Letter | Published:

Unified force law for granular impact cratering

Nature Physics volume 3, pages 420423 (2007) | Download Citation

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Abstract

Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events1,2,3,4,5 and to probe the unusual nature of the granular state of matter6,7,8,9,10. Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed6; linear in speed7; constant, proportional to the initial impact speed8; and proportional to depth9,10. This is reminiscent of high-speed ballistics impact in the nineteenth and twentieth centuries, when a plethora of empirical rules were proposed11,12. To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 μs precision. For a 1-inch-diameter steel sphere dropped from a wide range of heights into non-cohesive glass beads, we reproduce previous observations6,7,8,9,10 either as reasonable approximations or as limiting behaviours. Furthermore, we demonstrate that the interaction between the projectile and the medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. Thus, we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, although fundamentally different from that of liquids and solids, can be simply understood.

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Acknowledgements

This work was supported by the National Science Foundation (D.J.D.) and the Japan Society for the Promotion of Science Postdoctoral Fellowships for Research Abroad (H.K.).

Author information

Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA

    • Hiroaki Katsuragi
    •  & Douglas J. Durian
  2. Permanent address: Department of Applied Science for Electronics and Materials, Kyushu University, Kasuga, Fukuoka 816-8580, Japan

    • Hiroaki Katsuragi

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Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Hiroaki Katsuragi or Douglas J. Durian.

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https://doi.org/10.1038/nphys583

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