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Much of the Earth and many surfaces of extraterrestrial bodies are composed of non-cohesive particulate matter. Locomoting on such granular terrain is challenging for common robotic devices, either wheeled or legged. In this work, we discover a robust alternative locomotion mechanism on granular media-generating movement via self-vibration. To demonstrate the effectiveness of this locomotion mechanism, we develop a cube-shaped robot with an embedded vibratory motor and conduct systematic experiments on granular terrains of various particle properties and slopes. We investigate how locomotion changes as a function of vibration frequency/intensity on such granular terrains. Compared to hard surfaces, we find such a vibratory locomotion mechanism enables the robot to move faster, and more stably on granular surfaces, facilitated by the interaction between the body and surrounding grains. We develop a numerical simulation of a vibrating single cube on granular media, enabling us to justify our hypothesis that the cube achieves locomotion through the oscillations excited at a distance from the cube's center of mass. The simplicity in structural design and controls of this robotic system indicates that vibratory locomotion can be a valuable alternative way to produce robust locomotion on granular terrains. We further demonstrate that such cube-shaped robots can be used as modular units for vibratory robots with capabilities of maneuverable forward and turning motions, showing potential practical scenarios for robotic systems. [ABSTRACT FROM AUTHOR]

For terrestrial locomotion of animals and machines, physical characteristics of the substrate can strongly impact kinematics and performance. Snakes are an especially interesting system for studying substrate effects because their gait depends more on the environment than on their speed. We tested sidewinder rattlesnakes (Crotalus cerastes) on two surfaces: sand collected from their natural environment and vinyl tile flooring, an artificial surface often used to elicit sidewinding in laboratory settings. Of ten kinematic variables examined, two differed significantly between the substrates: the bodys waveform had an average of ∼17% longer wavelength on vinyl flooring (measured in body lengths), and snakes lifted their bodies an average of ∼40% higher on sand (measured in body lengths). Sidewinding may also differ among substrates in ways we did not measure (e.g. ground reaction forces and energetics), leaving open clear directions for future study.

This study presents a method for the inverse analysis of fluid flow problems. The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media, such as permeability, and fluid components, like viscosity. The primary aim is to deduce either constant pressure head or pressure profiles, given the known velocity field at a steady-state flow through a conduit containing obstacles, including walls, spheres, and grains. The lattice Boltzmann method (LBM) combined with automatic differentiation (AD) (AD-LBM) is employed, with the help of the GPU-capable Taichi programming language. A lightweight tape is used to generate gradients for the entire LBM simulation, enabling end-to-end backpropagation. Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media, leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity. The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency, making it a powerful tool for solving inverse fluid flow problems in various applications.

Biologically induced reactions in granular media (geomaterials) often rely on precipitates from enzymes or microbes to promote the formation of mineral precipitate crystals in its pores. However, there is a major knowledge gap in understanding the hypotheses behind the mechanisms of how, where, and when these biomineralization reactions influence the microbial or enzymatic precipitate growth in heterogeneous granular media, and its impact on its material properties at the pore scale. In this regard, we propose to identify the complex spatio-temporal mechanisms controlling enzymatic (EP) and microbial (MP) precipitates, the temporal distribution patterns (arrays) in heterogeneous granular media (rocks), and quantify the resultant alterations in its nanomechanical signatures due to enzymatic- or microbial-induced reactions. The rock material specimens were incubated with enzymes and microbial species followed by quantitatively analyzing their modified nanomechanical properties (Young's modulus, E; fracture toughness, KIC; hardness, H) and pore volume in addition to characterizing the nano-to-micro-structure. Analysis of the results reveals that bio-precipitates can occlude the nano-and-micro-pores in specimens with reduced pore volume (MP:12.4 %; EP:48.8 %), thereby yielding beneficial nanomechanical alterations (MP: +21.2 % H, +16 % E, +41.3 % KIC; EP: +38.5 % H, +17 % E, +22.2 % KIC) depending on distinct conditions of the bio-precipitated reactions. Looking forward, this work provides a blueprint for the rational design of inherently-heterogeneous granular media with further enhanced biomimicry toward more innovative and environmentally friendly solutions in natural and built infrastructure.

Origami folding is an ancient art which holds promise for creating compliant and adaptable mechanisms, but has yet to be extensively studied for granular environments. At the same time, biological systems exploit anisotropic body forces for locomotion, such as the frictional anisotropy of a snake's skin. In this work, we explore how foldable origami feet can be used to passively induce anisotropic force response in granular media, through varying their resistive plane. We present a reciprocating burrower which transfers pure symmetric linear motion into directed burrowing motion using a pair of deployable origami feet on either end. We also present an application of the reduced order model granular Resistive Force Theory to inform the design of deformable structures, and compare results with those from experiments and Discrete Element Method simulations. Through a single actuator, and without the use of advanced controllers or sensors, these origami feet enable burrowing locomotion. In this paper, we achieve burrowing translation ratios-net forward motion to overall linear actuation-over 46% by changing foot design without altering overall foot size. Specifically, anisotropic folding foot parameters should be tuned for optimal performance given a linear actuator's stroke length.

