Column collapse of granular rods

Experimental models for cohesive granular materials: a review

Granular materials are involved in most industrial and environmental processes, as well as many civil engineering applications. Although significant advances have been made in understanding the statics and dynamics of cohesionless grains over the past decades, most granular systems we encounter often display some adhesive forces between grains. The presence of cohesion has effects at distances substantially larger than the closest neighbors and consequently can greatly modify their overall behavior. While considerable progress has been made in understanding and describing cohesive granular systems through idealized numerical simulations, controlled experiments corroborating and expanding the wide range of behavior remain challenging to perform. In recent years, various experimental approaches have been developed to control inter-particle adhesion that now pave the way to further our understanding of cohesive granular flows. This article reviews different approaches for making particles sticky, controlling their relative stickiness, and thereby studying their granular and bulk mechanics. Some recent experimental studies relying on model cohesive grains are synthesized, and opportunities and perspectives in this field are discussed.

Entanglement transition in random rod packings

Random packings of stiff rods are self-supporting mechanical structures stabilized by long-range interactions induced by contacts. To understand the geometrical and topological complexity of the packings, we first deploy X-ray computerized tomography to unveil the structure of the packing. This allows us to directly visualize the spatial variations in density, orientational order, and the entanglement, a mesoscopic field that we define in terms of a local average crossing number, a measure of the topological complexity of the packing. We find that increasing the aspect ratio of the constituent rods in a packing leads to a proliferation of regions of strong entanglement that eventually percolate through the system and correlated with a sharp transition in the mechanical stability of the packing. To corroborate our experimental findings, we use numerical simulations of contacting elastic rods and characterize their stability to static and dynamic loadings. Our experiments and computations lead us to an entanglement phase diagram which we also populate using published experimental data from pneumatically tangled filaments, worm blobs, and bird nests along with additional numerical simulations using these datasets. Together, these show the regimes associated with mechanically stable entanglement as a function of the statistics of the packings and loading, with lessons for a range of systems from reconfigurable architectures and textiles to active morphable filamentous assemblies.

Geometric cohesion in two-dimensional systems composed of star-shaped particles

Using a discrete element method, we investigate the phenomenon of geometric cohesion in granular systems composed of star-shaped particles with 3 to 13 arms. This was done by analyzing the stability of columns built with these particles and by studying the microstructure of these columns in terms of density and connectivity. We find that systems composed of star-shaped particles can exhibit geometric cohesion (i.e., a solidlike behavior, in the absence of adhesive forces between the grains), depending on the shape of the particles and the friction between them. This phenomenon is observed up to a given critical size of the system, from which a transition to a metastable behavior takes place. We also have evidence that geometric cohesion is closely linked to the systems' connectivity and especially to the capability of forming interlocked interactions (i.e., multicontact interactions that hinder the relative rotation of the grains). Our results contribute to the understanding of the interesting and potentially useful phenomenon of geometric cohesion. In addition, our work supplements an important set of experimental observations and sheds light on the complex behavior of real, three-dimensional, granular systems.

Properties of packings and dispersions of superellipse sector particles

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We compare three computational processes: pair-wise Monte Carlo simulations that explore particle-particle geometric constraints, Monte Carlo simulations that reveal how these geometric constraints play out over dispersions of many particles, and Molecular Dynamics simulations that form random loose and close packings. We investigate the dependence of critical random loose and close packing fractions on particle parameters, finding that both values increase with opening aperture and decrease with increasing corner sharpness. The identified packing fractions are compared with the mean-field prediction of the random contact model; we find deviations from the model's prediction due to correlations between particle orientations. The complex interaction of spatial proximity and orientational alignment is also explored with a generalized spatioorientational distribution area (SODA) plot, which shows how higher density packings are achieved through particles assuming a small number of preferred configurations that depend sensitively on particle shape and system preparation.

