Intrusion rheology in grains and other flowable materials

Abstract

The interaction of intruding objects with deformable materials is a common phenomenon, arising in impact and penetration problems, animal and vehicle locomotion, and various geo-space applications. The dynamics of arbitrary intruders can be simplified using Resistive Force Theory (RFT), an empirical framework originally used for fluids but works surprisingly well, better in fact, in granular materials. That such a simple model describes behavior in dry grains, a complex nonlinear material, has invigorated a search to determine the underlying mechanism of RFT. We have discovered that a straightforward friction-based continuum model generates RFT, establishing a link between RFT and local material behavior. Our theory reproduces experimental RFT data without any parameter fitting and generates RFT's key simplifying assumption: a geometry-independent local force formula. Analysis of the system explains why RFT works better in grains than in viscous fluids, and leads to an analytical criterion to predict RFT's in other materials. IntroductionThe interaction of solid objects with a surrounding, plastically-deforming media is a common aspect of many natural and man-made processes. In the animal world, when organisms undulate, pulse, crawl, burrow, walk, or run on loose terrain they implicitly deform their environment to produce propulsive reaction forces giving rise to their motion (1). The physics of such interactions have been the subject of many studies, from aquatic organisms (2,3) to small insects and lizards (4,5) to humans and other legged-mammals (6,7). Similar principals are used for robotic applications to design machines that run (8), fly (9), swim (10), or walk in fluids or sand (11,12).Such complex interactions are also key to terramechanics of vehicular locomotion on granular substrates, models of excavation in sand and soil (13,14), and the study of similar problems in extraplanetary conditions (15,16). These topics and others, including cratering dynamics and penetration in plastic solids (17,18), all depend crucially on the way local material properties produce global resistive forces on arbitrary intruders.Motivated by past observations in fluids (19), a simple yet very effective empirical tool known as Resistive Force Theory (RFT) for granular materials has been proposed to approximate the forces on intruding objects moving through granular media. Despite the fact that a fundamental derivation is missing, when coupled with the force balance equations, the theory provides a simple and predictive tool for simulating the locomotion of arbitrarily shaped moving bodies in loose terrain (5,20,21). The simplicity of the theory and its predictive effectiveness are surprising in light of the complex, nonlinear, history-dependent, and oftentimes visibly nonlocal constitutive properties of granular media (22)(23)(24)(25)(26). RFT was initially developed to approximate 2 the speed of swimming micro-organisms at low Reynolds numbers (27) by studying the thrust and drag of individually moving elements of its bod...

The role of initial speed in projectile impacts into light granular media

“…In the past decades, the interest has been broadened in connection with crater formation [8][9][10][11] , partly motivated by space exploration 12,13 as well as deciphering the history of planet formation 4 . Moreover, it has been extended to the influence of air cavity collapsing as well as granular jet formation 14 , the projectile shape 11,15,16 and the role of gravity on the final penetration depth and time 17 . As an extreme case, infinite penetration of a projectile into light-weighted EPS (expanded polystyrene) particles was observed, when the weight of the projectile exceeds a critical value 18 .…”

Inertial drag in granular media

“…For vertical uplift loadings, the maximum drag F s is proportional to the vertical hydrostatic normal stress σ h at the object depth: reported values ranging from 1 to 100. Several studies have shown how this parameter varies with the internal friction angle φ of the packing [3,[7][8][9][10][11], the object shape [12][13][14][15][16] and the grain size [17][18][19]. The experimental method used to measure this parameter consists of uplifting the object at a constant and relatively slow velocity and monitoring the drag force during the uplift.…”

From the Lab to the Desert: Fast Prototyping and Learning of Robot Locomotion

“…Unfortunately, the dynamic response of granulate media during locomotion is difficult to predictively simulate or replicate [9,15,1]. In desert environments, this difficulty is compounded by the heterogeneous composition of the loose, sandy topsoil, making it nearly impossible to predict the effectiveness of any locomotor strategy a priori [9,1].…”

“…Unfortunately, the dynamic response of granulate media during locomotion is difficult to predictively simulate or replicate [9,15,1]. In desert environments, this difficulty is compounded by the heterogeneous composition of the loose, sandy topsoil, making it nearly impossible to predict the effectiveness of any locomotor strategy a priori [9,1]. In practice, the performance of robotic systems in heterogeneous granulate media, particularly in xeric habitats, must be evaluated post-hoc and iteratively improved (see for example [15]) through successive design refinements and adaptive learning of locomotion.…”

“…Specifically, adult sea turtles support themselves on the radial edge of the forelimbs to (1) elevate the body (thus reducing or eliminating drag) and (2) generate forward motion [25]. This unique behavior allows these large and exceedingly heavy animals (up to 915 kg in Dermochelys coriacea (Vandelli, 1761) 1 ) to move in a stable and effective manner through granular media [5].…”