Granular impact and the critical packing state

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  • DGDaniel I. Goldman
    Daniel I. Goldman
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Abstract
Impact dynamics during collisions of spheres with granular media reveal a pronounced and nontrivial dependence on volume fraction $\phi${}. Postimpact 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.
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