3. B modeling#
3.1. Characteristics of modeling#
B modeling is*tridimensional* and*static nonlinear*.
We first perform an elastic preconsolidation (\(\mathrm{ELAS}\)) of the sample up to \({p}_{c}=100\mathrm{kPa}\) (1st phase of the calculation). This preconsolidation takes place in \(1\), a time step between \(t=-2\) and \(t=0\).
The vertical displacement imposed on the upper facet varies between \(0.\) and \(-0.2\) (2nd phase of the calculation) in \(100\) time steps between \(t=0\) and \(t=10\). During this second phase, the automatic subdivision of the time step is activated to manage situations of non-convergence of local integration. In the integration of equilibrium equations, an update of the tangent matrix is required, which is provided by the routines of Hujeux’s law and significantly accelerates convergence. We also require the subdivision of the time step (command DEFI_LIST_INST) to deal with situations where local integration fails due to excessively large load increments. This feature is highly recommended.
3.2. Tested sizes and results#
3.2.1. Tested values#
The solutions are calculated at point \(C\) and compared to references GEFDYN. They are given in terms of equivalent stress \(Q\), 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:
\(Q=\sqrt{\frac{1}{2}\underline{\underline{s}}\mathrm{:}\underline{\underline{s}}}[\mathit{Pa}]\)
\({\varepsilon }_{\mathit{zz}}\) |
Code_Aster |
GEFDYN |
relative error |
-1% |
|
||
-2% |
|
||
-5% |
|
||
-10% |
|
||
-20% |
|
\({\epsilon }_{V}\mathrm{=}\text{trace}(\epsilon )\)
\({\varepsilon }_{\mathit{zz}}\) |
Code_Aster |
GEFDYN |
relative error |
-1% |
-5.47E-3 |
-5.53E-3 |
|
-2% |
-7.128E-3 |
-7.15E-3 |
|
-5% |
-6.684E-3 |
-6.64E-3 |
|
-10% |
-8.227E-4 |
-8.22E-4 |
|
-20% |
1.261E-2 |
1.25E-2 |
|
\(({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m})\)
\({\varepsilon }_{\mathit{zz}}\) |
Code_Aster |
GEFDYN |
relative error |
-1% |
0.659 |
0.665 |
|
-2% |
0.772 |
0.775 |
|
-5% |
0.882 |
0.883 |
|
-10% |
0.934 |
0.934 |
|
-20% |
0.965 |
0.965 |
|
\(({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m})\)
\({\varepsilon }_{\mathit{zz}}\) |
Code_Aster |
GEFDYN |
relative error |
-1% |
0.0575 |
0.0578 |
|
-2% |
0.0627 |
0.0630 |
|
-5% |
0.0723 |
0.0725 |
|
-10% |
0.0867 |
0.0868 |
|
-20% |
0.169 |
0.117 |
|
3.2.2. Comments#
The relative error is higher when the values tested are lower, which is not an anomalous step. In short, the difference between the two codes is very reasonable.