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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.

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.

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.

This paper proposes novel and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). To address the modeling of Newtonian fluids with incompressibility constraints, a new mixed implicit MPM formulation is proposed. Here, instead of solving the velocity and pressure fields as the unknown variables like the typical Eulerian computational fluid dynamics (CFD) solver, the proposed approach adopts a monolithic displacement–pressure formulation inspired by the mixed-form updated-Lagrangian Finite Element Method (FEM). To satisfy the inf–sup stability condition, two stabilization strategies are integrated into the formulation: the variational multiscale method (VMS) and the pressure-stabilization Petrov–Galerkin method (PSPG). By concurrently solving the displacement and pressure fields, the developed monolithic solver obviates the need for free-surface detection as well as Dirichlet and Neumann pressure imposition, in contrast to the fractional-step method. This attribute mitigates spurious pressure and velocity oscillations in simulating dynamic and transient flow problems. This study also addresses other prevalent challenges in MPM simulations, such as the pressure oscillations triggered by cell-crossing errors, particle-distribution-induced quadrature errors, and particle-grid information transfer. To resolve these issues, the quadratic B-Spline basis function, the delta-correction method, and the Taylor particle-in-cell method are incorporated into the proposed mixed MPM formulation, thereby enhancing numerical stability. The efficacy of the proposed stabilized incompressible MPM framework is validated through several benchmark cases, comparing the obtained results with other numerical methods and analytical solutions. Furthermore, the method’s capability in simulating real-world problems involving violent free-surface fluid motion is demonstrated through comparisons with experimental results of w

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.

This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both non-porous and porous domains. In contrast to the conventional Eulerian computational fluid dynamics (CFD) solver, which solves the velocity and pressure fields as unknown variables, the proposed method employs a monolithic displacement-pressure formulation adopted from the mixed-form updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup stability condition, a stabilization strategy based on the variational multiscale method (VMS) is derived and integrated into the proposed formulation. Another distinctive feature is the implementation of blurred interfaces, which facilitate a seamless and stable transition of flows between free and porous domains, as well as across two distinct porous media. The efficacy of the proposed formulation is verified and validated through several benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples demonstrate enhanced accuracy and stability compared to analytical, experimental, and other numerical solutions., Comment: 48 pages, 29 figures

Recently, there has been a surge of international interest in extraterrestrial exploration targeting the Moon, Mars, the moons of Mars, and various asteroids. This contribution discusses how current state-of-the-art Earth-based testing for designing rovers and landers for these missions currently leads to overly optimistic conclusions about the behavior of these devices upon deployment on the targeted celestial bodies. The key misconception is that gravitational offset is necessary during the \textit{terramechanics} testing of rover and lander prototypes on Earth. The body of evidence supporting our argument is tied to a small number of studies conducted during parabolic flights and insights derived from newly revised scaling laws. We argue that what has prevented the community from fully diagnosing the problem at hand is the absence of effective physics-based models capable of simulating terramechanics under low gravity conditions. We developed such a physics-based simulator and utilized it to gauge the mobility of early prototypes of the Volatiles Investigating Polar Exploration Rover (VIPER), which is slated to depart for the Moon in November 2024. This contribution discusses the results generated by this simulator, how they correlate with physical test results from the NASA-Glenn SLOPE lab, and the fallacy of the gravitational offset in rover and lander testing. The simulator developed is open sourced and made publicly available for unfettered use; it can support principled studies that extend beyond trafficability analysis to provide insights into in-situ resource utilization activities, e.g., digging, bulldozing, and berming in low gravity.

