Power law scaling of early-stage forces during granular impact

TL;DR

This study investigates the early forces during granular impact, revealing power-law scaling laws that depend on impact parameters and challenge existing models, with implications for similar soft materials.

Contribution

It introduces experimental and computational evidence of power-law scaling in early impact forces, contrasting with traditional models and suggesting broader applicability.

Findings

Peak impact force scales with impact velocity and grain properties.

Scaling laws deviate from Poncelet, shock, and added-mass models.

Results are insensitive to system details, applicable to other soft materials.

Abstract

We experimentally and computationally study the early-stage forces during intruder impacts with granular beds in the regime where the impact velocity approaches the granular force propagation speed. Experiments use 2D assemblies of photoelastic disks of varying stiffness, and complimentary discrete-element simulations are performed in 2D and 3D. The peak force during the initial stages of impact and the time at which it occurs depend only on the impact speed, the intruder diameter, the mass density of the grains, and the elastic modulus of the grains according to power-law scaling forms that are not consistent with Poncelet models, granular shock theory, or added-mass models. The insensitivity of our results to many system details suggest that they may also apply to impacts into similar materials like foams and emulsions.