Ultrafast X-ray computed tomography is an advanced imaging technique for multiphase flows. It has been used with great success for studying gas–liquid as well as gas–solid flows. Here, we apply this technique to analyze density-driven particle segregation in a rotating drum as an exemplary use case for analyzing industrial particle mixing systems. As glass particles are used as the denser of two granular species to be mixed, beam hardening artefacts occur and hamper the data analysis. In the general case of a distribution of arbitrary materials, the inverse problem of image reconstruction with energy-dependent attenuation is often ill-posed. Consequently, commonly known beam hardening correction algorithms are often quite complex. In our case, however, the number of materials is limited. We therefore propose a correction algorithm simplified by taking advantage of the known material properties, and demonstrate its ability to improve image quality and subsequent analyses significantly. [ABSTRACT FROM AUTHOR]

Here we demonstrate the use of magnetic resonance imaging for monitoring a laser-polarized xenon ( 129 Xe) gas working as a fluidizing phase for a glass bead pack, inside a straight circular tube, simulating a granular gas-fluidized bed. The imaging method enabled encoding spatially resolved velocity and diffusion 2D-axial maps of the gas vertical upflow at variable flow regimes. From these maps one could identify gas flow transitions, hysteresis loops, regions of stagnation, and reversed flow, all of which associated, as well as complementary, to reported flow dynamics probing the particles inside the bed. In particular, we focused on the initial stage of bubbling where quantitative data on gas flow spatial maps and their potential correlation with the granular particles dynamics are scarce. [ABSTRACT FROM AUTHOR]

The effective thermal characteristics of composite materials used in the theory of solid-state cooling are studied. Two classes of composites are considered: layered structures consisting of a large number of nano-sized layers and two-phase granular composites. It is assumed that the interfaces between media are imperfect. The Kapitza temperature jump occurs at the interfaces. The effective characteristics of layered structures are obtained using the matrix homogenization method. The homogenization of the characteristics of granular composites is based on the Bruggeman approach. Formulas taking into account the influence of the interlayer Kapitza resistance on the homogenized thermal characteristics of the structure are obtained. Expressions for average values of heat sources are derived. [ABSTRACT FROM AUTHOR]

Granular media constitute the most abundant form of solid matter on Earth and beyond. When external forces are applied to a granular medium, the forces are transmitted through it via chains of contacts among grains-force chains. Understanding the spatial structure and temporal evolution of force chains constitutes a fundamental goal of granular mechanics. Here, we introduce an experimental technique, interference optical projection tomography, to study force chains in threedimensional (3D) granular packs under triaxial shear loads and illustrate the technique with random assemblies of spheres and icosahedra. We find that, in response to an increasing vertical load, the pack of spheres forms intensifying vertical force chains, while the pack of icosahedra forms more interconnected force-chain networks. This provides microscopic insights into why particles with more angularity are more resistant to shear failure-the interconnected force-chain network is stronger (that is, more resilient to topological collapse) than the isolated force chains in round particles. The longer force chains with less branching in the pack of round particles are more likely to buckle, which leads to the macroscopic failure of the pack. This work paves the way for understanding the grain-scale underpinning of localized failure of 3D granular media, such as shear localization in landslides and stick-slip frictional motion in tectonic and induced earthquakes. [ABSTRACT FROM AUTHOR]

In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, we explore the maximum entropy states that are realized as resonant modes. For both circular and polygonal Chladni plates, a model is presented that successfully recreates the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive ability. [ABSTRACT FROM AUTHOR]

Pipe structures are commonly encountered in the geophysical context, and in particular in sedimentary basins, where they are associated with fluid migration structures. We investigate pipe formation through laboratory experiments by injecting water locally at a constant flow rate at the base of water-saturated sands in a Hele–Shaw cell (30 cm high, 35 cm wide, gap 2.3 mm). The originality of this work is to quantify the effect of a discontinuity. More precisely, bilayered structures are considered, where a layer of fine grains overlaps a layer of coarser grains. Different invasion structures are reported, with fluidization of the bilayered sediment over its whole height or over the finer grains only. The height and area of the region affected by the fluidization display a non-monotonous evolution, which can be interpreted in terms of fluid focusing vs. scattering. Theoretical considerations can predict the critical coarse grains height for the invasion pattern transition, as well as the maximum topography at the sediment free surface in the regime in which only the overlapping finer grains fluidize. These results have crucial geophysical implications, as they demonstrate that invasion patterns and pipe formation dynamics may control the fluid expulsion extent and localization at the seafloor. [ABSTRACT FROM AUTHOR]

Generating efficient locomotion in granular media is important, although it is difficult for robots. Inspired by the fact that sand vipers usually have saw-like scales, in this study, we design a soft undulation robot with tangential anisotropic friction to enhance the undulation performance of soft robots in granular media. A mathematical model was derived and numerical simulations were conducted accordingly to investigate the effectiveness of tangential friction anisotropy for undulation gait generation in granular media. In particular, we introduce a pseudo-rigid-body dynamics model consisting of links and joints while simulating the pneumatic actuation method to more closely approximate the response of soft robots. Moreover, a soft snake-like robot was fabricated, and its forward and reverse undulations were compared in two sets of controlled experiments. The consistency between the experimental results and the numerical simulations confirms that tangential anisotropic friction induces a propulsive effect in undulation, thereby increasing the robot’s locomotion speed. This discovery provides new insights into the design of undulation robots in granular environments.

