Archimedes’ law explains penetration of solids into granular media

Wenting Kang, Yajie Feng, Caishan Liu () and Raphael Blumenfeld
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Wenting Kang: Peking University
Yajie Feng: Peking University
Caishan Liu: Peking University
Raphael Blumenfeld: Imperial College London

Nature Communications, 2018, vol. 9, issue 1, 1-9

Abstract: 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.

Date: 2018
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DOI: 10.1038/s41467-018-03344-3

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