Archimedes’ law explains penetration of solids into granular media

Kang, Wenting; Feng, Yajie; Liu, Caishan; Blumenfeld, Raphaël

doi:10.1038/s41467-018-03344-3

Cited by 93 publications

(134 citation statements)

References 41 publications

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“…Further from the intruder we see a backwardbending region of deformation, in line with characteristic paths drawn in Ref. [52]. The extent of this region is substantially smaller for monomers, Fig.…”

Section: Deviatoric Strain Rate and Stagnant Zonesupporting

confidence: 88%

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Stagnant zone formation in a 2D bed of circular and elongated grains under penetration

2019

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When a large blunt object penetrates into a granular material, the force response exhibits an initial nonlinear relationship with depth that is widely attributed to the formation of a shear jammed stagnant zone. We present an experimental study of a model 2D granular system that preserves common aspects of slow granular penetration, such as a linear force law for large depths, while also allowing for direct and precise measurement of a stagnant zone. We also probe structural anisotropies throughout the bed and examine their characteristics inside and outside the stagnant zone. Finally, we simultaneously consider effects of concave elongated particle shapes (dimers) and find that while most results are not affected, the relationship between local structure and strain suggests a distinct fragility in the stagnant zone.

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Section: Deviatoric Strain Rate and Stagnant Zonesupporting

confidence: 88%

“…The theoretical model presented in Ref. [52] relates this fan angle to the friction angle by means of a Mohr-Coulomb construction. A 90 • fan angle in the stagnant zone would indicate grains with zero friction coefficient.…”

Section: Deviatoric Strain Rate and Stagnant Zonementioning

confidence: 99%

Stagnant zone formation in a 2D bed of circular and elongated grains under penetration

2019

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“…In our experiments corresponding to the vertical penetration of thin rods (L/D 1) we see a linear regime in the experimental range 10 0 z/D 10 1 followed by a supralinear (quadratic regime) in the experimental range 10 1 z/D 10 2 . Note that in the recent experiments of [25] corresponding to the vertical penetration of very thick "rods" (L/D ∼ 1) a first sublinear regime at very low penetration depth is observed, in the range 10 −2 z/d 10 −1 , followed by a linear regime at larger depth, in the range 10 −1 z/d 10 0 . The first sublinear regime, which corresponds to the transient growing of a conical static zone of grains at the bottom tip of the rod [25], is too small to be observed in the present experiments with very thin rods.…”

Section: Modelingmentioning

confidence: 81%

“…The container was chosen large enough to avoid any possible wall effect. In particular, the container-to-rod diameter ratio is in the range 13 < /D < 40, which is high enough for glass beads to avoid any sidewall effects [24,25]. The container was chosen also deep enough to avoid any bottom wall effect [24] with 40 < H/D < 400.…”

Section: Methodsmentioning

confidence: 99%

“…In the case of very large rod-to-grain size ratio (D/d 1), where the granular packing acts as a continuum medium on the rod, Ref. [25] shows that C 1 depends nonlinearly on the internal friction coefficient of the granular packing due to curved stress lines originating from a steady conical static zone at the bottom of the rod and developing through the Mohr-Coulomb slip criterion [18]. The C 1 values found by [25] for large rod-to-grain size ratio (D/d > 10) are between 14 and 32 for glass beads of internal friction angles ranging from 22 • to 28 • .…”

Section: Modelingmentioning

confidence: 99%

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Buckling of a rod penetrating into granular media

Seguin

Gondret

2018

Phys. Rev. E

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We investigate experimentally the possible buckling of a thin rod when penetrating downwards into a granular packing. When its bottom end reaches a specific depth, the rod may start buckling provided that the embrace is not enough to stop that phenomenon. The critical rod depth z_{c} at buckling is observed to scale with the rod length L either as 1/L or 1/L^{2}. These two scalings are shown to arise from the two resistant force terms that come into play during the rod penetration: a pressure force at the bottom of the rod that increases linearly with depth and a frictional force on the rod side that increases quadratically with depth. At the buckling point, the destabilizing force corresponds to the expected value given from conventional Euler's critical load for a rod bottom end considered as fixed in the granular clutch. Finally, we draw a buckling-nonbuckling phase diagram in a parameter space given by the rod aspect ratio and a rod-to-grain stress ratio.

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Programmable Granular Metamaterials for Reusable Energy Absorption

Zhao

Jin

2019

Adv Funct Materials

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Designing metamaterials with programmable features has emerged as a promising pathway for reusable energy absorption. While the current designs of reusable energy absorbers mainly exploit mechanical instability of flexible beams, here is created a new kind of metamaterial for reusable and programmable energy absorption by integrating rigid granular materials and compliant stretchable components. In each unit cell of the metamaterial, the stretchable components connect the granular particles to maintain the integrity and control the deformation pattern of the material. When the metamaterial is subjected to an external load, the input energy is partially trapped as elastic energy in the stretchable components, and partially dissipated by friction between the granular particles, forming hysteresis between the loading and unloading force-displacement curves. Through tuning the structural design of the metamaterial, the pretension and stiffness of the stretchable components, and the size of and friction between the particles, a vast design space is achieved to program the mechanical behavior of the metamaterial, such as the load-displacement curve, the multistability, and the amount of energy dissipation. Experimental impact tests on a thin glass panel confirm energy-absorbing capability of the proposed metamaterial. This design strategy opens a new avenue for creating reusable energy-absorbing metamaterials.The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.201901258. and a long working distance. Most commercial energy-absorbing products adopt plastic deformation or fragmentation of foams, [3] metals, [4] and ceramics, [5] to gain the desired hysteresis behavior, and introduce artificial defects, such as prefolding of origami, [6][7][8] to control the deformation mode. In the products with plastic deformation or fragmentation, dislocations and bond breakage occur at the molecule level, and a large amount of energy can be absorbed. However, they are only for one-time usage, since the materials are permanently damaged.In order to overcome the shortcoming of one-time usage, reusable energyabsorbing materials have been proposed by developing damage-tolerant micro [9] or nano lattices, [5] architectured composite materials, [10,11] and mechanical metamaterials. [12][13][14][15] Mechanical metamaterials are materials with microstructures, which give rise to unique mechanical properties that are otherwise hard to achieve. [12][13][14] By designing the microstructures, researchers have developed energy-absorbing metamaterials mainly through exploiting mechanical instability of the deformable microstructures. [16][17][18][19][20] A well-utilized strategy to achieve reusability is making use of bistability of curved beams and tilted straight beams under buckling, [21][22][23] since during the working process, deformation of these constituent structures is elastic. Although the energyabsorbing capability of these metamaterials is currently not comparable to those...

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Archimedes’ law explains penetration of solids into granular media

Cited by 93 publications

References 41 publications

Stagnant zone formation in a 2D bed of circular and elongated grains under penetration

Stagnant zone formation in a 2D bed of circular and elongated grains under penetration

Buckling of a rod penetrating into granular media

Programmable Granular Metamaterials for Reusable Energy Absorption

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