High speed impact on granular media: breakdown of conventional inertial drag models

In this study, we extensively explore the impact process on granular media, particularly focusing on situations where the ratio of impact speed to acoustic speed is on the order of 0.01-1. This range significantly exceeds that considered in existing literature (0.0001-0.001). Our investigation involves a comprehensive comparison between our simulation data, obtained under high-speed conditions, and the established macroscopic drag models. In the high-speed regime, conventional drag force models prove inadequate, and the drag force cannot be separated into a depth-dependent static pressure and a depth-independent inertial drag, as suggested in previous literature. A detailed examination of the impact process in the high-speed limit is also presented, involving the spatio-temporal evolution of the force chain network, displacement field, and velocity field at the particle length scale. Unlike prior works demonstrating the exponential decay of pulses, we provide direct evidence of acoustic pulses propagating over long distances, reflecting from boundaries, and interfering with the original pulses. These acoustic pulses, in turn, induce large scale reorganization of the force chain network, and the granular medium continuously traverses different jammed states to support the impact load. Reorientation of the force chains leads to plastic dissipation and the eventual dissipation of the impact energy. Furthermore, we study the scaling of the early stage peak forces with the impact velocity and find that spatial dimensionality strongly influences the scaling.