Bed load sediment transport, in which wind or water flowing over a bed of sediment causes grains to roll or hop along the bed, is a critically important mechanism in contexts ranging from river restoration1 to planetary exploration2. Despite its widespread occurrence, predictions of bed load sediment flux are notoriously imprecise3,4. Many studies have focused on grain size variability5 as a source of uncertainty, but few have investigated the role of grain shape, even though shape has long been suspected to influence transport rates6. Here we show that grain shape can modify bed load transport rates by an amount comparable to the scatter in many sediment transport datasets4,7,8. We develop a theory that accounts for grain shape effects on fluid drag and granular friction and predicts that the onset and efficiency of transport depend on the coefficients of drag and bulk friction of the transported grains. Laboratory experiments confirm these predictions and reveal that the effect of grain shape on sediment transport can be difficult to intuit from the appearance of grains. We propose a shape-corrected sediment transport law that collapses our experimental measurements. Our results enable greater accuracy in predictions of sediment transport and help reconcile theories developed for spherical particles with the behaviour of natural sediment grains.

We determine a constitutive equation for developed three-dimensional granular flows based on a series of discrete element method simulations. In order to capture non-local phenomena, normal stress differences, and secondary flows, we extend a previously proposed granular temperature-sensitive rheological model by considering Rivlin-Ericksen tensors up to second order. Three model parameters are calibrated with the inertial number and a dimensionless granular temperature. We validate our model by running finite difference method simulations of inclined chute flows. The model successfully predicts the velocity and stress fields in this geometry, including secondary vortical flows that previous first-order models could not predict and slow creeping zones that local models miss. It simultaneously captures the non-trivial variation among diagonal components of the stress tensor throughout the domain. Copyright © 2023 Kim and Kamrin.

Detecting hidden geometrical structures from surface measurements under electromagnetic, acoustic, or mechanical loading is the goal of noninvasive imaging techniques in medical and industrial applications. Solving the inverse problem can be challenging due to the unknown topology and geometry, the sparsity of the data, and the complexity of the physical laws. Physics-informed neural networks (PINNs) have shown promise as a simple-yet-powerful tool for problem inversion, but they have yet to be applied to general problems with a priori unknown topology. Here, we introduce a topology optimization framework based on PINNs that solves geometry detection problems without prior knowledge of the number or types of shapes. We allow for arbitrary solution topology by representing the geometry using a material density field that approaches binary values thanks to a novel eikonal regularization. We validate our framework by detecting the number, locations, and shapes of hidden voids and inclusions in linear and nonlinear elastic bodies using measurements of outer surface displacement from a single mechanical loading experiment. Our methodology opens a pathway for PINNs to solve various engineering problems targeting geometry optimization., Comment: 24 pages, 16 figures including supplementary information. Added supplementary movies

We determine a constitutive equation for developed three-dimensional granular flows based on a series of discrete element method simulations. In order to capture non-local phenomena, normal stress differences, and secondary flows, we extend a previously proposed granular temperature-sensitive rheological model by considering Rivlin-Ericksen tensors up to second order. Three model parameters are calibrated with the inertial number and a dimensionless granular temperature. We validate our model by running finite difference method simulations of inclined chute flows. The model successfully predicts the velocity and stress fields in this geometry, including secondary vortical flows that previous first-order models could not predict and slow creeping zones that local models miss. It simultaneously captures the non-trivial variation among diagonal components of the stress tensor throughout the domain.

We describe an analytical framework implemented in a general-purpose mobility simulation platform for enabling the design of control policies for improved rover mobility in granular terrain environments. We employ a homogenization of the granular material and use an elasto-plastic continuum model to capture the dynamics of the deformable terrain. The solution of the continuum problem is obtained using the smoothed particle hydrodynamics method. The Curiosity rover wheel geometry is defined through a mesh. The interaction between each wheel and the granular terrain is handled via cosimulation using so-called boundary conditions enforcing particles attached to the rover wheel. A traction control algorithm is implemented to reduce wheel slip and battery drain in hill-climbing scenario. Several parametric studies are carried out to assess rover simulation robustness for operation in uphill mobility scenario with different heights and friction coefficients. The analysis is carried out in an in-house developed simulation framework called Chrono. The implementation of the methods and models described herein is available on GitHub as open source for free use, modification, and redistribution, as well as reproducibility studies.

