RESUMO
We examine numerically the yielding or failure of small granular packings subjected to an increasing deviatoric stress. As the load increases, the packing softens and the number of sliding contacts rises. When the packing fails, the kinetic energy starts to rise exponentially in time. It is always possible to identify a contact status change that triggers the collapse of the packing. Furthermore, by use of the stiffness matrix, we show that this change often causes a mechanical instability or a motion with neutral stability. In some cases, the status change provokes an oscillation and a second status change following shortly thereafter introduces an instability. Failure can also be considered from the perspective of energy flux: before failure, the energy injected by the load is stored as potential energy in the contacts. When this is no longer possible, failure occurs and the injected energy is converted to kinetic energy. However, the force disequilibrium then soon becomes the dominant energy source.
RESUMO
Quasirigidity means that one builds a theory for assemblies of grains under a slowly changing external load by using the deformation of those grains as a small parameter. Is quasirigidity a complete theory for these granular assemblies? Does it provide unique predictions of the assembly's behavior, or must some other process be invoked to decide between several possibilities? We provide evidence that quasirigidity is a complete theory by showing that two possible sources of indeterminacy do not exist for the case of disk-shaped grains. One possible source of indeterminacy arises from zero-frequency modes present in the packing. This problem can be solved by considering the conditions required to obtain force equilibrium. A second possible source of indeterminacy is the necessity to choose the status (sliding or nonsliding) at each contact. We show that only one choice is permitted, if contacts slide only when required by Coulomb friction.