Experimental and computational data are presented for Areolas da Estefania, a geomaterial which is crucial for the development of the underground infrastructure of the city of Lisbon, Portugal. The experimental data comprise the particle size distribution of the material and measurements obtained during a series of strain-controlled triaxial compression tests performed on intact samples. The behaviour of this material at a wide range of strains, under constant mean effective stress levels of 130 kPa, 300 kPa and 400 kPa is established, with the presented dataset containing information on stress (mean effective stress and deviatoric stress) and strain states (axial strain and volumetric strain). These are complemented by the results of bender element tests imposing vertically-travelling waves for characterisation at very small strains. Complementarily, the computational dataset establishes a reference reproduction of the response of Areolas da Estefania using a material model which combines a non-linear small stiffness formulation with a state-dependent strength and plastic dilatancy. Overall, this dataset can be used as a reference when assessing the behaviour of other samples of Areolas da Estefania or comparable materials, or when evaluating constitutive models for granular geomaterials.

Using linear elasticity theory, we describe the mechanical response of dry non-cohesive granular masses of Ottawa sand contained by spherical rubber balloons subject to sudden bursting in the earliest instants of the event. Due to the compression imposed by the balloon, the rupture produces a fast radial expansion of the sand front that depends on the initial radius R 0 , the initial pressure p originated by the balloon, and the effective modulus of compression K e . The hydrostatic compression approximation allows for the theoretical study of this problem. We found a linear decompression wave that travels into the sand and that induces a radial expansion of the granular front in the opposite direction with similar behavior to the wave but with a slightly lower speed. [ABSTRACT FROM AUTHOR]

This review focuses on how the modeling of dense granular media has advanced over the last 15 years. The jumping-off point of our review is the μ(I) rheology for dry granular flow, which opened the door to generic flow field modeling but was primarily geared toward problems involving small monodisperse grains of simple shapes. Our review focuses on advances in modeling more material types and behaviors including new approaches for modeling finite-grain-size effects or nonlocality, polydispersity and unmixing, and nontrivial grain shapes. We also discuss growing application areas with tractable order-reduction strategies with a focus on intrusion and locomotion problems. [ABSTRACT FROM AUTHOR]

One novel method for disinfecting water is the use of silver nanoparticles. The aim of this work was to prepare a granular antibacterial composite based on chitosan boehmite, enhanced with silver nanoparticles (Ag-CHB), and evaluate its antibacterial activity. The composite was prepared by the sol-gel method and characterized by FTIR, AFM, FESEM, EDS, and UV-VIS techniques. The topographical study using the AFM revealed a clear change in the surface shape of the composite after it was reinforced with silver nanoparticles. Additionally, FESEM images displayed that the particles of chitosan-boehmite supported with silver nanoparticles are polygonal granules with an average size of 61.93 nm. The EDX analysis showed that the percentage of silver atoms in the composite is about 1.24 wt%. The results of FTIR indicated that chitosan's functional groups have specific interactions with silver and aluminum. According to XRD analysis, boehmite nanocrystals are orthorhombic, with a mean crystal size of 30 nm was confirmed. Optical characterization of the colloidal silver nanoparticles by UV-VIS technique revealed the presence of a clear surface plasmon band, with a peak wavelength of 389 nm. The stability in the water of the prepared composite was verified by the swelling test, and the swelling index was about 11.82%. The ability of the composite to kill bacteria was also verified before and after being reinforced with silver nanoparticles by the agar well diffusion method. The composite reinforced with silver nanoparticles showed antibacterial activity against E. coli, with a 10 mm inhibition zone diameter. Overall, these results indicated that the Ag-CHB composite has the potential for water disinfection and incorporation into household filtration systems. Highlights: Chitosan-boehmite, enhanced with silver nanoparticles, is synthesized by the sol-gel method. The successful formation of the composite was corroborated through several techniques. The composite exhibits full stability in water and demonstrates antibacterial properties. Chitosan-boehmite enhanced with silver nanoparticles granules, can be used in multimedia household filters. [ABSTRACT FROM AUTHOR]

We present EMBUR-EMerita BUrrowing Robot-the first legged robot inspired by the Pacific mole crab, Emerita analoga, capable of burrowing vertically downward. We choose Emerita analoga as a model organism for its rapid downward burrowing behaviors, as it is four times as fast as the most rapid bivalve mollusk. Vertical burrowing in granular media is a challenging endeavor due to the tendency for the media to create upwards resistive forces on an intruder, even during purely horizontal motions. Our robot is capable of vertically burrowing its body in granular substrate primarily through excavation using two leg pairs, which are functionally analogous to groupings of leg pairs of the mole crab. We implement a novel leg mechanism with a sweeping trajectory, using compliant fabric to enable an anisotropic force response. The maximum resistive force during the power stroke is 6.4 times that of the return stroke. We compare robot body pitch and spatial trajectories with results from biomechanical studies of the mole crabs. We characterize the sensitivity of the robot to initial depth, body pitch and leg pose, and propose bounds on initial conditions which predict various burrowing failure modes. Parametric studies utilizing Granular Resistive Force Theory inform our understanding of robot behavior in response to leg phasing and orientation. Not only does this robotic platform represent the first robophysical model of vertical mole crab-inspired burrowing, it is also one of the first legged, primarily excavative small-scale burrowing agents.

