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Archimedes’ law explains penetration of solids into granular media

Author

Listed:
  • Wenting Kang

    (Peking University)

  • Yajie Feng

    (Peking University)

  • Caishan Liu

    (Peking University)

  • Raphael Blumenfeld

    (Imperial College London
    University of Cambridge
    National University of Defence Technology)

Abstract

Understanding the response of granular matter to intrusion of solid objects is key to modelling many aspects of behaviour of granular matter, including plastic flow. Here we report a general model for such a quasistatic process. Using a range of experiments, we first show that the relation between the penetration depth and the force resisting it, transiently nonlinear and then linear, is scalable to a universal form. We show that the gradient of the steady-state part, K ϕ , depends only on the medium’s internal friction angle, ϕ, and that it is nonlinear in μ = tan ϕ, in contrast to an existing conjecture. We further show that the intrusion of any convex solid shape satisfies a modified Archimedes’ law and use this to: relate the zero-depth intercept of the linear part to K ϕ and the intruder’s cross-section; explain the curve’s nonlinear part in terms of the stagnant zone’s development.

Suggested Citation

  • Wenting Kang & Yajie Feng & Caishan Liu & Raphael Blumenfeld, 2018. "Archimedes’ law explains penetration of solids into granular media," Nature Communications, Nature, vol. 9(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:9:y:2018:i:1:d:10.1038_s41467-018-03344-3
    DOI: 10.1038/s41467-018-03344-3
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