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 |
|
PES background 1: G |
1.19751E-04 |
|
POST_K1_K2_K3 |
||
FI background 2: K1 |
5069.12 |
|
PES background2: K1 |
5069.12 |
|