Scaling and dynamics of sphere and disk impact into granular media

TL;DR

This study investigates the impact dynamics of spheres and disks into granular media, revealing power law scalings, complex force behaviors, and proposing a new force model based on experimental data.

Contribution

It introduces a new experimentally based granular force model that captures detailed impact dynamics and acceleration fluctuations.

Findings

Penetration depth scales linearly with impact velocity.

Collision duration remains constant at high impact velocities.

Acceleration exhibits two distinct jumps during impact.

Abstract

Direct measurements of the acceleration of spheres and disks impacting granular media reveal simple power law scalings along with complex dynamics which bear the signatures of both fluid and solid behavior. The penetration depth scales linearly with impact velocity while the collision duration is constant for sufficiently large impact velocity. Both quantities exhibit power law dependence on sphere diameter and density, and gravitational acceleration. The acceleration during impact is characterized by two jumps: a rapid, velocity dependent increase upon initial contact and a similarly sharp, depth dependent decrease as the impacting object comes to rest. Examining the measured forces on the sphere in the vicinity of these features leads to a new experimentally based granular force model for collision. We discuss our findings in the context of recently proposed phenomenological models that capture qualitative dynamical features of impact but fail both quantitatively and in their inability to capture significant acceleration fluctuations that occur during penetration and which depend on the impacted material.