2. Modeling A#
2.1. Characteristics of modeling#
The modeling is two-dimensional with plane deformations D_ PLAN and static non-linear.
The vertical displacement imposed on the upper facet varies between \(0\) and \(-\mathrm{0.2m}\) in \(280\) time steps between \(t=0.\) and \(t=10\). The automatic subdivision of the time step is activated to manage situations of non-convergence of local integration.
The calculation option INDL_ELGA, which allows the directions of the Rice tensor to be calculated, is also activated. The results provided by this option are tested in non-regression mode.
The calculation option PDIL_ELGA, which allows you to calculate the values of the parameter A1_ LC2, is also activated. The results provided by this option are tested in non-regression mode.
2.2. Tested sizes and results#
The solutions are calculated at point \(C\) and compared to references GEFDYN. They are given in terms of stress \({\sigma }_{\mathrm{yy}}\), total volume deformation \({\varepsilon }_{v}\) and isotropic work-hardening coefficients \(({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m})\) and deviatory \(({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m})\), and summarized in the following tables:
\({\sigma }_{\mathrm{yy}}(\mathrm{kPa})\)
\({\varepsilon }_{\mathrm{zz}}\) |
|
|
Tolerance (%) |
-1% |
“SOURCE_EXTERNE” |
-243.1 |
1.0 |
-2% |
“SOURCE_EXTERNE” |
-287.8 |
1.0 |
-5% |
“SOURCE_EXTERNE” |
-345.1 |
1.0 |
-10% |
“SOURCE_EXTERNE” |
-372.9 |
1.0 |
-20% |
“SOURCE_EXTERNE” |
-377.2 |
1.0 |
\({\varepsilon }_{V}=\text{trace}(\varepsilon )\)
\({\varepsilon }_{\mathrm{zz}}\) |
|
|
Tolerance (%) |
-1% |
“SOURCE_EXTERNE” |
-4.07E-3 |
1.0 |
-2% |
“SOURCE_EXTERNE” |
-6.04E-3 |
1.0 |
-5% |
“SOURCE_EXTERNE” |
-8.18E-3 |
2.0 |
-10% |
“SOURCE_EXTERNE” |
-7.19E-3 |
6.0 |
-20% |
“SOURCE_EXTERNE” |
-1.87E-3 |
4.0 |
\(({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m})\) (Map \(\mathrm{YZ}\))
\({\varepsilon }_{\mathrm{zz}}\) |
|
|
Tolerance (%) |
-1% |
“SOURCE_EXTERNE” |
0.398 |
2.0 |
-2% |
“SOURCE_EXTERNE” |
0.455 |
1.0 |
-5% |
“SOURCE_EXTERNE” |
0.517 |
2.0 |
-10% |
“SOURCE_EXTERNE” |
0.553 |
6.0 |
-20% |
“SOURCE_EXTERNE” |
0.582 |
1.0 |
\(({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m})\) (Map \(\mathrm{XY}\))
\({\varepsilon }_{\mathrm{zz}}\) |
|
|
Tolerance (%) |
-1% |
“SOURCE_EXTERNE” |
0.643 |
2.0 |
-2% |
“SOURCE_EXTERNE” |
0.755 |
1.0 |
-5% |
“SOURCE_EXTERNE” |
0.870 |
1.0 |
-10% |
“SOURCE_EXTERNE” |
0.926 |
1.0 |
-20% |
“SOURCE_EXTERNE” |
0.961 |
1.0 |
\(({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m})\)
\({\varepsilon }_{\mathrm{zz}}\) |
|
|
Tolerance (%) |
-1% |
“SOURCE_EXTERNE” |
0.146 |
1.0 |
-2% |
“SOURCE_EXTERNE” |
0.155 |
1.0 |
-5% |
“SOURCE_EXTERNE” |
0.166 |
1.0 |
-10% |
“SOURCE_EXTERNE” |
0.181 |
2.0 |
-20% |
“SOURCE_EXTERNE” |
0.214 |
1.0 |
2.3. Comments#
The comparison between Code_Aster and GEFDYN solutions is particularly good, with generally less than \(1\text{\%}\) errors. Relative errors greater than \(1\text{\%}\) appear for lower levels of tested values.