Energy processes and phase transition in granular assemblies

Granular assemblies are an illustrative example of complex material where unexpected macroscopic properties may emerge when they are subjected to a given loading. The complexity is the consequence of the huge geometrical disorder governed by particle rearrangements, entailing plastic dissipation at contacts. This local dissipation, associated with the global geometric disorder, is probably a key ingredient responsible for various macroscopic features, such as the strain localization in dense granular assemblies leading to the formation of a shear band. Based on a discrete element method (DEM), this manuscript investigates the energy processes at the microscopic scale in granular assemblies along biaxial loading paths for dense and loose assemblies. The localized shear band domain in a dense specimen is inspected. The analysis of elastic processes suggests a maximum capacity for storing elastic energy, giving rise to a phase transition from a homogeneous state to a heterogeneous one. This phase transition is marked by a significant release of elastic energy associated with plastic dissipation. The elastic-to-plastic energy transfer is shown to be a key ingredient to reach the stationary state regime characterized by a unique dynamic equilibrium. It is signaled by the constant ratios of elastic storage and plastic dissipation over the available energy, whatever the initial density of granular assemblies. Finally, the energy processes inside the shear band domain are shown to be largely dominated by intense plastic dissipation. This suggests that the shear band acts as an optimal dissipative structure in dense specimens where elastic mechanisms continue to be active at a much higher level than they are in the outside shear band domain.