Granular impact and the critical packing state

TL;DR

This study investigates how impact forces in granular media depend on volume fraction, revealing a critical packing state where the material's response changes and existing models fail to fully describe the observed dynamics.

Contribution

It identifies the critical packing state ps and demonstrates its significance in impact force behavior, highlighting limitations of current phenomenological models.

Findings

Impact force depends non-trivially on volume fraction .

Near ps, impact force becomes separable into linear and quadratic components.

Force response exhibits a Janssen-type exponential decay with depth, varying with .

Abstract

Impact dynamics during collisions of spheres with granular media reveal a pronounced and non-trivial dependence on volume fraction \phi. Post impact crater morphology identifies the critical packing state \phi_{cps}, where sheared grains neither dilate nor consolidate, and indicates an associated change in spatial response. Current phenomenological models fail to capture the observed impact force for most \phi; only near \phi_{cps} is force separable into additive terms linear in depth and quadratic in velocity. At fixed depth the quadratic drag coefficient decreases (increases) with depth for \phi < \phi_{cps} (\phi > \phi_{cps}). At fixed low velocity, depth dependence of force shows a Janssen-type exponential response with a length scale that decreases with increasing \phi; and is nearly constant for \phi > \phi_{cps}.