It is now well established that for non-associated materials such as geomaterials, a broad domain exists, strictly within the plastic limit, where different failure modes can coexist. In particular, material instability as defined by Hill, related to the vanishing of the second-order work, can potentially occur. In this paper, the notion of loss of sustainability of a mechanical state in a granular assembly is investigated. The vanishing of the second-order work, defined on the macroscopic scale from tensorial variables, is shown to play a fundamental role in detecting the occurrence of this type of bifurcation. Then, we enlarge the debate by addressing this question from a micro-mechanical point of view. By considering that each contact between ad-joining particles can be regarded as the fundamental constitutive unit of a grain assembly, the standard macro-scopic second-order work defined from tensorial variables was established to coincide with the sum of the mi-croscopic discrete second-order works defined on each contact with respect to a suitable frame. The microscopic second-order work can be computed at each contact as the scalar product of the incremental rela-tive displacement with the incremental contact force between the two adjoining particles in contact. This equivalence of both formulations is of great interest because the microscopic formulation, implying local vari-ables, can give rise to a micro-mechanical interpretation of the vanishing of the second-order work in granular materials.