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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]

Summary: The material point method (MPM) is a robust numerical simulation approach for continuum mechanics problems involving large material deformations coupled to changing surface topographies. These types of problems are present in many different engineering contexts, from understanding the failure processes of earthen slopes to predicting the strengths and failure mechanisms of body armor to modeling the impact forces of waves in fluid tanks. By using a set of persistent material point tracers to follow the motion and deformation of the continuum material while solving the equations of motion on a static simulation grid, the MPM avoids several shortcomings of more traditional numerical approaches including blurring of material surfaces — as in Eulerian finite element or finite volume methods (FEMs or FVMs) — and mesh tangling — as in Lagrangian FEMs. Despite its robustness, MPM is known to develop significant numerical errors: namely, (i) the particle ringing instability and (ii) solution dependent discretization and integration errors. In this work, we present an analysis of local‐in‐time, spatial integration errors in the MPM and several techniques designed to mitigate these errors. Error mitigation approaches previously described in the literature are compared to a new method we propose for problems involving very large material deformations. The proposed method is shown to offer substantial improvement over standard MPM for simulations of fluid‐like materials without requiring significant augmentation of existing MPM frameworks. [ABSTRACT FROM AUTHOR]

Near the threshold of grain motion, sediment transport is "on‐off" intermittent, characterized by large but rare bursts separated by long periods of low transport. Without models that can account for the effects of intermittency, measurements of average sediment flux can be in error by up to an order of magnitude. Despite its known presence and impact, it is not clear whether on‐off intermittency arises from the grain activity (the number of moving grains) or grain velocities, which together determine the sediment flux. We use laboratory flume experiments to show that the on‐off intermittency has its origins in the velocity distributions of grains that move by rolling along the bed, whereas grain activity is not on‐off intermittent. Incorporating the types of intermittency we identify into stochastic models of sediment transport could yield improved predictions of sediment flux, including physically based estimates of the uncertainty in time‐averaged sediment flux. Plain Language Summary: Sediment, such as sand and gravel, is transported across the surface of the Earth and other planets by wind and water. Predicting the amount of sediment that can be transported given a certain flow rate is crucial for predicting how a landscape will change over time. For low flow rates, little to no grain motion occurs. Just beyond the flow rate required for motion, sediment transport occurs mostly in rare bursts. This so‐called "on‐off" intermittency creates difficulties when trying to measure the average transport rate, which must be done over longer time periods as the bursts become larger but less frequent. While on‐off intermittency has been identified in previous studies of sediment transport, there is currently no understanding of its physical origin. We use a series of experiments in a small laboratory river to show that the on‐off intermittency is due to large fluctuations in the speed of the grains rolling on the bed, and that the sediment transport becomes less bursty as more grains are lifted off the river bed and into the fluid. Our results will pave the way for better measurements and predictions of sediment transport in rivers. Key Points: We use grain tracking data from laboratory experiments to separately study the statistics of grain velocities and grain activityWe show that on‐off intermittency has its origins in the velocity distributions of grains, not in the grain activityOn‐off intermittency comes from grains rolling on the bed, and disappears as more and more grains are lifted into the bulk of the flow [ABSTRACT FROM AUTHOR]

The gut-brain axis, which is mediated via enteric and central neurohormonal signaling, is known to regulate a broad set of physiological functions from feeding to emotional behavior. Various pharmaceuticals and surgical interventions, such as motility agents and bariatric surgery, are used to modulate this axis. Such approaches, however, are associated with off-target effects or post-procedure recovery time and expose patients to substantial risks. Electrical stimulation has also been used to attempt to modulate the gut-brain axis with greater spatial and temporal resolution. Electrical stimulation of the gastrointestinal (GI) tract, however, has generally required invasive intervention for electrode placement on serosal tissue. Stimulating mucosal tissue remains challenging because of the presence of gastric and intestinal fluid, which can influence the effectiveness of local luminal stimulation. Here, we report the development of a bioinspired ingestible fluid-wicking capsule for active stimulation and hormone modulation (FLASH) capable of rapidly wicking fluid and locally stimulating mucosal tissue, resulting in systemic modulation of an orexigenic GI hormone. Drawing inspiration from Moloch horridus, the "thorny devil" lizard with water-wicking skin, we developed a capsule surface capable of displacing fluid. We characterized the stimulation parameters for modulation of various GI hormones in a porcine model and applied these parameters to an ingestible capsule system. FLASH can be orally administered to modulate GI hormones and is safely excreted with no adverse effects in porcine models. We anticipate that this device could be used to treat metabolic, GI, and neuropsychiatric disorders noninvasively with minimal off-target effects. [ABSTRACT FROM AUTHOR]