Mixtures of fluids and granular sediments play an important role in many industrial, geotechnical, and aerospace engineering problems, from waste management and transportation (liquid–sediment mixtures) to dust kick-up below helicopter rotors (gas–sediment mixtures). These mixed flows often involve bulk motion of hundreds of billions of individual sediment particles and can contain both highly turbulent regions and static, non-flowing regions. This breadth of phenomena necessitates the use of continuum simulation methods, such as the material point method (MPM), which can accurately capture these large deformations while also tracking the Lagrangian features of the flow (e.g. the granular surface, elastic stress, etc.). Recent works using two-phase MPM frameworks to simulate these mixtures have shown substantial promise; however, these approaches are hindered by the numerical limitations of MPM when simulating pure fluids. In addition to the well-known particle ringing instability and difficulty defining inflow/outflow boundary conditions, MPM has a tendency to accumulate quadrature errors as materials deform, increasing the rate of overall error growth as simulations progress. In this work, we present an improved, two-phase continuum simulation framework that uses the finite volume method (FVM) to solve the fluid phase equations of motion and MPM to solve the solid phase equations of motion, substantially reducing the effect of these errors and providing better accuracy and stability for long-duration simulations of these mixtures.

Generalizing Maxwells (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157, 49-88 (doi:10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtls (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8, 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T, with a nonlinear viscous response that becomes a plastic response for T → 0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.

© The Author(s), 2020. Published by Cambridge University Press. 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.

© 2019 Elsevier Inc. Soft solids in fluids find wide range of applications in science and engineering, especially in the study of biological tissues and membranes. In this study, an Eulerian finite volume approach has been developed to simulate fully resolved incompressible hyperelastic solids immersed in a fluid. We have adopted the recently developed reference-map technique (RMT) by Valkov et al. (2015) [122] and assessed multiple improvements for this approach. These modifications maintain the numerical robustness of the solver and allow the simulations without any artificial viscosity in the solid regions (to stabilize the solver). This has also resulted in eliminating the striations (“wrinkles”) of the fluid-solid interface that was seen before and hence obviates the need for any additional routines to achieve a smooth interface. An approximate projection method has been used to project the velocity field onto a divergence free field. Cost and accuracy improvements of the modifications on the method have also been discussed.

© Copyright © 2019 Kamrin. This paper reviews the emergence of non-local flow phenomena in granular materials and discusses a range of models that have been proposed to integrate an intrinsic length-scale into granular rheology. The frameworks discussed include micro-polar modeling, kinetic theory, three particular order-parameter-based models, and strongly non-local integral-based models. An extensive commentary is included discussing the current capabilities of these existing models as well as their implementational ease, physical motivation, and breadth of predictive ability.

© 2019 National Academy of Sciences. All rights reserved. Fine-particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Examination of these mixtures in simple flow geometries suggests intergranular repulsion and its influence on the frictional nature of granular contacts is central to this effect—for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to 2D, steady, simple shearing flows. In this work, we introduce a predictive and general, 3D continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a microstructural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, nonuniform flow configurations where it is shown to accurately capture a variety of key behaviors: 1) the continuous shear-thickening (CST) and discontinuous shear-thickening (DST) behavior observed in steady flows, 2) the time-dependent propagation of “shear jamming fronts,” 3) the time-dependent propagation of “impact-activated jamming fronts,” and 4) the non-Newtonian, “running on oobleck” effect, wherein fast locomotors stay afloat while slow ones sink.

© 2019 We analyze the capabilities of various recently developed techniques, namely granular Resistive Force Theory (RFT) and continuum plasticity implemented with the Material Point Method (MPM), in capturing dynamics of wheel-dry granular media interactions. We compare results to more conventionally accepted methods of modeling wheel locomotion. While RFT is an empirical force model for arbitrarily-shaped bodies moving through granular media, MPM-based continuum modeling allows the simulation of full granular flow and stress fields. RFT allows for rapid evaluation of interaction forces on arbitrary shaped intruders based on a local surface stress formulation depending on depth, orientation, and movement of surface elements. We perform forced-slip experiments for three different wheel types and three different granular materials, and results are compared with RFT, continuum modeling, and a traditional terramechanics semi-empirical method. Results show that for the range of inputs considered, RFT can be reliably used to predict rigid wheel granular media interactions with accuracy exceeding that of traditional terramechanics methodology in several circumstances. Results also indicate that plasticity-based continuum modeling provides an accurate tool for wheel-soil interaction while providing more information to study the physical processes giving rise to resistive stresses in granular media.

