Robust self-propulsion in sand using simply controlled vibrating cubes.

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.

Simplified Beam Hardening Correction for Ultrafast X-ray CT Imaging of Binary Granular Mixtures.

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.

Embedded Printing of Hydrogels and Watery Suspensions of Cells in Patterned Granular Baths.

Bioprinting within support media has emerged as the superior alternative to conventional extrusion printing. Not only because it allows for more freedom over the shapes that can be printed but also because it allows for the printing of inks that would not retain shape fidelity in freeform deposition such as watery liquids. Apart from functioning as mechanical support during embedded printing, hydrogel microparticle support media can provide the unique advantage of offering distinct chemotactic cues to cells printed in the baths by varying the composition of the hydrogel microparticles. There is great potential in compartmentalized granular baths consisting of different hydrogel particle materials in the field of tissue engineering, as these allow for the local inclusion of properties or cues to guide tissue development. In this work, we present a method to create compartmentalized embedding baths by printing multiple granular hydrogel materials that are widely used in tissue engineering. After adapting the volume fraction (φp) of the particles in the bath, we print within them using both inks composed of hydrogel or of cells and other particles suspended in watery liquid. Our process consists of the following three steps: First, the hydrogel microparticles are packed at a φp that allows them to be extruded while being reversibly jammed, facilitating the localized deposition of the granular media to form a compartmentalized bath. Second, each granular media is deposited in succession to create a packed suspension compartment, and by adding liquid post deposition, φp is reduced to allow for embedded printing. Finally, we demonstrate the printing of multiple inks within the compartmentalized embedding bath and highlight the distinct differences between using inks composed of hydrogels or inks composed of particles suspended in watery liquid. This approach combines the advantages of embedded printing through the use of granular media with the added ability to pattern multiple bioactive granular materials to locally affect the behavior of cells printed within the bath. We expect that this workflow will allow researchers to create spatially compartmentalized, customized bioactive embedding baths that allow for the embedded printing of inks composed of hydrogels, cells, and other particles adapted to their need.

Dataset on the behaviour of the Areolas da Estefania formation in Lisbon and its modelling using a state-dependent soil model.

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.

Exploration of Resonant Modes for Circular and Polygonal Chladni Plates.

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.

Dynamic imaging of force chains in 3D granular media.

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 three-dimensional (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.

Locomotor kinematics on sand versus vinyl flooring in the sidewinder rattlesnake Crotalus cerastes.

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 body's 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.

Toward a 3D physical model of diffusive polymer chains.

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.

Efficient reciprocating burrowing with anisotropic origami feet.

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.

Mechanistic framework for reduced-order models in soft materials: Application to three-dimensional granular intrusion.

Soft materials often display complex behaviors that transition through apparent solid- and fluid-like regimes. While a growing number of microscale simulation methods exist for these materials, reduced-order models that encapsulate the macroscale physics are often desired to predict how external bodies interact with soft media. Such an approach could provide direct insights in diverse situations from impact and penetration problems to locomotion over natural terrains. This work proposes a systematic program to develop three-dimensional (3D) reduced-order models for soft materials from a fundamental basis using continuum symmetries and rheological principles. In particular, we derive a reduced-order, 3D resistive force theory (3D-RFT), which is capable of accurately and quickly predicting the resistive stress distribution on arbitrary-shaped bodies intruding through granular media. Aided by a continuum description of the granular medium, a comprehensive set of spatial symmetry constraints, and a limited amount of reference data, we develop a self-consistent and accurate 3D-RFT. We verify the model capabilities in a wide range of cases and show that it can be quickly recalibrated to different media and intruder surface types. The premises leading to 3D-RFT anticipate application to other soft materials with strongly hyperlocalized intrusion behavior.

Application of combined granular media with opposite wettability for demulsification of oily wastewater by microchannel filter.

Oil-water separation with high efficiency and low energy consumption is a tremendous challenge in the green treatment of oily wastewater. In this paper, a novel filtration method with combined granular media for collaborative removal emulsified oil and suspended solids (SS) was proposed, followed by the exploration of demulsification feasibility and oil removal mechanism. The effect of the operation and structural parameters of the filter bed on oil separation performance was thoroughly investigated, and its feasibility for raw oily wastewater treatment was also explored. A remarkable demulsification performance was observed with the combined granular media filter, and a balance of separation efficiency and pressure drop in the emulsified oily wastewater filtration was also achieved subsequently. Effective oil droplet capture and coalescence were observed with a high speed camera system, and pore clogging could be avoided in combined media. The optimal parameters of the combined media filter (CMF) were concluded to be a combined media ratio of 1:1, a superficial velocity of 0.20 m min-1, and a bed porosity of 58.1%. The average oil and suspended solids concentrations in raw oily wastewater was decreased to 8.4 mg/L and 23.3 mg/L during the pilot-scale operation, which indicated that the novel filter composed of combined media had better performance in collaboratively removing oil and SS, even in the period of fluctuating influent parameters. It is believed that a novel and efficient oil removal method, especially including of emulsified oil removal was provided, which also shows great potential and value for the green treatment of industrial oily wastewater.