Amorphous entangled active matter

The design of amorphous entangled systems, specifically from soft and active materials, has the potential to open exciting new classes of active, shape-shifting, and task-capable 'smart' materials. However, the global emergent mechanics that arise from the local interactions of individual particles are not well understood. In this study, we examine the emergent properties of amorphous entangled systems in an in silico collection of u-shaped particles ("smarticles") and in living entangled aggregate of worm blobs (L. variegatus). In simulations, we examine how material properties change for a collective composed of smarticles as they undergo different forcing protocols. We compare three methods of controlling entanglement in the collective: external oscillations of the ensemble, sudden shape-changes of all individuals, and sustained internal oscillations of all individuals. We find that large-amplitude changes of the particle's shape using the shape-change procedure produce the largest average number of entanglements, with respect to the aspect ratio (l/w), thus improving the tensile strength of the collective. We demonstrate applications of these simulations by showing how the individual worm activity in a blob can be controlled through the ambient dissolved oxygen in water, leading to complex emergent properties of the living entangled collective, such as solid-like entanglement and tumbling. Our work reveals principles by which future shape-modulating, potentially soft robotic systems may dynamically alter their material properties, advancing our understanding of living entangled materials, while inspiring new classes of synthetic emergent super-materials.

Micromechanical Origin of Plasticity and Hysteresis in Nestlike Packings

Disordered packings of unbonded, semiflexible fibers represent a class of materials spanning contexts and scales. From twig-based bird nests to unwoven textiles, bulk mechanics of disparate systems emerge from the bending of constituent slender elements about impermanent contacts. In experimental and computational packings of wooden sticks, we identify prominent features of their response to cyclic oedometric compression: nonlinear stiffness, transient plasticity, and eventually repeatable velocity-independent hysteresis. We trace these features to their micromechanic origins, identified in characteristic appearance, disappearance, and displacement of internal contacts.

Column to pile transition in quasi-static deposition of granular chains

The repose angle is a key geometric property that characterises the inter-particle friction and thereby granular flows. One of the common methods to measure this property is to deposit a pile by extracting a pre-filled cylinder and letting the material flow out. While the repose angle of spherical beads is insensitive to the aspect ratio of this pre-filled column, we find that long flexible granular chains show a remarkable transition from stable vertical columns to conical piles depending on the aspect ratio. Below a critical aspect ratio, the cessation of flow of granular chains due to inter-chain entanglement stabilises the columns, while above the critical aspect ratio the conical piles of long granular chains arise not out of shear flow but instead through a series of column collapse instabilities during the deposition process. We also identify the critical chain length below which the granular chains flow and behave similar to spherical particles.

Collapse dynamics of dry granular columns: From free-fall to quasistatic flow

Gravity-driven collapses involving large amounts of dense granular material, such as landslides, avalanches, or rock falls, in a geophysical context, represent significant natural hazards. Understanding their complex dynamics is hence a key concern for risk assessment. In the present work, we report experiments on the collapse of quasi-two-dimensional dry granular columns under the effect of gravity, where both the velocity at which the grains are released and the aspect ratio of the column are varied to investigate the dynamics of the falling grains. At high release velocity, classical power laws for the final deposit are recovered, meaning those are representative of a free-fall-like regime. For sufficiently high aspect ratios, the top of the column undergoes an overall free-fall-like motion. In addition, for all experiments, the falling grains also spread horizontally in a free-fall-like motion, and the characteristic time of spreading is related to the horizontal extension reached by the deposit at all altitudes. At low release velocity, a quasistatic state is observed, with scaling laws for the final geometry identical to those of the viscous regime of granular-fluid flow. The velocity at which the grains are released governs the collapse dynamics. Between these two asymptotic regimes, higher release velocity correlates with smaller impact on the collapse dynamics. The criterion V[over ¯]≥0.4sqrt[gH_{0}], where H_{0} is the initial height of the column, is found for the mean release velocity V[over ¯] not to influence the granular collapse.

