6. Verification and validation

6.1. Test cases

The references of the test cases and associated documentation are given in the following table.

6.2. Examples of answers to the material point

The following three figures show some answers obtained using the executable MTest (answers to the hardware point):

• Isotropic compression test;

• Isotropic tensile test;

• Triaxial compression tests for several confinement stresses.

The model parameters used in these simulations are grouped together in the table below.

Fig. 6.1 Isotropic compression test driven by mean stress \(\sigma_m\). In the load phase, the response is elastic non-linear (\(Ip=0\)) up to \(-\sigma_m=2p_{c0}+\sigma_0=2.01\) MPa, then irreversible (\(Ip=1\)). The work hardening is then positive. The discharge from \(-\sigma_m=10\) MPa to zero is elastic non-linear (\(Ip=0\)).

Fig. 6.2 Isotropic tensile test driven by vertical deformation \(\epsilon_{zz}\). After the elastic load phase, the stress saturates at \(\sigma_m=\sigma_0=10\) kPa, without showing any positive or negative work hardening. It should be noted that the nonlinearity of the elasticity is imperceptible. The expression for constraint expression_contrainte explains it by condition \(\sigma_m\ll K/\kappa\), a situation encountered in this load with the parameters of the simulated model.

Fig. 6.3 Triaxial compression tests with multiple confinement stresses \(-\sigma_{xx}=-\sigma_{yy}\). Equivalent stress \(\sigma_{eq}\) has negative work hardening at the weakest confinements and positive work hardening at the strongest. In parallel, the evolution of volume plastic deformation \(\xi=\mathrm{tr}(\boldsymbol{\epsilon}^p)\) goes from a regime of dilatance (\(\dot{\xi}>0\)) to contraction (\(\dot{\xi}<0\)). It should be noted that the first loading phase at equivalent stress \(\sigma_{eq}=0\) corresponds to confinement with \(-\sigma_{xx}=-\sigma_{yy}=-\sigma_{zz}\).