3. Modeling A#
3.1. Characteristics of modeling#
Modeling \(A\) is three-dimensional and static, non-linear, 3D.
First, an anelastic preconsolidation (Hujeux) of the sample is carried out until \(p=-300\mathrm{kPa}\) (1st phase of the calculation). This preconsolidation takes place in \(100\), a time step between \(t=-10\) and \(t=0\). This phase uses the monotonic isotropic mechanism of Hujeux’s law.
The isotropic traction phase from \(p=-300\mathrm{kPa}\) to \(p=-100\mathrm{kPa}\) (2nd phase of the calculation) takes place in \(100\) time step 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. 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.
The new isotropic compression phase from \(p=-100\mathrm{kPa}\) to \(p=-340\mathrm{kPa}\) (3rd calculation phase) takes place in \(100\) time step between the times \(t=10\) and \(t=20\). The automatic subdivision of the time step is activated again to manage the passages of cyclic/cyclic and cyclic/monotonic mechanisms. The new cyclic consolidation mechanism created follows mixed work hardening, then during the transition to the monotonic mechanism, this one collapses isotropically.
3.2. 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
and monotonic isotropic work hardening coefficients
and cyclical
, and summarized in the following tables:
(kPa) |
Reference type |
Reference value |
Tolerance (%) |
-200 |
SOURCE_EXTERNE |
-6.78E-3 |
1.0 |
-300 |
SOURCE_EXTERNE |
-1.28E-2 |
1.0 |
-200 |
SOURCE_EXTERNE |
-7.49E-3 |
1.0 |
-100 |
SOURCE_EXTERNE |
-9.15E-4 |
4.0 |
-220 |
SOURCE_EXTERNE |
-8.29E-3 |
1.0 |
-340 |
SOURCE_EXTERNE |
-1.50E-2 |
1.0 |
(kPa) |
Reference type |
Reference value |
Tolerance (%) |
-200 |
SOURCE_EXTERNE |
6.8E-2 |
1.0 |
-300 |
SOURCE_EXTERNE |
8.83E-2 |
1.0 |
-200 |
SOURCE_EXTERNE |
8.83E-2 |
1.0 |
-100 |
SOURCE_EXTERNE |
8.83E-2 |
1.0 |
-220 |
SOURCE_EXTERNE |
8.83E-2 |
1.0 |
-340 |
SOURCE_EXTERNE |
9.48E-2 |
1.0 |
(kPa) |
Reference type |
Reference value |
Tolerance (%) |
-200 |
SOURCE_EXTERNE |
1.E-3 |
1.0 |
-300 |
SOURCE_EXTERNE |
1.E-3 |
1.0 |
-200 |
SOURCE_EXTERNE |
2.14E-2 |
1.0 |
-100 |
SOURCE_EXTERNE |
4.91E-2 |
1.0 |
-220 |
SOURCE_EXTERNE |
3.29E-2 |
1.0 |
-340 |
SOURCE_EXTERNE |
4.91E-2 |
1.0 |
3.3. notes#
The difference between the two codes is very small for all the values tested.