3. B modeling#

In this modeling, the extended finite element method (\(\text{X-FEM}\)) is used. A radius of geometric enrichment is defined with a number of element layers equal to 3.

3.1. Characteristics of the mesh#

The structure is modelled by a regular mesh (identical to modeling \(A\)) composed of \(100\times 100\) QUAD4, respectively along the \(x,y\) axes. The crack is not meshed.

3.2. Tested sizes and results#

For each value of the angle \(\theta\) (\(0°\) and \(45°\)), and for each load: internal force (\(\mathrm{FI}\)) and gravity (\(\mathrm{PESA}\)), we test the value of the stress intensity factor \(\mathrm{KI}\) given by CALC_G (for the two crack bottoms) as well as that given by K1 of POST_K1_K2_K3 (for the 2nd crack bottom). We also test the value of \(G\) given by CALC_G, option CALC_G, which we compare to that obtained by CALC_G, option CALC_K_G.

For method \(G-\mathrm{thêta}\) (command CALC_G), the following theta field crowns are chosen: \({R}_{\mathrm{inf}}=\mathrm{0,1}a\) and \({R}_{\text{sup}}=\mathrm{0,3}a\);

For the method by extrapolation of movement jumps (POST_K1_K2_K3), the maximum curvilinear abscissa is equal to \(\mathrm{0,3}a\).

3.2.1. Results for \(\theta \mathrm{=}0°\)#

Identification

Code_Aster

Tolerance

CALC_G

FI background 1: K1

5013.598

0.1%

FI background 2: K1

5013.586

0.1%

PES background1: K1

5013.598

0.1%

PES background2: K1

5013.586

0.1%

FI background 1: G

1.19751E-04

0.1%

PES background 1: G

1.19751E-04

0.1%

POST_K1_K2_K3

FI background 2: K1

5069.12

0.1%

PES background2: K1

5069.12

0.1%

3.2.2. Results for \(\theta =45°\)#