Three fundamentally different models: a phenomenological constitutive relation, a micro-mechanical model and direct numerical simulations by DEM are compared in this paper. In addition, the local form of Hill's sufficient condition of stability (i.e., the vanishing of the second order work d2W) is considered to describe material instabilities in granular assemblies. Stress probes in the axisymmetric plane of stress increments are achieved with all three models to check if d2W vanishes at different stress-strain states. For all the models, cones of unstable stress directions (cones of stress probe directions for which d2W = 0) are found and they appear for stress states strictly inside the plastic limit condition. Thus independently of the model, a bifurcation domain exists inside the plastic limit condition which can describe the sudden collapses of sand samples observed in laboratory tests before reaching the Mohr-Coulomb criterion. Taking advantage of the different models considered, the vanishing of the second order work is linked to the existence of non associated plastic strains and to micro-mechanical bases.