4. C modeling#
4.1. Characteristics of modeling#
C modeling is performed on a hardware point, using SIMU_POINT_MAT.
The axial deformation imposed during the isotropic compression phase is equal to \(-{\mathrm{\sigma }}_{0}/3K\) (axial deformation making it possible to reach \({\mathrm{\sigma }}_{\mathit{zz}}={\mathrm{\sigma }}_{0}\), applied in \(t=1s\)). During the same time interval, lateral constraints change from \({\mathrm{\sigma }}_{\mathit{xx}}={\mathrm{\sigma }}_{\mathit{yy}}=0\) to \({\mathrm{\sigma }}_{\mathit{xx}}={\mathrm{\sigma }}_{\mathit{yy}}={\mathrm{\sigma }}_{0}\). The maximum axial deformation applied during the deviatoric phase is \({\mathrm{ϵ}}_{\mathit{zz}}=-0.03\text{\%}\) (final instant \(t=30s\)). During the deviatoric phase, the lateral stresses are kept constant, equal to \({\mathrm{\sigma }}_{\mathit{xx}}={\mathrm{\sigma }}_{\mathit{yy}}={\mathrm{\sigma }}_{0}\).
4.2. Tested sizes and results#
4.2.1. Tested values#
Five non-regression tests are carried out at the end of the test at \(t=30s\), on:
SIXX — lateral constraint that must be equal to the imposed lockdown, i.e. \({\mathrm{\sigma }}_{0}\);
SIZZ — constraint resulting from the law of behavior;
V7— plastic multiplier (equal to the equivalent plastic deformation of Von-Mises);
V8— plastic volume deformation (\({\mathrm{ϵ}}_{\mathit{kk}}-{\mathrm{ϵ}}_{\mathit{kk}}^{e}\));
V9— dissipation (\(\int {\mathrm{\sigma }}_{\mathit{ij}}\left(\mathrm{\delta }{\mathrm{ϵ}}_{\mathit{ji}}-\mathrm{\delta }{\mathrm{ϵ}}_{\mathit{ji}}^{e}\right)\)).
\(t=30\mathit{sec}\) |
Analytical solution from modeling A |
Calculated solution from modeling C |
SIZZ (Pa) |
\(-173289.5416041\) |
|
SIXX (Pa) |
\(-50000.\) |
|
V8 |
|
|
V7 |
|
|
V9 (Pa) |
\(2.7623234303334216\) |
Table 4.2.1-1: Validation of results for modeling C
It is normal to notice some differences with the analytical solution for components SIZZ, V7, and V8 since the smoothed criterion used by the Mohr-Coulombas law deviates somewhat from the original Mohr-Coulomb criterion.