Abstract:

The force chain network is a crucial basis for characterizing the essential features of granular media microscopic mechanics and for studying the mechanical behavior of their macroscopic structures. Due to the complexity and multiformity of the force chain configuration, the topological data analysis (TDA) method provides a simple, effective, and manageable method to quantitatively describe the force network. Based on the theory of persistent homology in TDA, the analysis method of granules from contact network to force network to topological model is established. The two key factors affecting the structure of a force chain network are its connectivity and closure. β0 reflects the number of particle clusters whose normal force is greater than the provided threshold. β1 reflects the number of holes in the force chain cluster. Persistent homology, a mathematical method to calculate the topological features of structures in metric spaces with different resolutions, is applied to the structural analysis of force chain networks. Different from other methods that separately consider force threshold levels, the evolution of a force chain structure at the force threshold level is helpful in understanding the persistence characteristics of geometric structures at various force levels and describing the force chain network completely and deeply. For example, the top coal and overburden force chain evolution in top-coal caving mining is investigated through photoelastic experiments, and the TDA of the top-coal caving force network chain is performed. The research shows that when the particle stress is obtained as the threshold ε of persistent homology analysis in top-coal caving mining, the Betti number in persistent homology analysis can be used to evaluate periodic weighting. In the overlying strata and front of the working face, the curves of β0 are parabolic, of which the peak values under the periodic weighting are higher than that under the initial condition. Furthermore, the difference between them is that the peak values in the overlying strata are located in the range of strong force chains, whereas those in front of the working face are located in the range of sub-strong force chains. The curves of β1 show L-shaped, suggesting that within [0.3, 1], β1 approaches 0; within [0, 0.2], β1 is approximately inversely proportional to ε; and within [0.3, 1], β1 trends to 0. Topological studies of persistent homology provide an effective method for quantitative analysis of the complicated force chain network evolution and macroscopic mechanical behavior in granular media.

This study examines the flow of dense granular materials under external shear stress and pressure using discrete element method simulations. In this method, the material is allowed to strain along all periodic directions and adapt its solid volume fraction in response to an imbalance between the internal state of stress and the external applied stress. By systematically varying the external shear stress and pressure, the steady rheological response is simulated for: (1) rate-independent quasi-static flow; and (2) rate-dependent inertial flow. The simulated flow is viscometric with non-negligible first and second normal stress differences. While both normal stress differences are negative in inertial flows, the first normal stress difference switches from negative to slightly positive, and second normal stress difference tends to zero in quasi-static flows. The first normal stress difference emerges from a lack of coaxiality between a second-rank contact fabric tensor and strain rate tensor in the flow plane, while the second normal stress difference is linked to an excess of contacts in the shear plane compared with the vorticity direction. A general rheological model of second order (in terms of strain rate tensor) is proposed to describe the two types of flow, and the model is calibrated for various values of interparticle friction from simulations on nearly monodisperse spheres. The model incorporates normal stress differences in both regimes of flow and provides a complete viscometric description of steady dense granular flows.

Abstract:

Ultrafast X-ray computed tomography is an advanced imaging technique for multiphase flows. It has been used with great success for studying gas–liquid as well as gas–solid flows. Here, we apply this technique to analyze density-driven particle segregation in a rotating drum as an exemplary use case for analyzing industrial particle mixing systems. As glass particles are used as the denser of two granular species to be mixed, beam hardening artefacts occur and hamper the data analysis. In the general case of a distribution of arbitrary materials, the inverse problem of image reconstruction with energy-dependent attenuation is often ill-posed. Consequently, commonly known beam hardening correction algorithms are often quite complex. In our case, however, the number of materials is limited. We therefore propose a correction algorithm simplified by taking advantage of the known material properties, and demonstrate its ability to improve image quality and subsequent analyses significantly.

In general, sound waves propagate radially outwards from a point source. These waves will continue in the same direction, decreasing in intensity, unless a boundary condition is met. To arrive at a universal understanding of the relation between frequency and wave propagation within spatial boundaries, we explore the maximum entropy states that are realized as resonant modes. For both circular and polygonal Chladni plates, a model is presented that successfully recreates the nodal line patterns to a first approximation. We discuss the benefits of such a model and the future work necessary to develop the model to its full predictive ability.