Granular materials have a strange propensity to behave as either a complex media or a simple media depending on the precise question being asked. This review paper offers a summary of granular flow rheologies for well-developed or steady-state motion, and seeks to explain this dichotomy through the vast range of complexity intrinsic to these models. A key observation is that to achieve accuracy in predicting flow fields in general geometries, one requires a model that accounts for a number of subtleties, most notably a nonlocal effect to account for cooperativity in the flow as induced by the finite size of grains. On the other hand, forces and tractions that develop on macro-scale, submerged boundaries appear to be minimally affected by grain size and, barring very rapid motions, are well represented by simple rate-independent frictional plasticity models. A major simplification observed in experiments of granular intrusion, which we refer to as the ‘resistive force hypothesis’ of granular Resistive Force Theory, can be shown to arise directly from rate-independent plasticity. Because such plasticity models have so few parameters, and the major rheological parameter is a dimensionless internal friction coefficient, some of these simplifications can be seen as consequences of scaling.

Bedload sediment transport is ubiquitous in shaping natural and engineered landscapes, but the variability in the relation between sediment flux and driving factors is not well understood. At a given Shields number, the observed dimensionless transport rate can vary over a range in controlled systems and up to several orders of magnitude in natural streams. Here, we (a) experimentally validate a resolved fluid‐grain numerical scheme (Lattice Boltzmann Method‐Discrete Element Method or DEM‐LBM), and use it to (b) explore the parameter space controlling sediment transport in simple systems. Wide wall‐free simulations show the dimensionless transport rate is not influenced by the slope, fluid depth, mean particle size, particle surface friction, or grain‐grain damping for gentle slopes (0.01–0.03) at a medium to high fixed Shields number. (c) Examination of small‐scale fluid‐grain interactions shows fluid torque is non‐negligible for the entrainment and sediment transport near the threshold. And (d) the simulations guide the formulation of continuum models for the transport process. We present an upscaled two‐phase continuum model for grains in a turbulent fluid and validate it against bedload transport DEM‐LBM simulations. To model the creeping granular flow under the bed surface, we use an extension of the Nonlocal Granular Fluidity model, which was previously shown to account for flow cooperativity from grain‐size‐effects in dry media. The model accurately predicts the exponentially decaying velocity profile deeper into the bed. Plain Language Summary: Sediment transport caused by particles rolling, sliding, and hopping on a river bed is called bedload transport. Semi‐empirical formulas to predict bedload sediment flux from the driving factors, known as the transport relation, can be highly inaccurate. Simulations where the sediment particles are fully resolved are carried out to find if the predictions can be improved by considering more particle parameters. After being validated against flume experiments, the numerical scheme is used to simulate bedload transport under many conditions, and its results show that at a fixed relative hydrodynamic driving force, varying river slope (on gentle slopes), fluid depth, mean particle size, particle surface sliding friction coefficient, and grain‐grain damping coefficient cause almost no variation of the transport rate. The simulations also shed light on the microscopic mechanisms such as how the fluid torque on particles helps initiate rolling and subsequent grain transport. We further use the numerical scheme to guide development of an alternative framework that can predict the flow profiles for the fast transport as well as the gradual transport beneath the bed surface without resolving the individual particles, which is a more tractable way to model large‐scale bedload sediment transport problems. Key Points: Particle‐scale bedload transport simulations agree with flume experimentsSimulations probe the small‐scale mechanisms and parameter dependences in the transport relationParticle simulations guide continuum model development for turbulent sediment transport and bed creep [ABSTRACT FROM AUTHOR]

Granular flow in a silo demonstrates multiple non-local rheological phenomena due to the finite size of grains. We solve the non-local granular fluidity continuum model in quasi-two-dimensional silo geometries and evaluate its ability to predict these non-local effects, including flow spreading and, importantly, clogging (arrest) when the opening is small enough. The model is augmented to include a free-separation criterion and is implemented numerically with an extension of the trans-phase granular flow solver described in Dunatunga & Kamrin (J. Fluid Mech., vol. 779, 2015, pp. 483–513), to produce full-field solutions. The implementation is validated against analytical results of the model in the inclined chute geometry, such as the solution for the critical thickness for flow arrest, and the velocity profile as a function of layer height. We then implement the model in the silo geometry and vary the apparent grain size. The model predicts a clogging criterion when the opening competes with the scale of the mean grain size, which agrees with previous experimental studies. For larger openings, the flow within the silo obtains a diffusive characteristic whose spread depends on the model’s non-local amplitude and the mean grain size. The numerical tests are controlled for grid effects and a comparison study of coarse vs refined numerical simulations shows agreement in the pressure field, the shape of the arch in a clogged silo configuration and the velocity field in a flowing configuration. [ABSTRACT FROM AUTHOR]

