This chapter has dealt with the notion of loss of sustainability of an equilibrium state with constant control parameters. It was shown that an equilibrium state was non sustainable if and only if at least one incremental loading direction exists that leads to the vanishing of the macroscopic second-order work defined on the specimen scale. Loss of sustainability corresponds therefore to a proper bifurcation mode. Specifying to granular materials, a micro-macro correspondence relation was derived; this relation expresses the macroscopic second-order work as the sum of all microscopic second-order works extended to all contacts of the assembly. It is worth stressing that this relation is general in the sense that no assumption was required about the constitutive nature of contacts. Moreover, two main origins of the vanishing of the second-order work were identified. A material origin (involving sliding between granules) could concern the weak phase, whereas the strong phase could be associated with a material cause related to the collapse of force chains. These microstructural events could play a fundamental role in the loss of sustainability of an equilibrium state within a granular assembly.