On this, we can see: in black the numerical results of Mariani and Perego, in dotted lines the experimental results and in blue the results of the Code_Aster mesh method. The mesh method gives results similar to the experimental data.