Designing architectural materials: from granular form to functional granular material

Designed granular materials are a novel class of architectural material system. Following one of the key paradigms of designed matter, material form and material function are closely interrelated in these systems. In this context, the article aims to contribute a parametric particle design model as an interface for this interrelation. A granular material is understood as an aggregation of large numbers of individual particles between which only short-range repulsive contact forces are acting. Granular materials are highly pertinent material systems for architecture. Due to the fact that they can act both as a solid and a liquid, they can be recycled and reconfigured multiple times and are thus highly sustainable. Designed granular materials have the added potential that the function of the granular material can be calibrated through the definition of the particles' form. Research on the design of granular materials in architecture is nascent. In physics they have been explored mainly with respect to different particle shapes. However, no coherent parametric particle design model of designed particle shapes for granular material systems in architecture has yet been established which considers both fabrication constraints and simulation requirements. The parametric particle design model proposed in this article has been based on a design system which has been developed through feasibility tests and simulations conducted in research and teaching. Based on this design system the parametric particle design model is developed integrating both fabrication constraints for architecture-scale particle systems and the geometric requirements of established simulation methods for granular materials. Initially the design system and related feasibility tests are presented. The parametric particle design model resulting from that is then described in detail. Directions of further research are discussed especially with respect to the integration of the parametric particle design model in 'inverse' design methods.

Excluded area of superellipse sector particles

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We investigate the space of allowable (nonoverlapping) configurations of two SeSPs, which depends on both the center-of-mass separation and relative orientation. Radial correlation plots of the allowed configurations reveal circular regions centered at each of the particle's two end points that indicate configurations of mutually entangled particle interactions. Simultaneous entanglement with both end points is geometrically impossible; the overlap of these two regions therefore represents an excluded area in which no particles can be placed regardless of orientation. The regions' distinct boundaries indicate a translational frustration with implications for the dynamics of particle rearrangements (e.g., under shear). Representing translational and rotational degrees of freedom as a hypervolume, we find a topological change that suggests geometric frustration arises from a phase transition in this space. The excluded area is a straightforward integration over excluded states; for arbitrary relative orientation this decreases sigmoidally with increasing opening aperture, with sharper SeSP corners resulting in a sharper decrease. Together, this work offers a path towards a unified theory for particle shape control of bulk material properties.

Planar column collapse of elongated grains

The granular column collapse is a benchmark configuration for the study of granular flows in dry, saturated, and submerged conditions. The collapse sequence and resultant mobility is acknowledged to be controlled by the column aspect ratio, while grain properties define the relative transition of each stage. Grain shape effects are found to modify the global shear resistance of granular media, with a strong and coupled interaction when interacting with a fluid. In this work, we present the first steps towards the study of grain shape effects in a column collapse when interacting with an ambient fluid. For this purpose, we use a planar configuration and explore the collapse of a column consisting of rod-like grains and study the initial and after collapse grain orientations. On it, the mobilized grains deposit in a preferential horizontal orientation, but further experiments are required to confirm if a nematic configuration can be achieved.

Packings of frictionless spherocylinders

We present simulation results on the properties of packings of frictionless spherocylindrical particles. Starting from a random distribution of particles in space, a packing is produced by minimizing the potential energy of interparticle contacts until a force-equilibrated state is reached. For different particle aspect ratios α=10⋯40, we calculate contacts z, pressure as well as bulk and shear modulus. Most important is the fraction f_{0}(α) of spherocylinders with contacts at both ends, as it governs the jamming threshold z_{c}(α)=8+2f_{0}(α). These results highlight the important role of the axial "sliding" degree of freedom of a spherocylinder, which is a zero-energy mode but only if no end contacts are present.

