Unifying Impacts in Granular Matter from Quicksand to Cornstarch

Abstract

A sharp transition between liquefaction and transient solidification is observed during impact on a granular suspension depending on the initial packing fraction. We demonstrate, via high-speed pressure measurements and a two-phase modeling, that this transition is controlled by a coupling between the granular pile dilatancy and the interstitial fluid pressure generated by the impact. Our results provide a generic mechanism for explaining the wide variety of impact responses in particulate media, from dry quicksand in powders to impact-hardening in shear-thickening suspensions like cornstarch.Impacts on particulate media like granular materials and suspensions present an astonishingly rich phenomenology [1, 2]. Along with its astrophysical [3] and ballistics applications [4], impact dynamics is an object of active research to understand the high-speed response of granular matter [5]. In dry granular media, impact by a solid object results in the formation of a corona of granular ejecta and a solid-like plastic deformation leading to a permanent crater [6][7][8][9][10][11]. For fine powders in air, granular jets and cavity collapse occur during impact [12,13]. Subsequent studies showed that the ambient pressure of the interstitial fluid (air) is an important element for the observed fluid-like behavior [14][15][16], while for denser packing the impact penetration is much reduced [17]. However, the question of the physical mechanisms and control parameters that give rise to such a wide variety of phenomena is still largely open. Recently, studies on shearthickening suspensions (cornstarch) showed completely different behaviors. Above a critical velocity, an impacting object immediately stops [18], or in some cases generates cracks [19], as if hitting a solid. This phenomenon has been related to the propagation of dynamic jamming fronts in the bulk [18] but the mechanism remains unclear and overlooks the role of fluid/grains couplings, which are known to strongly affect the transient behavior of saturated granular materials [2,20,21]. Whether impact-activated solidification relies on such couplings or on the complex rheology of the suspension is a pivotal question for clarifying the physics of shear-thickening fluids -a still highly debated topic [23][24][25][26][27].The objective of this Letter is to address these questions and elucidate the role of the interstitial fluid and the initial volume fraction on the diverse impact phenomenology observed in granular materials and dense suspensions during the last decade. To avoid difficulties associated with colloidal interactions between particles (like in shear-thickening suspensions) or fluid compressibility (like in powders in air), we study here the impact of a freely-falling rigid sphere on a simple granular suspension [28] made up of macroscopic, heavy particles (glass beads in the range 0.1-1 mm) immersed in an incompressible liquid (water, viscous oil). The initial packing fraction of the suspension φ 0 (the ratio of the volume of the glass beads to the total v...

Revealing the frictional transition in shear-thickening suspensions

“…By systematically investigating steady avalanches, compaction, and dilatancy effects in rotating drum experiments, we provide direct proof that shear-thickening suspensions have a frictionless state under low confining pressure. Unlike Newtonian suspensions of frictional particles (9,20,28,29), shearthickening suspensions under low stress flow with a very small avalanche angle, do not compact, and show no dilatancy effect. This phenomenology clearly indicates the absence of friction between particles (23).…”

“…It then slowly flows, relaxing to θs . Such a drastic change in the avalanche dynamics with the packing of the initial sediment relies on a well-known pore pressure feedback mechanism (27)(28)(29), which applies only for dilatant (i.e., frictional) systems (23). As first described by Reynolds (30), deformation of a dense granular packing of frictional grains requires its dilation.…”

On the kinematics and dynamics of crystal‐rich systems

“…A corollary to the rapid onset of frictional behavior as a function of the applied stress is the observation that hydrogranular materials can undergo progressive mechanical "solidification," upon impact [Jerome et al, 2016;Peters et al, 2016;Waitukaitis and Jaeger, 2012], a condition that occurs under extension as well [Majumdar et al, 2017]. Although pore pressure excursions associated with either dilation or compression upon impact (particle volume increase or decrease) mediate the onset of the boundary-lubrication frictional regime [Jerome et al, 2016], the occurrence of a jamming front that propagates away from the point of impact is well documented. This process may explain the observation that a crystal-bearing magma can temporarily manifest elastic-like behavior, for example, by supporting the injection by a dike with rather sharp boundaries, which as the dike progresses into the interior of the magma body where there is a deceasing crystal fraction, breaks up into a fountain-like feature.…”

The Soft-Landing Problem: Minimizing Energy Loss by a Legged Robot Impacting Yielding Terrain

“…Granular media (collections of discrete particles that interact only through repulsion and friction [17]) are a common material which can be used as a versatile proxy for naturally-occuring soft substrates by tuning their packing density and fluidizing with air [18], [19]. Even with the relative simplicity of a homogeneous granular bed, the resulting GRFs are not trivial, and various models have been proposed to account for their dependence on intruder kinematics (i.e., intrusion depth and speed) and particle packing density (see, e.g., [20], [21], [18], [22]). For the simplest case of quasi-static vertical intrusion, the GRF increases linearly with penetration depth due to the increase in the frictional force between particles with increasing lithostatic pressure.…”

“…The GRF in granular materials is also velocity dependent, with various models having been proposed depending on the packing density [20], the packing density and interstitial fluid [22], and accreted material beneath the foot leading to an "added-mass" effect [1]. However, at low impact velocities typical of legged locomotion, the work done by the velocitydependent GRF term is small relative to the work done by the depth-dependent term.…”