Session L33: Invited Session: Frontiers of Granular Physics

Packing Nonspherical Particles: All Shapes Are Not Created Equal

Over the past decade there has been increasing interest in the effects of particle shape on the characteristics of dense particle packings, since deviations from sphericity can lead to more realistic models of granular media, nanostructured materials, and tissue architecture. It is clear the that the broken rotational symmetry of a nonspherical particle is a crucial aspect in determining its resulting packing characteristics, but given the infinite variety of possible shapes (ellipsoids, superballs, regular and irregular polyhedra, etc.) it is desirable to formulate packing organizing principles based the particle shape. Such principles are beginning to be elucidated; see Refs. 1 and 2 and references therein. Depending upon whether the particle has central symmetry, inequivalent principle axes, and smooth or flat surfaces, we can describe the nature of its densest packing (which is typically periodic) as well as its disordered jammed states (which may or may not be isostatic). Changing the shape of a particle can dramatically alter its packing attributes. This tunability capability via particle shape could be used to tailor many-particle systems (e.g., colloids and granular media) to have designed crystal, liquid and glassy states. \\[4pt] [1] S. Torquato and F. H. Stillinger, ``Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond," {\it Rev. Modern Phys.} {\bf 82}, 2633 (2010). \\[0pt] [2] Y. Jiao and S. Torquato, Communication: ``A Packing of Truncated Tetrahedra That Nearly Fills All of Space and its Melting Properties," {\it J. Chem. Phys.} {\bf 135}, 151101 (2011).   

Network Analysis of Granular Flows

The flow of granular materials is important to many natural and industrial processes, yet connecting microscale materials properties of grains to bulk flow behavior has remained a challenging task. Our work leverages tools from complex network theory to study granular flow at multiple scales. By characterizing the statistical properties of time-evolving contact networks using metrics like average path length, giant component size, and modularity, we are able to identify how macroscale system features like the loss of reversibility are connected to micro- and meso- scale rearrangements in the contact network. In addition, we employ a network-based approach to explore the role of rotations in facilitating cooperative rearrangements. For both the reversibility and rotation studies, we apply network analysis to time-dependent contact network data obtained from both experiments and simulations and show that this approach can provide new insights on how bulk system properties are connected to particle-scale motion.   

Swimming in a granular frictional fluid

X-ray imaging reveals that the sandfish lizard swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. To model the locomotion of the sandfish, we previously developed an empirical resistive force theory (RFT), a numerical sandfish model coupled to an experimentally validated Discrete Element Method (DEM) model of the granular medium, and a physical robot model. The models reveal that only grains close to the swimmer are fluidized, and that the thrust and drag forces are dominated by frictional interactions among grains and the intruder. In this talk I will use these models to discuss principles of swimming within these granular ``frictional fluids". The empirical drag force laws are measured as the steady-state forces on a small cylinder oriented at different angles relative to the displacement direction. Unlike in Newtonian fluids, resistive forces are independent of speed. Drag forces resemble those in viscous fluids while the ratio of thrust to drag forces is always larger in the granular media than in viscous fluids. Using the force laws as inputs, the RFT overestimates swimming speed by approximately 20\%. The simulation reveals that this is related to the non-instantaneous increase in force during reversals of body segments. Despite the inaccuracy of the steady-state assumption, we use the force laws and a recently developed geometric mechanics theory to predict optimal gaits for a model system that has been well-studied in Newtonian fluids, the three-link swimmer. The combination of the geometric theory and the force laws allows us to generate a kinematic relationship between the swimmer's shape and position velocities and to construct connection vector field and constraint curvature function visualizations of the system dynamics. From these we predict optimal gaits for forward, lateral and rotational motion. Experiment and simulation are in accord with the theoretical prediction, and demonstrate that swimming in sand can be viewed as movement in a localized frictional fluid.   

Geometrically Cohesive Granular Materials

Geometrically cohesive granular materials (GCGM) are collections of particles whose individual shape leads to entanglements that resist extension forces, resulting in a non-zero Young's modulus. Examples include long, thin (anisometric) rods, arcs of varying length, and U-shaped staples. I will report on experimental and computational work that investigates the peculiar rigidity of GCGM. These include canonical stress-strain and vibration-induced melting experiments on U-shaped staples that have revealed a non-monotonic dependence of collective rigidity on particle shape. For concave particles, rigidity appears proportional to an ``entanglement number'' --- the number of neighbors that pass through the area partially bounded by the particle. Computational and analytic work on arcs and staples confirm the non-monotonic behavior of the entanglement number, and simulations that match the experimental conditions are underway to confirm entanglement as the basic mechanism of GCGM's rigidity.   

Strain-stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model polymer system to investigate the consequences of entanglements in the absence of Brownian motion. The packings are compressed uniaxially and the structure is characterized by x-ray tomography. For short chain lengths, these packings yield when the shear stress exceeds the scale of the confining pressure, similar to packings of spherical particles. In contrast, packings of chains which are long enough to bend into closed loops exhibit strain-stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. These strain-stiffening packings are found to contain system-spanning clusters of entangled chains.