4. C modeling#
4.1. Characteristics of modeling#
The modeling is \(\mathrm{3D}\) sub-integrated (3D_ HM_SI) with a hydro-mechanical coupling in non-linear quasistatics.
In loading phase \(1\), the sample is brought to consolidation pressure \({\sigma }_{\mathrm{xx}}^{0}={\sigma }_{\mathrm{yy}}^{0}={\sigma }_{\mathrm{zz}}^{0}={\sigma }_{0}=-50\mathrm{kPa}\). This state of confinement makes it possible to consider the sample as dense sand.
We use Hujeux’s law cyclic.
4.2. Characteristics of the mesh#
Number of knots: \(20\)
Number of meshes and type: 1 \(\mathit{HEXA20}\) and 6 \(\mathit{QUAD8}\).
4.3. Tested sizes and results#
The solutions are calculated at point \(C\) and compared to references GEFDYN. They are given in terms of isotropic pressure, plastic volume deformation \({\varepsilon }_{v}^{p}\) and mobilization factors, and summarized in the following tables:
\(Q\mathrm{=}\sqrt{\frac{1}{2}{\sigma }_{\text{ij}}^{d}\mathrm{:}{\sigma }_{\text{ij}}^{d}}(\mathit{kPa})\)
\({\varepsilon }_{\text{zz}}\) |
Reference type |
GEFDYN (\(\mathit{kPa}\)) |
tolerance (%) |
-1.E-3 |
|
3.154E+1 |
3.0 |
-2.E-3 |
|
4.013E+1 |
2.0 |
-5.E-3 |
|
5.194E+1 |
1.0 |
-1.E-2 |
|
6.829E+1 |
1.0 |
-2.E-2 |
|
1.032E+2 |
1.0 |
\(3\text{.}P\text{'}\mathrm{=}{\sigma }_{\text{ij}}\mathrm{\cdot }{\delta }_{\text{ij}}(\mathit{kPa})\)
\({\varepsilon }_{\text{zz}}\) |
Reference type |
GEFDYN (\(\mathit{kPa}\)) |
tolerance (%) |
-1.E-3 |
|
-1.389E+2 |
1.0 |
-2.E-3 |
|
-1.338E+2 |
1.0 |
-5.E-3 |
|
-1.250E+2 |
1.0 |
-1.E-2 |
|
-1.368E+2 |
1.0 |
-2.E-2 |
|
-1.860E+2 |
1.0 |
\({\varepsilon }_{v}^{p}\mathrm{=}\text{trace}({\varepsilon }^{p})\)
\({\varepsilon }_{\text{zz}}\) |
Reference type |
GEFDYN |
tolerance (%) |
-1.E-3 |
|
-2.42E-5 |
6.0 |
-2.E-3 |
|
-3.55E-5 |
4.0 |
-5.E-3 |
|
-5.56E-5 |
3.0 |
-1.E-2 |
|
-2.88E-5 |
5.0 |
-2.E-2 |
|
7.437E-5 |
5.0 |
\(({r}_{\text{iso}}^{m}+{r}_{\text{ela}}^{s,m})\)
\({\varepsilon }_{\text{zz}}\) |
Reference type |
GEFDYN |
tolerance (%) |
-1.E-3 |
|
0.02 |
1.0 |
-2.E-2 |
|
0.0248 |
1.0 |
\(({r}_{\text{iso}}^{c}+{r}_{\text{ela}}^{s,c})\)
\({\varepsilon }_{\text{zz}}\) |
Reference type |
GEFDYN |
tolerance (%) |
-1.E-3 |
|
1.49E-3 |
2.0 |
-2.E-3 |
|
2.18E-3 |
2.0 |
-5.E-3 |
|
3.36E-3 |
2.0 |
-1.E-2 |
|
1.68E-3 |
3.0 |
\(({r}_{\text{dev}}^{m}+{r}_{\text{ela}}^{d,m})\)
\({\varepsilon }_{\text{zz}}\) |
Reference type |
GEFDYN |
tolerance (%) |
-1.E-3 |
|
0.353 |
3.0 |
-2.E-3 |
|
0.451 |
2.0 |
-5.E-3 |
|
0.593 |
1.0 |
-1.E-2 |
|
0.699 |
1.0 |
-2.E-2 |
|
0.794 |
1.0 |
4.4. notes#
The comparison between Code_Aster and GEFDYN solutions is relatively good, with generally fewer \(1\text{\%}\) errors. Relative errors greater than \(1\text{\%}\) appear for levels of test values that are relatively low and close to the numerical precision applied during the calculation.