2. Modeling A#
2.1. Characteristics of modeling#
The modeling is two-dimensional with plane deformations D_ PLAN and static non-linear.
The horizontal displacement imposed on the upper facet varies between \(0\) and \(-1\mathit{mm}\) in \(100\) 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.
2.2. Tested sizes and results#
The solutions are calculated at point \(C\) for orthotropic material and compared to code_aster modeling with isotropic material. They are given in terms of stress \({\mathrm{\sigma }}_{\mathit{xy}}\), total volume deformation \({\mathrm{\epsilon }}_{v}\) and isotropic work-hardening coefficients \(\left({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m}\right)\) and deviatory \(\left({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m}\right)\), and summarized in the following tables:
\({\mathrm{\sigma }}_{\mathit{xy}}(\mathit{kPa})\)
\(t\) |
|
|
Tolerance (%) |
10.0 |
“AUTRE_ASTER” |
-9.905E+03 |
0.1 |
\({\mathrm{\epsilon }}_{V}=\text{trace}\left(\mathrm{\epsilon }\right)\)
\(t\) |
|
|
Tolerance (%) |
10.0 |
“AUTRE_ASTER” |
-6.604E-05 |
0.1 |
\(\left({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m}\right)\) (Map \(\mathit{YZ}\))
\(t\) |
|
|
Tolerance (%) |
10.0 |
“AUTRE_ASTER” |
1.69732E-02 |
0.1 |
\(\left({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m}\right)\) (Map \(\mathit{XY}\))
\(t\) |
|
|
Tolerance (%) |
10.0 |
“AUTRE_ASTER” |
1.43123E-01 |
0.1 |
\(\left({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m}\right)\)
\(t\) |
|
|
Tolerance (%) |
10.0 |
“AUTRE_ASTER” |
1.00107E-01 |
0.1 |