Quasirigidity: Some uniqueness issues
Sean C. McNamara, Hans Jürgen Herrmann · Physical Review E · 2006
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.