Granular Impact: A Grain-scale Approach
  This work summarizes a series of studies on two-dimensional granular impact, where an intruding object strikes a granular material at high speed. Many previous studies on granular impact have used a macroscopic force law, which is dominated by an inertial drag term proportional to the intruder velocity squared. The primary focus here is on the microscopic force response of the granular material, and how the grain-scale effects give rise to this inertial drag term. We show that the inertial drag arises from intermittent collisions with force-chain-like structures. We construct a simple collisional model to explain the inertial drag, as well as off-axis instability and rotations. Finally, we show how the granular response changes when the intruder speed approaches $d/t_c$, leading to a failure of the inertial drag description in this regime. Here, $d$ is the mean particle diameter and $t_c$ the characteristic momentum-transfer time between two grains. 
Abram H. Clark, Alec Petersen, Lou Kondic, Corey O'Hern, Robert P.   Behringer
cond-mat.soft