5. C modeling#
5.1. Characteristics of modeling#
C modeling is three-dimensional and static non-linear, (3D).
First, an elastic preconsolidation (\(\mathit{ELAS}\)) of the sample is carried out until \(p=-100\mathit{kPa}\) (1st phase of the calculation). This preconsolidation takes place in \(1\), a time step between \(t=-10\) and \(t=0\). This phase is purely elastic.
The isotropic traction phase, controlled in imposed displacement, up to \({u}_{x}={u}_{y}={u}_{z}=5\mathit{mm}\) (displacement imposed on faces \(\mathit{HAUT}\), \(\mathit{DROIT}\), \(\mathit{ARRIERE}\)) takes place in \(100\) step between \(t=0\) and \(t=5\). The maximum movements imposed correspond to a deformation of \(0.5\text{\%}\). During this second phase, the automatic subdivision of the time step is activated to manage situations of non-convergence of local integration. This phase makes it possible to treat the transition between the monotonic and cyclic isotropic mechanisms and then to follow the mixed work hardening of the cyclic mechanism until reaching a state of stresses close to traction for the material. This test makes it possible to ensure that the perfectly plastic mechanisms controlling the traction of the Hujeux model are activated correctly.
The next phase of isotropic compression up to \({u}_{x}={u}_{y}={u}_{z}=-5\mathit{mm}\) (3rd calculation phase) takes place in \(100\) no time between the moments \(t=5\) and \(t=10\). The automatic subdivision of the time step is again activated to manage the changes from traction mechanisms to isotropic and cyclic/monotonic cyclic mechanisms. The new cyclic consolidation mechanism created follows mixed work hardening, then during the transition to the monotonic mechanism, this one collapses isotropically.
5.2. Tested sizes and results#
The solutions are calculated at point \(C\) and compared to references GEFDYN. They are given in terms of plastic volume deformation.
, of cyclic isotropic work hardening coefficients
and isotropic stress \(p\), and summarized in the following tables:
\({\varepsilon }_{a}\) |
Reference type |
Reference value |
Tolerance (%) |
0.003 |
|
7.43E-3 |
1.0 |
-0.005 |
|
-2.06E-2 |
3.0 |
\({\varepsilon }_{a}\) |
Reference type |
Reference value |
Tolerance (%) |
0.003 |
|
4.00E-2 |
1.0 |
\(({r}_{\mathrm{ela}}^{s}+{r}_{\mathrm{iso}}^{m})\)
\({\varepsilon }_{a}\) |
Reference type |
Reference value |
Tolerance (%) |
0.003 |
|
1.094E-1 |
1.0 |
\(p(\mathit{Pa})\)
\({\varepsilon }_{a}\) |
Reference type |
Reference value |
Tolerance (%) |
0.003 |
|
-2.000 |
1.0 |
-0.005 |
|
-4.482E5 |
2.0 |
5.2.1. Comments#
The difference between the two codes is very small for all the values tested.