Yielding, rigidity, and tensile stress in sheared columns of hexapod granules

Granular packings of nonconvex or elongated particles can form freestanding structures like walls or arches. For some particle shapes, such as staples, the rigidity arises from interlocking of pairs of particles, but the origins of rigidity for noninterlocking particles remains unclear. We report on experiments and numerical simulations of sheared columns of "hexapods," particles consisting of three mutually orthogonal sphero-cylinders whose centers coincide. We vary the length-to-diameter aspect ratio, α, of the sphero-cylinders and subject the packings to quasistatic direct shear. For small α, we observe a finite yield stress. For large α, however, the column becomes rigid when sheared, supporting stresses that increase sharply with increasing strain. Analysis of x-ray microcomputed tomography (micro-CT) data collected during the shear reveals that the stiffening is associated with a tilted, oblate cluster of hexapods near the nominal shear plane in which particle deformation and average contact number both increase. Simulation results show that the particles are collectively under tension along one direction, even though they do not interlock pairwise. These tensions comes from contact forces carrying large torques, and they are perpendicular to the compressive stresses in the packing. They counteract the tendency to dilate, thus stabilizing the particle cluster.

Granular column collapse: Analysis of grain-size effects

The column collapse experiment is a simplified version of the complex granular flows observed in both natural and industrial contexts. Due to its simple setup and rich behavior, the column collapse has been studied experimentally and numerically by several authors. The purpose of the analyses presented in this paper is to verify whether some of the results presented in these publications are affected by grain-size effects. In order to do so, we simulate two-dimensional granular columns by means of a discrete-element method, i.e., contact dynamics. Specifically, we study the influence of the grain size, as compared to the system size, on the resultant deposit geometry and collapse duration. We show that (i) some of the previously published results may be affected by grain-size effects, (ii) in order to avoid these effects, the system-size to grain-size ratio must be larger than 75 for short columns and larger than 50 for tall columns, and (iii) the quantities that are the most affected by grain-size effects are the column mobility and the collapse duration. Our findings serve as a tool for comparing results obtained by different researchers and draw guidelines on the number of grains that must be used in order to avoid grain-size effects.

Outflow and clogging of shape-anisotropic grains in hoppers with small apertures

Outflow of granular material through a small orifice is a fundamental process in many industrial fields, for example in silo discharge, and in everyday's life. Most experimental studies of the dynamics have been performed so far with monodisperse disks in two-dimensional (2D) hoppers or spherical grains in 3D. We investigate this process for shape-anisotropic grains in 3D hoppers and discuss the role of size and shape parameters on avalanche statistics, clogging states, and mean flow velocities. It is shown that an increasing aspect ratio of the grains leads to lower flow rates and higher clogging probabilities compared to spherical grains. On the other hand, the number of grains forming the clog is larger for elongated grains of comparable volumes, and the long axis of these blocking grains is preferentially aligned towards the center of the orifice. We find a qualitative transition in the hopper discharge behavior for aspect ratios larger than ≈6. At still higher aspect ratios >8-12, the outflowing material leaves long vertical holes in the hopper that penetrate the complete granular bed. This changes the discharge characteristics qualitatively.

Ant aggregations self-heal to compensate for the Ringelmann effect

Fire ants, Solenopsis invicta, link their bodies together to form structures such as rafts, bivouacs and bridges. Such structures are in danger of being damaged by natural disturbances such as passing water currents. In this combined experimental and theoretical study, we investigate the self-healing of ant assemblages. We press two ant aggregations together and measure the forces to pull them apart. As the group size increases, the contribution of each ant decreases. This phenomenon, known as the Ringelmann effect, or social loafing, has previously been shown for cattle and humans. In this study, we show that it is a challenge for ants as well. We rationalize this effect with an agent-based simulation which exhibits the Ringelmann effect of ants that periodically make and break links with each other, but grip with higher probability if the ants are stretched. Over time, ants compensate for the Ringelmann effect by building more links. We use a mathematical model to show that the rate of new links is proportional to the number of free ants in the cluster. The principles found here may inspire new directions in self-healing and active materials.