Mole crab-inspired vertical self-burrowing.

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.

Sideways crab-walking is faster and more efficient than forward walking for a hexapod robot.

Articulated legs enable the selection of robot gaits, including walking in different directions such as forward or sideways. For longer distances, the best gaits might maximize velocity or minimize the cost of transport (COT). While animals often have morphology suited to walking either forward (like insects) or sideways (like crabs), hexapod robots often default to forward walking. In this paper, we compare forward walking with crab-like sideways walking. To do this, a simple gait design method is introduced for determining forward and sideways gaits with equivalent body heights and step heights. Specifically, the frequency and stride lengths are tuned within reasonable constraints to find gaits that represent a robot's performance potential in terms of speed and energy cost. Experiments are performed in both dynamic simulation in Webots and a laboratory environment with our 18 degree-of-freedom hexapod robot, Sebastian. With the common three joint leg design, the results show that sideways walking is overall better (75% greater walking speed and 40% lower COT). The performance of sideways walking was better on both hard floors and granular media (dry play sand). This supports development of future crab-like walking robots for future applications. In future work, this approach may be used to develop nominal gaits without extensive optimization, and to explore whether the advantages of sideways walking persist for other hexapod designs.

Fabrication, Flow Assembly, and Permeation of Microscopic Any-Shape Particles.

Today, millimeter-sized nonspherical any-shape particles serve as flexible, functional scaffold material in chemical and biochemical reactors tailoring their hydrodynamic properties and active surface-to-volume ratio based on the particle's shape. Decreasing the particle size to smaller than 100 µm would be desired as it increases the surface-to-volume ratio and promotes a particle assembly based on surface interactions, allowing the creation of tailored self-assembling 3D scaffolds. This study demonstrates a continuous high-throughput fabrication of microscopic 3D particles with complex shape and sub-micron resolution using continuous two-photon vertical flow lithography. Evolving from there, in-channel particle fabrication into a confined microfluidic chamber with a resting fluid enables the precise fabrication of a defined number of particles. 3D assemblies with various particle shapes are fabricated and analyzed regarding their permeability and morphology, representing convective accessibility of the assembly's porosity. Differently shaped particles highlight the importance of contact area regarding particle-particle interactions and the respective hydraulic resistance of an assembly. Finally, cell culture experiments show manifold cell-particle interactions promising applicability as bio-hybrid tissue. This study pushes the research boundaries of adaptive, responsive, and permeable 3D scaffolds and granular media by demonstrating a high throughput fabrication solution and a precise hydrodynamic analysis method for micro-particle assemblies.

Coupled photocatalytic alkaline media as a destructive technology for per- and polyfluoroalkyl substances in aqueous film-forming foam impacted stormwater.

The release of aqueous film forming foam (AFFF) from fuel fire events, fire training events, and other activities has resulted in the presence of persistent and recalcitrant per- and polyfluoroalkyl substances (PFAS) in soil and water nationwide. This study describes the degradation and defluorination of PFAS in stormwater collected from an AFFF-impacted site. Silica-based granular media (SGM) containing titanium dioxide was packed into a column reactor and placed between ultraviolet (UV) lamps to excite the photocatalyst within the SGM and generate free radicals to degrade PFAS present in water that was passed through the media. The system was amended with nucleophiles (hydroxyls) to facilitate the destruction of PFAS. Results showed rapid degradation of 17 identified PFAS, including perfluoroalkyl acid (PFAA) precursors, perfluorosulfonic acids (PFSAs), and perfluorocarboxylic acids (PFCAs). Significant defluorination was observed, indicating PFAS destruction as a result of the coupled photocatalytic and nucleophilic attack. Column reactor experiment findings indicate SGM in the presence of UV light passively degraded a mixture of PFAS in a concentrated waste stream at ambient conditions.

Legged locomotion in resistive terrains.