Pipe structures are commonly encountered in the geophysical context, and in particular in sedimentary basins, where they are associated with fluid migration structures. We investigate pipe formation through laboratory experiments by injecting water locally at a constant flow rate at the base of water-saturated sands in a Hele–Shaw cell (30 cm high, 35 cm wide, gap 2.3 mm). The originality of this work is to quantify the effect of a discontinuity. More precisely, bilayered structures are considered, where a layer of fine grains overlaps a layer of coarser grains. Different invasion structures are reported, with fluidization of the bilayered sediment over its whole height or over the finer grains only. The height and area of the region affected by the fluidization display a non-monotonous evolution, which can be interpreted in terms of fluid focusing vs. scattering. Theoretical considerations can predict the critical coarse grains height for the invasion pattern transition, as well as the maximum topography at the sediment free surface in the regime in which only the overlapping finer grains fluidize. These results have crucial geophysical implications, as they demonstrate that invasion patterns and pipe formation dynamics may control the fluid expulsion extent and localization at the seafloor.

Hydrological behaviour of granular substrates is of critical interest in Nature-based solutions (NBS) like green roofs. To simulate this behaviour in a physically realistic manner it is indispensable to model the substrate’s hydraulic conductivity (HC) as it determines infiltration rate at various degrees of saturation. Since HC is directly dependent on water content retained by the substrate, it is necessary to physically model this water retention (WR) behaviour too. Capillary water is stored or retained in pore spaces and this water content that can be retained by a substrate under different suction pressures is therefore dependent upon its pore size distribution (PSD). Since pores in any granular media are spaces where grains are absent, their size distribution too is intrinsically related to the substrate’s grain size distribution (GSD) which provides the probability of finding grains smaller than some threshold diameter dg,t. Although earlier studies have attempted to model PSD, WR and HC, they frequently use simplifying mono-fractal approximations, whereas this study proposes a more generalized multifractal-based approach. Furthermore, while it is quite usual to incorporate pore tortuosity through some indirect parameter l in the HC model, a related ink-bottle effect which even though capable of affecting WR behaviour is commonly ignored. Therefore, this paper attempts to address the aforementioned research gaps in modelling GSD, PSD, WR and HC by i) investigating the somewhat overlooked question of similarity in multifractal behaviour between grain size fields and substrate density fields, and consequently suggesting an improved method for estimating universal multifractal (UM) parameters of grain size fields in a more reliable manner from just conventional GSD measurements in order to be directly used in the multifractal GSD model, ii) proposing a new UM-based PSD model, and subsequently using it to obtain a new UM-based WR model with a parameter to directly represent ink-bottle effect - a consequence of the substrate’s pore configuration or arrangement, iii) using this UM-based WR model to suggest a new UM-based HC model without the necessity for a separate pore tortuosity parameter. Finally, the proposed models have been validated by using experimental measurements from 4 different commercially used green roof substrates.

Granular environments, such as sand, are one of the most challenging substrates for robots to move within due to large depth‐dependent forces, unpredictable fluid/solid resistance forces, and limited sensing capabilities. An untethered robot is presented, inspired by biological diggers like sea turtles, which utilize underactuated appendages to enable propulsion and obstacle sensing in granular environments. To guide the robot's design, experiments are conducted on test appendages to identify the morphological and actuation parameters for forward thrust generation. Obstacle sensing is observed in granular media by measuring the increased force on the moving appendage caused by changes in the granular flow around it. These results are integrated into an untethered robot capable of subsurface locomotion in a controlled granular bed like natural, loosely packed sand. The robot achieves subsurface "swimming" at a speed of 1.2 mm s−1, at a depth of 127 mm, faster than any other reported untethered robot at this depth, while also detecting obstacles during locomotion via force sensors embedded in the appendages. Finally, subsurface robot locomotion in natural sand at the beach is demonstrated, a feat no other robot has accomplished, showcasing how underactuated structures enable movement and sensing in granular environments with limited limb control. [ABSTRACT FROM AUTHOR]

This study examines the flow of dense granular materials under external shear stress and pressure using discrete element method simulations. In this method, the material is allowed to strain along all periodic directions and adapt its solid volume fraction in response to an imbalance between the internal state of stress and the external applied stress. By systematically varying the external shear stress and pressure, the steady rheological response is simulated for: (1) rate-independent quasi-static flow; and (2) rate-dependent inertial flow. The simulated flow is viscometric with non-negligible first and second normal stress differences. While both normal stress differences are negative in inertial flows, the first normal stress difference switches from negative to slightly positive, and second normal stress difference tends to zero in quasi-static flows. The first normal stress difference emerges from a lack of coaxiality between a second-rank contact fabric tensor and strain rate tensor in the flow plane, while the second normal stress difference is linked to an excess of contacts in the shear plane compared with the vorticity direction. A general rheological model of second order (in terms of strain rate tensor) is proposed to describe the two types of flow, and the model is calibrated for various values of interparticle friction from simulations on nearly monodisperse spheres. The model incorporates normal stress differences in both regimes of flow and provides a complete viscometric description of steady dense granular flows.