Mixtures of fluids and granular sediments play an important role in many industrial, geotechnical, and aerospace engineering problems, from waste management and transportation (liquid--sediment mixtures) to dust kick-up below helicopter rotors (gas--sediment mixtures). These mixed flows often involve bulk motion of hundreds of billions of individual sediment particles and can contain both highly turbulent regions and static, non-flowing regions. This breadth of phenomena necessitates the use of continuum simulation methods, such as the material point method (MPM), which can accurately capture these large deformations while also tracking the Lagrangian features of the flow (e.g.\ the granular surface, elastic stress, etc.). Recent works using two-phase MPM frameworks to simulate these mixtures have shown substantial promise; however, these approaches are hindered by the numerical limitations of MPM when simulating pure fluids. In addition to the well-known particle ringing instability and difficulty defining inflow/outflow boundary conditions, MPM has a tendency to accumulate quadrature errors as materials deform, increasing the rate of overall error growth as simulations progress. In this work, we present an improved, two-phase continuum simulation framework that uses the finite volume method (FVM) to solve the fluid phase equations of motion and MPM to solve the solid phase equations of motion, substantially reducing the effect of these errors and providing better accuracy and stability for long-duration simulations of these mixtures.

Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157, 49-88 (doi:10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8, 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T, with a nonlinear viscous response that becomes a plastic response for T → 0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.

Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157, 49-88 (doi:10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8, 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T, with a nonlinear viscous response that becomes a plastic response for T → 0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.

A numerical method for particle-laden fluids interacting with a deformable solid domain and mobile rigid parts is proposed and implemented in a full engineering system. The fluid domain is modeled with a lattice Boltzmann representation, the particles and rigid parts are modeled with a discrete element representation, and the deformable solid domain is modeled using a Lagrangian mesh. The main issue of this work, since separately each of these methods is a mature tool, is to develop coupling and model-reduction approaches in order to efficiently simulate coupled problems of this nature, as in various geological and engineering applications. The lattice Boltzmann method incorporates a large eddy simulation technique using the Smagorinsky turbulence model. The discrete element method incorporates spherical and polyhedral particles for stiff contact interactions. A neo-Hookean hyperelastic model is used for the deformable solid. We provide a detailed description of how to couple the three solvers within a unified algorithm. The technique we propose for rubber modeling/coupling exploits a simplification that prevents having to solve a finite-element problem at each time step. We also developed a technique to reduce the domain size of the full system by replacing certain zones with quasi-analytic solutions, which act as effective boundary conditions for the lattice Boltzmann method. The major ingredients of the routine are separately validated. To demonstrate the coupled method in full, we simulate slurry flows in two kinds of piston valve geometries. The dynamics of the valve and slurry are studied and reported over a large range of input parameters.

A numerical method for particle-laden fluids interacting with a deformable solid domain and mobile rigid parts is proposed and implemented in a full engineering system. The fluid domain is modeled with a lattice Boltzmann representation, the particles and rigid parts are modeled with a discrete element representation, and the deformable solid domain is modeled using a Lagrangian mesh. The main issue of this work, since separately each of these methods is a mature tool, is to develop coupling and model-reduction approaches in order to efficiently simulate coupled problems of this nature, as in various geological and engineering applications. The lattice Boltzmann method incorporates a large eddy simulation technique using the Smagorinsky turbulence model. The discrete element method incorporates spherical and polyhedral particles for stiff contact interactions. A neo-Hookean hyperelastic model is used for the deformable solid. We provide a detailed description of how to couple the three solvers within a unified algorithm. The technique we propose for rubber modeling/coupling exploits a simplification that prevents having to solve a finite-element problem at each time step. We also developed a technique to reduce the domain size of the full system by replacing certain zones with quasi-analytic solutions, which act as effective boundary conditions for the lattice Boltzmann method. The major ingredients of the routine are separately validated. To demonstrate the coupled method in full, we simulate slurry flows in two kinds of piston valve geometries. The dynamics of the valve and slurry are studied and reported over a large range of input parameters.

