Yielding in granular materials: from riverbeds to renormalization group

Granular media, like many other amorphous materials, possess a yield stress. The nature of yielding in granular materials is relevant to many industrial and geophysical problems, such as the onset of sediment motion in riverbeds or near-shore environments. When the applied shear stress Σ is below the yield stress Σ_c, grains move temporarily, but only until finding a mechanically stable (MS) configuration that is able to resist the applied shear stress. When Σ > Σ_c, the material is no longer able to find MS configurations. However, the geometrical reasons why MS states vanish at the yield stress is not well understood. In this talk, I will show evidence from molecular dynamics simulations, both in a riverbed-like geometry as well as simple shear, that yielding in granular materials is akin to a second-order critical point, where the behavior near the yield stress is dominated by a correlation length ξ that diverges at the yield stress as ξ ∼ |Σ - Σ_c|^-ν. MS states exist above the yield stress for finite systems, but they vanish as the system size becomes large according to a critical scaling function. The packing fraction and coordination number for MS states are independent of the applied shear stress, implying that the critical behavior we observe is distinct from the jamming scenario. Additionally, the critical behavior persists for overcompressed systems, confirming that jamming and yielding are distinct. Instead, we observe that MS states at nonzero shear stress possess anisotropic force and contact networks, suggesting that the yield stress is set by the maximum anisotropy that can be realized in the large-system limit.