Feasibility of Crosslinked Acrylic Shape Memory Polymer for a Thrombectomy Device

Purpose

To evaluate the feasibility of utilizing a system of SMP acrylates for a thrombectomy device by determining an optimal crosslink density that provides both adequate recovery stress for blood clot removal and sufficient strain capacity to enable catheter delivery.

Methods

Four thermoset acrylic copolymers containing benzylmethacrylate (BzMA) and bisphenol A ethoxylate diacrylate (Mn~512, BPA) were designed with differing thermomechanical properties. Finite element analysis (FEA) was performed to ensure that the materials were able to undergo the strains imposed by crimping, and fabricated devices were subjected to force-monitored crimping, constrained recovery, and bench-top thrombectomy.

Results

Devices with 25 and 35 mole% BPA exhibited the highest recovery stress and the highest brittle response as they broke upon constrained recovery. On the contrary, the 15 mole % BPA devices endured all testing and their recovery stress (5 kPa) enabled successful bench-top thrombectomy in 2/3 times, compared to 0/3 for the devices with the lowest BPA content.

Conclusion

While the 15 mole% BPA devices provided the best trade-off between device integrity and performance, other SMP systems that offer recovery stresses above 5 kPa without increasing brittleness to the point of causing device failure would be more suitable for this application.

Computer simulations of the collapse of columns formed by elongated grains

A numerical investigation of the collapse of granular columns has been conducted. In particular, we address the effect of the grain shape on the properties of the collapse. We show that the final runout and height of the deposits scale as a power law of the initial aspect ratio of the column, a, independently of the elongation of the grains used. We describe this process in terms of an energy balance, and construct an "inertial number" that can be used to describe the flow in terms of a recently proposed granular rheology. We argue that an effective friction that results from this dimensionless quantity explains why the shape of the grains is irrelevant for the final properties of the collapse.

Entangled granular media

We study the geometrically induced cohesion of ensembles of granular "u particles" that mechanically entangle through particle interpenetration. We vary the length-to-width ratio l/w of the u particles and form them into freestanding vertical columns. In a laboratory experiment, we monitor the response of the columns to sinusoidal vibration (with peak acceleration Γ). Column collapse occurs in a characteristic time τ which follows the relation τ∝exp(Γ/Δ). Δ resembles an activation energy and is maximal at intermediate l/w. A simulation reveals that optimal strength results from competition between packing and entanglement.

Entangled granular media

We study the geometrically induced cohesion of ensembles of granular "u particles" that mechanically entangle through particle interpenetration. We vary the length-to-width ratio l/w of the u particles and form them into freestanding vertical columns. In a laboratory experiment, we monitor the response of the columns to sinusoidal vibration (with peak acceleration Γ). Column collapse occurs in a characteristic time τ which follows the relation τ∝exp(Γ/Δ). Δ resembles an activation energy and is maximal at intermediate l/w. A simulation reveals that optimal strength results from competition between packing and entanglement.

Relation between self-organized criticality and grain aspect ratio in granular piles

We investigate experimentally whether self-organized criticality (SOC) occurs in granular piles composed of different grains, namely, rice, lentils, quinoa, and mung beans. These four grains were selected to have different aspect ratios, from oblong to oblate. As a function of aspect ratio, we determined the growth (β) and roughness (α) exponents, the avalanche fractal dimension (D), the avalanche size distribution exponent (τ), the critical angle (γ), and its fluctuation. At superficial inspection, three types of grains seem to have power-law-distributed avalanches with a well-defined τ. However, only rice is truly SOC if we take three criteria into account: a power-law-shaped avalanche size distribution, finite size scaling, and a universal scaling relation relating characteristic exponents. We study SOC as a spatiotemporal fractal; in particular, we study the spatial structure of criticality from local observation of the slope angle. From the fluctuation of the slope angle we conclude that greater fluctuation (and thus bigger avalanches) happen in piles consisting of grains with larger aspect ratio.