A systematic approach is presented to achieve the stable grasping of objects through a two-finger robotic hand, in which each finger cavity was filled with granular media. The compaction of the latter, controlled by vacuum pressure, was used to adjust the structural and contact stiffness of the finger. The grasping stability was studied under the concurrent effect of an external torque and applied vacuum pressure. Stable grasping was defined as the no slippage condition between the grasped object and the two fingers. Three control schemes were adopted and applied experimentally to ensure the effectiveness of the grasping process. The results showed that stable and unstable grasping regions exist for each combination of applied torque and vacuum pressure. The two-finger robotic hands can be further improved for applications that require high load-carrying capabilities. [ABSTRACT FROM AUTHOR]

Excavation of regolith is the enabling process for many of the in situ resource utilization (ISRU) efforts that are being considered to aid in the human exploration of the moon and Mars. Most proposed planetary excavation systems are integrated with a wheeled vehicle, but none yet have used a screw‐propelled vehicle which can significantly enhance the excavation performance. Therefore, CASPER, a novel screw‐propelled excavation rover, is developed and analyzed to determine its effectiveness as a planetary excavator. The excavation rate, power, velocity, cost of transport, and a new parameter, excavation transport rate, are analyzed for various configurations of the vehicle through mobility and excavation tests performed in silica sand. The optimal configuration yields a 30 kg h−1 excavation rate and 10.2 m min−1 traverse rate with an overall system mass of 3.4 kg and power draw of less than 30 W. These results indicate that this architecture shows promise as a planetary excavation because it provides significant excavation capability with low mass and power requirements. An interactive preprint version of the article can be found here: https://doi.org/10.22541/au.162823910.04538641/v1. [ABSTRACT FROM AUTHOR]

Granular environments, such as sand, are one of the most challenging substrates for robots to move within due to large depth‐dependent forces, unpredictable fluid/solid resistance forces, and limited sensing capabilities. An untethered robot is presented, inspired by biological diggers like sea turtles, which utilize underactuated appendages to enable propulsion and obstacle sensing in granular environments. To guide the robot's design, experiments are conducted on test appendages to identify the morphological and actuation parameters for forward thrust generation. Obstacle sensing is observed in granular media by measuring the increased force on the moving appendage caused by changes in the granular flow around it. These results are integrated into an untethered robot capable of subsurface locomotion in a controlled granular bed like natural, loosely packed sand. The robot achieves subsurface “swimming” at a speed of 1.2 mm s−1, at a depth of 127 mm, faster than any other reported untethered robot at this depth, while also detecting obstacles during locomotion via force sensors embedded in the appendages. Finally, subsurface robot locomotion in natural sand at the beach is demonstrated, a feat no other robot has accomplished, showcasing how underactuated structures enable movement and sensing in granular environments with limited limb control.

Origami folding is an ancient art which holds promise for creating compliant and adaptable mechanisms, but has yet to be extensively studied for granular environments. At the same time, biological systems exploit anisotropic body forces for locomotion, such as the frictional anisotropy of a snake’s skin. In this work, we explore how foldable origami feet can be used to passively induce anisotropic force response in granular media, through varying their resistive plane. We present a reciprocating burrower which transfers pure symmetric linear motion into directed burrowing motion using a pair of deployable origami feet on either end. We also present an application of the reduced order model granular Resistive Force Theory to inform the design of deformable structures, and compare results with those from experiments and Discrete Element Method simulations. Through a single actuator, and without the use of advanced controllers or sensors, these origami feet enable burrowing locomotion. In this paper, we achieve burrowing translation ratios—net forward motion to overall linear actuation—over 46% by changing foot design without altering overall foot size. Specifically, anisotropic folding foot parameters should be tuned for optimal performance given a linear actuator’s stroke length.

Recent studies in polymer physics have created macro-scale analogs to solute microscopic polymer chains like DNA by inducing diffusive motion on a chain of beads. These bead chains have persistence lengths of O(10) links and undergo diffusive motion under random fluctuations like vibration. We present a bead chain model within a new stochastic forcing system: an air fluidizing bed of granular media. A chain of spherical 6 mm resin beads crimped onto silk thread are buffeted randomly by the multiphase flow of grains and low density rising air “bubbles”. We “thermalize” bead chains of various lengths at different fluidizing airflow rates, while X-ray imaging captures a projection of the chains’ dynamics within the media. With modern 3D printing techniques, we can better represent complex polymers by geometrically varying bead connections and their relative strength, e.g., mimicking the variable stiffness between adjacent nucleotide pairs of DNA. We also develop Discrete Element Method (DEM) simulations to study the 3D motion of the bead chain, where the bead chain is represented by simulated spherical particles connected by linear and angular spring-like bonds. In experiment, we find that the velocity distributions of the beads follow exponential distributions rather than the Gaussian distributions expected from polymers in solution. Through use of the DEM simulation, we find that this difference can likely be attributed to the distributions of the forces imparted onto the chain from the fluidized bed environment. We anticipate expanding this study in the future to explore a wide range of chain composition and confinement geometry, which will provide insights into the physics of large biopolymers.

