Molecular dynamics simulation of complex particles in three dimensions and the study of friction due to nonconvexity

Secondary flow in ensembles of nonconvex granular particles under shear

Studies of granular materials, both theoretical and experimental, are often restricted to convex grain shapes. We demonstrate that a nonconvex grain shape can lead to a qualitatively novel macroscopic dynamics. Spatial crosses (hexapods) are continuously sheared in a split-bottom container. Thereby, they develop a secondary flow profile that is completely opposite to that of rod-shaped or lentil-shaped convex grains in the same geometry. The crosses at the surface migrate towards the rotation center and sink there mimicking a "reverse Weissenberg effect." The observed surface flow field suggests the existence of a radial outward flow in the depth of the granular bed, thus, forming a convection cell. This flow field is connected with a dimple formed in the rotation center. The effect is strongly dependent on the particle geometry and the height of the granular bed.

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.

The effect of particle shape on discharge and clogging

Granular flow is common across different fields from energy resource recovery and mineral processing to grain transport and traffic flow. Migrating particles may jam and form arches that span constrictions and hinder particle flow. Most studies have investigated the migration and clogging of spherical particles, however, natural particles are rarely spherical, but exhibit eccentricity, angularity and roughness. New experiments explore the discharge of cubes, 2D crosses, 3D crosses and spheres under dry conditions and during particle-laden fluid flow. Variables include orifice-to-particle size ratio and solidity. Cubes and 3D crosses are the most prone to clogging because of their ability to interlock or the development of face-to-face contacts that can resist torque and enhance bridging. Spheres arriving to the orifice must be correctly positioned to create stable bridges, while flat 2D crosses orient their longest axes in the direction of flowlines across the orifice and favor flow. Intermittent clogging causes kinetic retardation in particle-laden flow even in the absence of inertial effects; the gradual increase in the local particle solidity above the constriction enhances particle interactions and the probability of clogging. The discharge volume before clogging is a Poisson process for small orifice-to-particle size ratio; however, the clogging probability becomes history-dependent for non-spherical particles at large orifice-to-particle size ratio and high solidities, i.e., when particle–particle interactions and interlocking gain significance.

Shear strength and microstructure of polydisperse packings: The effect of size span and shape of particle size distribution

By means of extensive contact dynamics simulations, we analyzed the effect of particle size distribution (PSD) on the strength and microstructure of sheared granular materials composed of frictional disks. The PSDs are built by means of a normalized β function, which allows the systematic investigation of the effects of both, the size span (from almost monodisperse to highly polydisperse) and the shape of the PSD (from linear to pronouncedly curved). We show that the shear strength is independent of the size span, which substantiates previous results obtained for uniform distributions by packing fraction. Notably, the shear strength is also independent of the shape of the PSD, as shown previously for systems composed of frictionless disks. In contrast, the packing fraction increases with the size span, but decreases with more pronounced PSD curvature. At the microscale, we analyzed the connectivity and anisotropies of the contacts and forces networks. We show that the invariance of the shear strength with the PSD is due to a compensation mechanism which involves both geometrical sources of anisotropy. In particular, contact orientation anisotropy decreases with the size span and increases with PSD curvature, while the branch length anisotropy behaves inversely.

Random three-dimensional jammed packings of elastic shells acting as force sensors

In a jammed solid of granular particles, the applied stress is in-homogeneously distributed within the packing. A full experimental characterization requires measurement of all the interparticle forces, but so far such measurements are limited to a few systems in two and even fewer in three dimensions. Particles with the topology of (elastic) shells are good local force sensors as relatively large deformations of the shells result from relatively small forces. We recently introduced such fluorescent shells as a model granular system in which force distributions can be determined in three dimensions using confocal microscopy and quantitative image analysis. An interesting aspect about these shells that differentiates them from other soft deformable particles is their buckling behavior at higher compression. This leads to deformations that do not conserve the inner volume of the particle. Here we use this system to accurately measure the contact forces in a three-dimensional packing of shells subjected to a static anisotropic compression and to shear. At small deformations forces are linear, however, for a buckled contact, the restoring force is related to the amount of deformation by a square root law, as follows from the theory of elasticity of shells. Near the unjamming-jamming transition (point J), we found the probability distribution of the interparticle forces P(f) to decay nearly exponentially at large forces, with little evidence of long-range force chains in the packings. As the packing density is increased, the tail of the distribution was found to crossover to a Gaussian, in line with other experimental and simulation studies. Under a small shear strain, up to 0.216, applied at an extremely low shear rate, we observed a shear-induced anisotropy in both the pair correlation function and contact force network; however, no appreciable change was seen in the number of contacts per particle.

Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles

We investigated the settling dynamics of irregularly shaped particles in a still fluid under a wide range of conditions with Reynolds numbers Re varying between 1 and 2000, sphericity ϕ and circularity c both greater than 0.5, and Corey shape factor (CSF) less than 1. To simulate the particle settling process, a modified lattice Boltzmann model combined with a turbulence module was adopted. This model was first validated using experimental data for particles of spherical and cubic shapes. For irregularly shaped particles, two different types of settling behaviors were observed prior to particles reaching a steady state: accelerating and accelerating-decelerating, which could be distinguished by a critical CSF value of approximately 0.7. The settling dynamics were analyzed with a focus on the projected areas and angular velocities of particles. It was found that a minor change in the starting projected area, an indicator of the initial particle orientation, would not strongly affect the settling velocity for low Re. Periodic oscillations developed for all simulated particles when Re>100. The amplitude of these oscillations increased with Re. However, the periods were not sensitive to Re. The critical Re that defined the transition between the steady and periodically oscillating behaviors depended on the inertia tensor. In particular, the maximum eigenvalue of the inertia tensor played a major role in signaling this transition in comparison to the intermediate and minimum eigenvalues.

Optimizing packing fraction in granular media composed of overlapping spheres

What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution. Arbitrary particle shape is represented by a set of overlapping spheres of varying diameter, enabling us to approximate smooth surfaces with a resolution proportional to the number of spheres included. We discover a family of planar triangular particles, whose packing fraction of ϕ ∼ 0.73 is among the highest experimental results for disordered packings of frictionless particles. We investigate how ϕ depends on the arrangement of spheres comprising an individual particle and on the smoothness of the surface. We validate the simulations with experiments using 3D-printed copies of the simplest member of the family, a planar particle consisting of three overlapping spheres with identical radius. Direct experimental comparison with 3D-printed aspherical ellipsoids demonstrates that the triangular particles pack exceedingly well not only in the limit of large system size but also when confined to small containers.

Celebrating Soft Matter's 10th Anniversary: toward jamming by design

In materials science, high performance is typically associated with regularity and order, while disorder and the presence of defects are assumed to lead to sub-optimal outcomes. This holds for traditional solids such as crystals as well as for many types of nanoscale devices. However, there are circumstances where disorder can be harnessed to achieve performance not possible with approaches based on regularity. Recent research has shown opportunities specifically for soft matter. There, the phenomenon of jamming leads to unique emergent behavior that enables disordered, amorphous systems to switch reversibly between solid-like rigidity and fluid-like plasticity. This makes it possible to envision materials that can change stiffness or even shape adaptively. We review some of the progress in this direction, discussing examples where jamming has been explored from micro to macro scales in colloidal systems, suspensions, granular-materials-enabled soft robotics, and architecture. We focus in particular on how the jammed aggregate state can be tailored by controlling particle level properties and discuss very recent ideas that provide an important first step toward actual design of specifically targeted jamming behavior.

Particle alignment and clustering in sheared granular materials composed of platy particles

By means of molecular dynamics simulations, we investigate the texture and local ordering in sheared packings composed of cohesionless platy particles. The morphology of large packings of platy particles in quasistatic equilibrium is complex due to the combined effects of local nematic ordering of the particles and anisotropic orientations of contacts between particles. We find that particle alignment is strongly enhanced by the degree of platyness and leads to the formation of face-connected clusters of exponentially decaying size. Interestingly, due to dynamics in continuous shearing, this ordering phenomenon emerges even in systems composed of particles of very low platyness differing only slightly from spherical shape. The number of clusters is an increasing function of platyness. However, at high platyness the proportion of face-face interactions is too low to allow for their percolation throughout the system.

Isostaticity at frictional jamming

Amorphous packings of frictionless, spherical particles are isostatic at jamming onset, with the number of constraints (contacts) equal to the number of degrees of freedom. Their structural and mechanical properties are controlled by the interparticle contact network. In contrast, amorphous packings of frictional particles are typically hyperstatic at jamming onset. We perform extensive numerical simulations in two dimensions of the geometrical asperity (GA) model for static friction to further investigate the role of isostaticity. In the GA model, interparticle forces are obtained by summing up purely repulsive central forces between periodically spaced circular asperities on contacting grains. We compare the packing fraction, contact number, mobilization distribution, and vibrational density of states (in the harmonic approximation) using the GA model to those generated using the Cundall-Strack approach. We find that static packings of frictional disks obtained from the GA model are mechanically stable and isostatic when we consider interactions between asperities on contacting particles. The crossover in the structural and mechanical properties of static packings from frictionless to frictional behavior as a function of the static friction coefficient coincides with a change in the type of interparticle contacts and the disappearance of a peak in the density of vibrational modes for the GA model. These results emphasize that mesoscale features of the model for static friction play an important role in determining the properties of granular packings.

