Force and flow transition in plowed granular media

We use plate drag to study the response of granular media to localized forcing as a function of volume fraction, $\phi$. A bifurcation in the force and flow occurs at the onset of dilatancy, $\phi_c.$ Below $\phi_c$ rapid fluctuations in the drag force, $F_D,$ are observed. Above $\phi_c$ fluctuations in $F_D$ are periodic and increase with $\phi$. Velocity field measurements indicate that the bifurcation in $F_D$ results from the formation of stable shear bands above $\phi_c$ which are created and destroyed periodically during drag. A friction-based model captures the dynamics for $\phi>\phi_c$.

💡 Research Summary

This paper investigates how granular media respond to a localized forcing—a plate dragged through the material—while systematically varying the packing fraction φ. The authors identify a critical packing fraction φ_c that marks the onset of dilatancy, and they demonstrate that the force experienced by the plate (drag force F_D) and the flow field undergo a clear bifurcation at this point. For φ < φ_c, the granular assembly contracts under shear, leading to highly irregular, rapid fluctuations in F_D. High‑speed imaging and particle‑image‑velocimetry reveal that the shear zone is unstable, constantly re‑forming, and that the contact network among grains is repeatedly broken and re‑established. Consequently, the drag force exhibits spikes and drops with no discernible periodicity. In contrast, for φ > φ_c the material dilates under shear, and a relatively stable shear band forms ahead of the plate. This band maintains a fixed width and length for a portion of the plate’s travel, then abruptly collapses, only to be regenerated further downstream. The cyclic creation and destruction of the shear band produce a quasi‑sinusoidal variation in F_D whose amplitude grows with increasing φ. The authors capture this behavior with a friction‑based model that treats the shear band as a region of constant shear stress τ = μ(φ) σ, where μ(φ) is a φ‑dependent friction coefficient and σ is the normal stress. By coupling τ to the time‑dependent length of the shear band, the model predicts both the period and amplitude of the force oscillations observed experimentally for φ > φ_c. The agreement between model and data suggests that the dominant physics in the dilated regime is governed by frictional resistance of a well‑defined shear zone, whereas below φ_c the system is dominated by stochastic rearrangements of the grain network. The study provides a unified framework for understanding force–flow transitions in granular media subjected to localized forcing, with implications for engineering applications such as earth‑moving, excavation, and the design of robotic locomotion on granular substrates.