Using linear elasticity theory, we describe the mechanical response of dry non-cohesive granular masses of Ottawa sand contained by spherical rubber balloons subject to sudden bursting in the earliest instants of the event. Due to the compression imposed by the balloon, the rupture produces a fast radial expansion of the sand front that depends on the initial radius R0, the initial pressure p originated by the balloon, and the effective modulus of compression Ke. The hydrostatic compression approximation allows for the theoretical study of this problem. We found a linear decompression wave that travels into the sand and that induces a radial expansion of the granular front in the opposite direction with similar behavior to the wave but with a slightly lower speed.

Abstract In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb’s friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset A $\mathcal{A}$ of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method.

Excavation of regolith is the enabling process for many of the in situ resource utilization (ISRU) efforts that are being considered to aid in the human exploration of the moon and Mars. Most proposed planetary excavation systems are integrated with a wheeled vehicle, but none yet have used a screw‐propelled vehicle which can significantly enhance the excavation performance. Therefore, CASPER, a novel screw‐propelled excavation rover, is developed and analyzed to determine its effectiveness as a planetary excavator. The excavation rate, power, velocity, cost of transport, and a new parameter, excavation transport rate, are analyzed for various configurations of the vehicle through mobility and excavation tests performed in silica sand. The optimal configuration yields a 30 kg h−1 excavation rate and 10.2 m min−1 traverse rate with an overall system mass of 3.4 kg and power draw of less than 30 W. These results indicate that this architecture shows promise as a planetary excavation because it provides significant excavation capability with low mass and power requirements. An interactive preprint version of the article can be found here: https://doi.org/10.22541/au.162823910.04538641/v1.

Earthquake-induced liquefaction is always a concern when the soil near the surface of a site is composed of relatively loose saturated sand. One of liquefaction mitigation methods is to induce gas bubbles into the deposit to reduce the degree of saturation. A coupled pore-scale model is presented herein to investigate liquefaction resistance of desaturated granular materials. The multiphase fluid, which mimics the behavior of air and water, is modeled using the multiphase single component lattice Boltzmann method. The solid phase is modeled using the discrete element method. The coupled framework was utilized to study the behavior of a soil deposit with the different degrees of saturation of 100%, 92%, and 82% during an earthquake loading. Based on the results of the simulations performed, liquefaction occurred in the fully saturated granular deposit and was not observed anywhere at depth in the desaturated deposits. It has also been found that reducing the saturation level from 100% to 92% significantly affects behavior. In desaturated deposits, higher average coordination number, lower pore pressure buildup, and slower effective stress decay were observed compared to fully saturated deposits. However, it turned out that a further reduction in the degree of saturation from 92% to 82% does not have a significant impact on the calculated parameters. [ABSTRACT FROM AUTHOR]

Terrain irregularities in natural environments present mobility challenges for autonomous robots and vehicles. Loosely consolidated sandy slopes flow unpredictably when perturbed, often leading to locomotion failure. Systematic experiments with various robot morphologies on flowable terrains feature open‐loop quasistatic gait strategies that remodel the terrain to aid locomotor kinematics. On a sloped terrain of granular media near the critical angle, a laboratory‐scale rover robot induces a flow via a localized fluidization gait to remodel local terrain and succeed in locomotion. A Bayesian optimization machine learning approach that modulates this gait strategy then finds a pattern of selectively fluidizing and solidifying terrain to climb slopes rapidly. In a biped walker robot, a cleated foot design dynamically manipulates the stress fields of flowable slopes. The deeply submerged cleats remodel the shear response of the material by creating jammed regions behind them which then improve forward progression by reducing slip when compared to a flat foot. The "robophysics" approach of systematic experiments exploring terrain reconfiguration combined with future machine learning models of flowable terrain evolution can augment gait discovery for future robots. [ABSTRACT FROM AUTHOR]

Terrain irregularities in natural environments present mobility challenges for autonomous robots and vehicles. Loosely consolidated sandy slopes flow unpredictably when perturbed, often leading to locomotion failure. Systematic experiments with various robot morphologies on flowable terrains feature open‐loop quasistatic gait strategies that remodel the terrain to aid locomotor kinematics. On a sloped terrain of granular media near the critical angle, a laboratory‐scale rover robot induces a flow via a localized fluidization gait to remodel local terrain and succeed in locomotion. A Bayesian optimization machine learning approach that modulates this gait strategy then finds a pattern of selectively fluidizing and solidifying terrain to climb slopes rapidly. In a biped walker robot, a cleated foot design dynamically manipulates the stress fields of flowable slopes. The deeply submerged cleats remodel the shear response of the material by creating jammed regions behind them which then improve forward progression by reducing slip when compared to a flat foot. The “robophysics” approach of systematic experiments exploring terrain reconfiguration combined with future machine learning models of flowable terrain evolution can augment gait discovery for future robots.