Sediment transport by wind or water near the threshold of grain motion is dominated by rare transport events. This intermittency makes it difficult to calibrate sediment transport laws, or to define an unambiguous threshold for grain entrainment, both of which are crucial for predicting sediment transport rates. We present a model that captures this intermittency and shows that the noisy statistics of sediment transport contain useful information about the sediment entrainment threshold and the variations in driving fluid stress. Using a combination of laboratory experiments and analytical results, we measure the threshold for grain entrainment in a novel way and introduce a new property, the "shear stress variability", which predicts conditions under which transport will be intermittent. Our work suggests strategies for improving measurements and predictions of sediment flux and hints that the sediment transport law may change close to the threshold of motion. Plain Language Summary: Sediment transport by wind or water is intermittent―Displaying long periods of low transport followed by sudden large transport events. Intermittency is commonly seen as unwanted noise that makes it difficult to predict sediment flux. We introduce a mathematical model for sediment transport near the threshold of motion which provides a possible explanation for why and when intermittency occurs, and show that the noisy statistics of intermittent sediment transport encode information about the threshold of sediment motion and the variations in driving fluid forces. This knowledge can help improve the accuracy of sediment transport predictions, which are central to many engineering and geological applications. The ingredients necessary for intermittency―Noise near a transition―apply to many systems beyond sediment transport. Key Points: Sediment transport near the threshold of motion is intermittent, making it hard to measure average flux, which is crucial for predictionsWe use bifurcation theory in the presence of multiplicative noise to understand and describe the intermittencyApplying this to flume experiments, we find a new way of measuring the threshold of motion and predicting when intermittency will be present [ABSTRACT FROM AUTHOR]

We present a general simulation approach for incompressible fluid–structure interactions in a fully Eulerian framework using the reference map technique. The approach is suitable for modeling one or more rigid or finitely deformable objects or soft objects with rigid components interacting with the fluid and with each other. It is also extended to control the kinematics of structures in fluids. The model is based on our previous Eulerian fluid–soft solver [Rycroft et al., "Reference map technique for incompressible fluid–structure interaction," J. Fluid Mech. 898, A9 (2020)] and generalized to rigid structures by constraining the deformation-rate tensor in a projection framework. Several numerical examples are presented to illustrate the capability of the method. [ABSTRACT FROM AUTHOR]

We present a general simulation approach for fluid–solid interactions based on the fully Eulerian reference map technique. The approach permits the modelling of one or more finitely deformable continuum solid bodies interacting with a fluid and with each other. A key advantage of this approach is its ease of use, as the solid and fluid are discretized on the same fixed grid, which greatly simplifies the coupling between the phases. We use the method to study a number of illustrative examples involving an incompressible Navier–Stokes fluid interacting with multiple neo-Hookean solids. Our method has several useful features including the ability to model solids with sharp corners and the ability to model actuated solids. The latter permits the simulation of active media such as swimmers, which we demonstrate. The method is validated favourably in the flag-flapping geometry, for which a number of experimental, numerical and analytical studies have been performed. We extend the flapping analysis beyond the thin-flag limit, revealing an additional destabilization mechanism to induce flapping. [ABSTRACT FROM AUTHOR]

In this work, we examine the predictions of the constitutive model proposed in Baumgarten and Kamrin [Baumgarten and Kamrin, Proc. Natl. Acad. Sci. U.S.A. 116, 20828–20836 (2019)], as it relates to the transient relaxation of shear stresses in dense, fine-particle suspensions such as water-cornstarch or water-poly(methyl methacrylate) mixtures. Such mixtures are known to exhibit dramatic increases in viscosity when impacted or sheared, and in rate-controlled experiments, these mixtures are also observed to support shear stresses long after all macroscopic flow has stopped. We show that the experimental observations of substantially longer stress decay in these mixtures compared with standard Newtonian fluids can be captured by the model through its evolution of the internal state variable, f , which reflects the fraction of frictional contacts at the microscale. Analysis of the behavior of f suggests that the presence of system spanning granular contact networks and the associated rate of decay of the elastic energy stored in these networks is responsible for the observed phenomena. [ABSTRACT FROM AUTHOR]

We propose a technique to simulate granular materials that exploits the dual strengths of discrete and continuum treatments. Discrete element simulations provide unmatched levels of detail and generality, but prove excessively costly when applied to large scale systems. Continuum approaches are computationally tractable, but limited in applicability due to built-in modeling assumptions; e.g., models suitable for granular flows typically fail to capture clogging, bouncing and ballistic motion. In our hybrid approach, an oracle dynamically partitions the domain into continuum regions where safe, and discrete regions where necessary. The domains overlap along transition zones, where a Lagrangian dynamics mass-splitting coupling principle enforces agreement between the two simulation states. Enrichment and homogenization operations allow the partitions to evolve over time. This approach accurately and efficiently simulates scenarios that previously required an entirely discrete treatment. [ABSTRACT FROM AUTHOR]