Rheology of three-dimensional packings of aggregates: microstructure and effects of nonconvexity

We use three-dimensional contact dynamics simulations to analyze the rheological properties of granular materials composed of rigid aggregates. The aggregates are made from four overlapping spheres and described by a nonconvexity parameter depending on the relative positions of the spheres. The macroscopic and microstructural properties of several sheared packings are analyzed as a function of the degree of nonconvexity of the aggregates. We find that the internal angle of friction increases with the nonconvexity. In contrast, the packing fraction first increases to a maximum value but declines as the nonconvexity increases further. At a high level of nonconvexity, the packings are looser but show a higher shear strength. At the microscopic scale, the fabric and force anisotropy, as well as the friction mobilization, are enhanced by multiple contacts between aggregates and interlocking, thus revealings the mechanical and geometrical origins of shear strength.

Adapting granular materials through artificial evolution

Over 200 years after Coulomb's studies, a general connection between the mechanical response of a granular material and the constituents' shape remains unknown. The key difficulty in articulating this relationship is that shape is an inexhaustible parameter, making its systematic exploration infeasible. Here we show that the role of particle shape can, however, be explored efficiently when granular design is viewed in the context of artificial evolution. By introducing a mutable representation for particle shapes, we demonstrate with computer simulation how shapes can be evolved. As proof of principle, we predicted motifs that link shape to packing stiffness, discovered a particle that produces aggregates that stiffen-rather than weaken-under compression, and verified the results using three-dimensional printing. More generally, our approach facilitates the exploration of the role of arbitrary particle geometry in jammed systems, and invites the discovery and design of granular matter with optimized properties.

Influence of the feeding mechanism on deposits of square particles

In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ.

Stress distribution of faceted particles in a silo after its partial discharge

We present experimental and numerical results of the effect that a partial discharge has on the morphological and micro-mechanical properties of non-spherical, convex particles in a silo. The comparison of the particle orientation after filling the silo and its subsequent partial discharge reveals important shear-induced orientation, which affects stress propagation. For elongated particles, the flow induces an increase in the packing disorder which leads to a reduction of the vertical stress propagation developed during the deposit generated prior to the partial discharge. For square particles, the flow favors particle alignment with the lateral walls promoting a behavior opposite to the one of the elongated particles: vertical force transmission, parallel to gravity, is induced. Hence, for elongated particles the flow developed during the partial discharge of the silo leads to force saturation with depth whereas for squares the flow induces hindering of the force saturation observed during the silo filling.

Minkowski-Voronoi diagrams as a method to generate random packings of spheropolygons for the simulation of soils

Minkowski operators (dilation and erosion of sets in vector spaces) have been extensively used in computer graphics, image processing to analyze the structure of materials, and more recently in molecular dynamics. Here, we apply those mathematical concepts to extend the discrete element method to simulate granular materials with complex-shaped particles. The Voronoi-Minkowski diagrams are introduced to generate random packings of complex-shaped particles with tunable particle roundness. Contact forces and potentials are calculated in terms of distances instead of overlaps. By using the Verlet method to detect neighborhood, we achieve CPU times that grow linearly with the body's number of sides. Simulations of dissipative granular materials under shear demonstrate that the method maintains conservation of energy in accord with the first law of thermodynamics. A series of simulations for biaxial test, shear band formation, hysteretic behavior, and ratcheting show that the model can reproduce the main features of real granular-soil behavior.

Molecular dynamics simulations of complex-shaped particles using Voronoi-based spheropolyhedra

The spheropolyhedra method has been used earlier for efficient and accurate molecular dynamics simulations of granular matter with particles with complex shapes. Also the Voronoi construction is a tool of proved utility for the virtual representation of powders and grains. In this paper a technique that combines the two methods and provides a framework for the study of the three-dimensional mechanical behavior of granular matter is proposed. In order to understand the capabilities of the new method, a number of computer simulations of the cubic (true) triaxial test, measuring the mechanical behavior of packing of particles, is carried out. Results from tests with packing of complex-shaped particles represented by "Voronoi particles" are compared with corresponding results of packing of spherical particles. Features such as the saturation value for the macroscopically observed coefficient of friction, as reported in the literature, are compared for the packing of spheres and for the packing of "Voronoi particles," showing that the difference in shape strongly affects the results. The proposed technique and simulation results can be used to help understand how the individual shape of grains affects the macroscopic mechanical behavior of granular matter such as cohesionless soils.