This article deals with the Hadamard instability of the so-called$\unicode[STIX]{x1D707}(I)$model of dense rapidly sheared granular flow, as reported recently by Barkeret al.(J. Fluid Mech., vol. 779, 2015, pp. 794–818). The present paper presents a more comprehensive study of the linear stability of planar simple shearing and pure shearing flows, with account taken of convective Kelvin wavevector stretching by the base flow. We provide a closed-form solution for the linear-stability problem and show that wavevector stretching leads to asymptotic stabilization of the non-convective instability found by Barkeret al.(J. Fluid Mech., vol. 779, 2015, pp. 794–818). We also explore the stabilizing effects of higher velocity gradients achieved by an enhanced-continuum model based on a dissipative analogue of the van der Waals–Cahn–Hilliard equation of equilibrium thermodynamics. This model involves a dissipative hyperstress, as the analogue of a special Korteweg stress, with surface viscosity representing the counterpart of elastic surface tension. Based on the enhanced-continuum model, we also present a model of steady shear bands and their nonlinear stability against parallel shearing. Finally, we propose a theoretical connection between the non-convective instability of Barkeret al.(J. Fluid Mech., vol. 779, 2015, pp. 794–818) and the loss of generalized ellipticity in the quasi-static field equations. Apart from the theoretical interest, the present work may suggest stratagems for the numerical simulation of continuum field equations involving the$\unicode[STIX]{x1D707}(I)$rheology and variants thereof.

This article deals with the Hadamard instability of the so-called$\unicode[STIX]{x1D707}(I)$model of dense rapidly sheared granular flow, as reported recently by Barkeret al.(J. Fluid Mech., vol. 779, 2015, pp. 794–818). The present paper presents a more comprehensive study of the linear stability of planar simple shearing and pure shearing flows, with account taken of convective Kelvin wavevector stretching by the base flow. We provide a closed-form solution for the linear-stability problem and show that wavevector stretching leads to asymptotic stabilization of the non-convective instability found by Barkeret al.(J. Fluid Mech., vol. 779, 2015, pp. 794–818). We also explore the stabilizing effects of higher velocity gradients achieved by an enhanced-continuum model based on a dissipative analogue of the van der Waals–Cahn–Hilliard equation of equilibrium thermodynamics. This model involves a dissipative hyperstress, as the analogue of a special Korteweg stress, with surface viscosity representing the counterpart of elastic surface tension. Based on the enhanced-continuum model, we also present a model of steady shear bands and their nonlinear stability against parallel shearing. Finally, we propose a theoretical connection between the non-convective instability of Barkeret al.(J. Fluid Mech., vol. 779, 2015, pp. 794–818) and the loss of generalized ellipticity in the quasi-static field equations. Apart from the theoretical interest, the present work may suggest stratagems for the numerical simulation of continuum field equations involving the$\unicode[STIX]{x1D707}(I)$rheology and variants thereof.

We present EMBUR—EMerita BUrrowing Robot—the first legged robot inspired by the Pacific mole crab, Emerita analoga, capable of burrowing vertically downward. We choose Emerita analoga as a model organism for its rapid downward burrowing behaviors, as it is four times as fast as the most rapid bivalve mollusk. Vertical burrowing in granular media is a challenging endeavor due to the tendency for the media to create upwards resistive forces on an intruder, even during purely horizontal motions. Our robot is capable of vertically burrowing its body in granular substrate primarily through excavation using two leg pairs, which are functionally analogous to groupings of leg pairs of the mole crab. We implement a novel leg mechanism with a sweeping trajectory, using compliant fabric to enable an anisotropic force response. The maximum resistive force during the power stroke is 6.4 times that of the return stroke. We compare robot body pitch and spatial trajectories with results from biomechanical studies of the mole crabs. We characterize the sensitivity of the robot to initial depth, body pitch and leg pose, and propose bounds on initial conditions which predict various burrowing failure modes. Parametric studies utilizing Granular Resistive Force Theory inform our understanding of robot behavior in response to leg phasing and orientation. Not only does this robotic platform represent the first robophysical model of vertical mole crab-inspired burrowing, it is also one of the first legged, primarily excavative small-scale burrowing agents.

In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb's friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset A of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The purpose of this study is to develop a micromechanical-based microstructure model for transversely isotropic granular media and then use it to investigate the propagation characteristics of particle rotation waves. In this paper, the particle translation and rotation are selected as basic independent variables and the particle displacement at contact due to particle rotation is ignored. The relative deformation tensors are introduced to describe the local deformational fluctuation because of their discrete nature and microstructure effect. Based on micro–macro deformation energy conservation, the constitutive relations are derived through transferring the summation into an integral and introducing the contact fabric tensor. The governing equations and corresponding boundary conditions can then be obtained based on Hamilton's principle. Subsequently, the dispersion characteristics and bandgap features of particle rotation waves in transversely isotropic granular media are analyzed based on the present model. The research shows that: the present microstructure model can predict 12 particle rotation waves and reflect 8 dispersion relations; the effect of the change in fabric on the dispersion relation of particle rotation waves can be mainly attributed to the effect of equivalent stiffness on frequency; and the degree of anisotropy has significant effects on the width of frequency bandgap of longitudinal waves, while it has little effect on the width of frequency bandgap of transverse and in-plane shear waves. [ABSTRACT FROM AUTHOR]