3. A, B, C, D, E, and F models#
3.1. Characteristics of modeling#
These 6 models correspond to 6 meshes where 3 topological parameters are varied. The table below summarizes the various cases studied:
\(\mathrm{NS}=8\), \(\mathrm{NC}=4\) |
|
|
\(\mathrm{rt}=\mathrm{0,001}\ast a\) |
A |
B |
\(\mathrm{rt}=\mathrm{0,01}\ast a\) |
C |
D |
\(\mathrm{rt}=\mathrm{0,1}\ast a\) |
E |
F |
The topological parameters that vary are:
\(\mathrm{NS}\): |
number of sectors over 90° |
\(\mathrm{NC}\): |
number of crowns |
\(\mathrm{rt}\): |
the radius of the largest crown (with a: half length of the crack) |
3.1.1. A and B models#
Half mesh - Modeling A
Fissure point zoom - Model A
Half mesh - B modeling
Fissure point zoom - B modeling
3.1.2. C and D modeling#
Full mesh - C modeling
Full mesh - D modelling
3.1.3. E and F models#
Full mesh - E modeling
Full mesh - F modeling
3.1.4. Definition of crown radii#
For these different cases, we define the values of the upper and lower radii, to be specified in the CALC_G command:
Modeling A
1st crown |
2nd crown |
3rd crown |
4th crown |
||
\(\mathrm{rinf}(m)\) |
3,75E—5 |
7,500E—5 |
1,125E—4 |
1,500E—4 |
1,500E—4 |
\(\text{rsup}(m)\) |
7,50E—5 |
1,125E—4 |
1,500E—4 |
1,875E—4 |
B Modeling
1st crown |
2nd crown |
3rd crown |
|
\(\mathrm{rinf}(m)\) |
5.00E—5 |
1.00E—4 |
1.50E—4 |
\(\text{rsup}(m)\) |
1.00E—4 |
1.50E—4 |
2.00E—4 |
C Modeling
1st crown |
2nd crown |
3rd crown |
4th crown |
||
\(\mathrm{rinf}(m)\) |
3,75E—4 |
7,500E—4 |
1,125E—3 |
1,500E—3 |
1,500E—3 |
\(\text{rsup}(m)\) |
7,50E—4 |
1,125E—3 |
1,500E—3 |
1,875E—3 |
1,875E—3 |
D Modeling
1st crown |
2nd crown |
3rd crown |
||
\(\mathrm{rinf}(m)\) |
5.00E—4 |
1.00E—4 |
1.00E—3 |
1.50E—3 |
\(\text{rsup}(m)\) |
1.00E—3 |
1.50E—3 |
2.00E—3 |
E Modeling
1st crown |
2nd crown |
3rd crown |
4th crown |
||
\(\mathrm{rinf}(m)\) |
3,75E—3 |
7,500E—3 |
1,125E—2 |
1,500E—2 |
1,500E—2 |
\(\text{rsup}(m)\) |
7,50E—3 |
1,125E—2 |
1,500E—2 |
1,875E—2 |
F Modeling
1st crown |
2nd crown |
3rd crown |
|
\(\mathrm{rinf}(m)\) |
5.00E—3 |
1.00E—2 |
1.50E—2 |
\(\text{rsup}(m)\) |
1.00E—2 |
1.50E—2 |
2.00E—2 |
3.2. Characteristics of the mesh#
Half-mesh; mesh radiating at the right end of the crack.
The table below gives the constitution of the meshes studied:
\(\mathrm{NS}=8\), \(\mathrm{NC}=4\) |
|
|
\(\mathrm{rt}=\mathrm{0,001}\ast a\) |
3831 knots, 1516 elements, 884 TRI6, 632 QUA8. |
3507 knots, 1388 elements, 820 TRI6, 568 QUA8. |
\(\mathrm{rt}=\mathrm{0,01}\ast a\) |
1179 knots, 400 elements, 104 TRI6, 296 QUA8. |
855 knots, 272 elements, 40 TRI6, 232 QUA8. |
\(\mathrm{rt}=\mathrm{0,1}\ast a\) |
659 knots, 240 elements, 104 TRI6, 136 QUA8. |
335 knots, 112 elements, 40 TRI6, 72 QUA8. |