Nonlinear Force Propagation during Granular Impact

TL;DR

This study investigates how nonlinear forces propagate through granular materials during impact, revealing a dependence on a key dimensionless parameter and showing a transition from chain-like to dense force transmission as impact conditions change.

Contribution

The paper introduces a new experimental framework to analyze nonlinear force propagation in granular impact, linking force response characteristics to a dimensionless parameter $M'$ and identifying a transition in propagation regimes.

Findings

Force propagation speed scales with $d/t_c$ when $M' o 0$

Force response becomes dense and collective at larger $M'$

Transition from chain-like to dense force transmission regimes

Abstract

We experimentally study nonlinear force propagation into granular material during impact from an intruder, and we explain our observations in terms of the nonlinear grain-scale force relation. Using high-speed video and photoelastic particles, we determine the speed and spatial structure of the force response just after impact. We show that these quantities depend on a dimensionless parameter, $M'=t_c v_0/d$, where $v_0$ is the intruder speed at impact, $d$ is the particle diameter, and $t_c$ is the collision time for a pair of grains impacting at relative speed $v_0$. The experiments access a large range of $M'$ by using particles of three different materials. When $M' \ll 1$, force propagation is chain-like with a speed, $v_f$, satisfying $v_f \propto d/t_c$. For larger $M'$, the force response becomes spatially dense and the force propagation speed departs from $v_f\propto d/t_c$, corresponding to collective stiffening of a strongly compressed packing of grains.