The utility, efficiency, and reliability of legged robots has increased dramatically in recent years. Limbed robots are now capable of locomotion across a variety of terrains, however, achieving both rapid and efficient operation when ground conditions are complex or deformable is still challenging. Resistive terrains such as streams, snow, mud, littoral regions, and tall grass are an important class or set of complex and difficult terrain which are commonly found in the desired operating environments of legged robots. This work presents a reduced-order, dynamic model designed to capture the effect of these environments on the legs of a robot while running. This model, and an experimental platform, are used to evaluate the efficacy of a pair of strategies for adapting running to the inevitable slowing that occurs in resistive terrains. Simulation and experimental results show that intelligent retraction of the foot during flight has a more beneficial effect on the maximum achievable velocity and cost of transport of the runner than a 'punting gait' for a range of fluid depths. However, this performance gap became much smaller in deep fluids suggesting that fluid depth may drive transition from a foot retraction gait to a punting gait.

Simulation of Bullet Fragmentation and Penetration in Granular Media.

The aim of this work is to simulate the fragmentation of bullets impacted through granular media, in this case, sand. In order to validate the simulation, a group of experiments were conducted with the sand contained in two different box prototypes. The walls of the first box were constructed with fiberglass and the second with plywood. The prototypes were subjected to the impact force of bullets fired 15 m away from the box. After the shots, X-ray photographs were taken to observe the penetration depth. Transient numerical analyses were conducted to simulate these physical phenomena by using the smooth particle hydrodynamics (SPH) module of ANSYS® 2019 AUTODYN software. Advantageously, this module considers the granular media as a group of uniform particles capable of transferring kinetic energy during the elastic collision component of an impact. The experimental results demonstrated a reduction in the maximum bullet kinetic energy of 2750 J to 100 J in 0.8 ms. The numerical results compared with the X-ray photographs showed similar results demonstrating the capability of sand to dissipate kinetic energy and the fragmentation of the bullet caused at the moment of impact.

Effects of clogging on ultrasonic transmission through saturated granular single and double porosity media.

The clogging caused by the deposition of suspended particles modifies in depth several mechanical parameters (permeability, porosity, bulk moduli, etc.) of porous media and influences the acoustic behaviour. Consequently, at a fixed position in the medium, changes in phase velocity and attenuation are observed in the amplitude of the temporal signal of the transmitted waves. In this work, ultrasonic techniques are presented both for detecting and measuring the clogging in a water saturated porous medium. The acoustic measurements from the clogged samples are compared with the deposition profiles obtained at the end of injection experiments. Moreover, links are established between on the one hand phase velocity and the total porosity, and on the other hand the transmitted signal energy and the variation of porosity as consequence of particle deposition.

Surprising simplicities and syntheses in limbless self-propulsion in sand.

Animals moving on and in fluids and solids move their bodies in diverse ways to generate propulsion and lift forces. In fluids, animals can wiggle, stroke, paddle or slap, whereas on hard frictional terrain, animals largely engage their appendages with the substrate to avoid slip. Granular substrates, such as desert sand, can display complex responses to animal interactions. This complexity has led to locomotor strategies that make use of fluid-like or solid-like features of this substrate, or combinations of the two. Here, we use examples from our work to demonstrate the diverse array of methods used and insights gained in the study of both surface and subsurface limbless locomotion in these habitats. Counterintuitively, these seemingly complex granular environments offer certain experimental, theoretical, robotic and computational advantages for studying terrestrial movement, with the potential for providing broad insights into morphology and locomotor control in fluids and solids, including neuromechanical control templates and morphological and behavioral evolution. In particular, granular media provide an excellent testbed for a locomotion framework called geometric mechanics, which was introduced by particle physicists and control engineers in the last century, and which allows quantitative analysis of alternative locomotor patterns and morphology to test for control templates, optimality and evolutionary alternatives. Thus, we posit that insights gained from movement in granular environments can be translated into principles that have broader applications across taxa, habitats and movement patterns, including those at microscopic scales.

Violations of the Clausius-Duhem inequality in Couette flows of granular media.

Spontaneous violations of the Clausius-Duhem (CD) inequality in Couette-type collisional flows of model granular media are studied. Planar systems of monosized circular discs (with disc numbers from 10 to 204, and disc diameters from 0.001 m to 1 m) with frictional-Hookean contacts are simulated under periodic boundary conditions by a molecular dynamics. The scale-dependent homogenization of micropolar media is used to determine the energy balances and mechanical entropy production. The dissipation function exhibits spontaneous negative entropy increments described by the fluctuation theorem. The boundary between violations and non-violations of the CD inequality is mapped in the parameter space, where the probability of such events diminishes with the disc diameter, the disc number and the area fraction increasing. The dissipation function is a random process, tending to Gaussian as the number of discs increases, and possessing non-trivial fractal and anti-persistent Hurst properties.