A numerical method for particle-laden fluids interacting with a deformable solid domain and mobile rigid parts is proposed and implemented in a full engineering system. The fluid domain is modeled with a lattice Boltzmann representation, the particles and rigid parts are modeled with a discrete element representation, and the deformable solid domain is modeled using a Lagrangian mesh. The main issue of this work, since separately each of these methods is a mature tool, is to develop coupling and model-reduction approaches in order to efficiently simulate coupled problems of this nature, as in various geological and engineering applications. The lattice Boltzmann method incorporates a large eddy simulation technique using the Smagorinsky turbulence model. The discrete element method incorporates spherical and polyhedral particles for stiff contact interactions. A neo-Hookean hyperelastic model is used for the deformable solid. We provide a detailed description of how to couple the three solvers within a unified algorithm. The technique we propose for rubber modeling/coupling exploits a simplification that prevents having to solve a finite-element problem at each time step. We also developed a technique to reduce the domain size of the full system by replacing certain zones with quasi-analytic solutions, which act as effective boundary conditions for the lattice Boltzmann method. The major ingredients of the routine are separately validated. To demonstrate the coupled method in full, we simulate slurry flows in two kinds of piston valve geometries. The dynamics of the valve and slurry are studied and reported over a large range of input parameters.

A numerical method for particle-laden fluids interacting with a deformable solid domain and mobile rigid parts is proposed and implemented in a full engineering system. The fluid domain is modeled with a lattice Boltzmann representation, the particles and rigid parts are modeled with a discrete element representation, and the deformable solid domain is modeled using a Lagrangian mesh. The main issue of this work, since separately each of these methods is a mature tool, is to develop coupling and model-reduction approaches in order to efficiently simulate coupled problems of this nature, as occur in various geological and engineering applications. The lattice Boltzmann method incorporates a large-eddy simulation technique using the Smagorinsky turbulence model. The discrete element method incorporates spherical and polyhedral particles for stiff contact interactions. A neo-Hookean hyperelastic model is used for the deformable solid. We provide a detailed description of how to couple the three solvers within a unified algorithm. The technique we propose for rubber modeling/coupling exploits a simplification that prevents having to solve a finite-element problem each time step. We also develop a technique to reduce the domain size of the full system by replacing certain zones with quasi-analytic solutions, which act as effective boundary conditions for the lattice Boltzmann method. The major ingredients of the routine are are separately validated. To demonstrate the coupled method in full, we simulate slurry flows in two kinds of piston-valve geometries. The dynamics of the valve and slurry are studied and reported over a large range of input parameters.

Continuum mechanics relies on the fundamental notion of a mesoscopic volume "element" in which properties averaged over discrete particles obey deterministic relationships. Recent work on granular materials suggests a continuum law may be inapplicable, revealing inhomogeneities at the particle level, such as force chains and slow cage breaking. Here, we analyze large-scale Discrete-Element Method (DEM) simulations of different granular flows and show that a "granular element" can indeed be defined at the scale of dynamical correlations, roughly three to five particle diameters. Its rheology is rather subtle, combining liquid-like dependence on deformation rate and solid-like dependence on strain. Our results confirm some aspects of classical plasticity theory (e.g., coaxiality of stress and deformation rate), while contradicting others (i.e., incipient yield), and can guide the development of more realistic continuum models.

Continuum mechanics relies on the fundamental notion of a mesoscopic volume "element" in which properties averaged over discrete particles obey deterministic relationships. Recent work on granular materials suggests a continuum law may be inapplicable, revealing inhomogeneities at the particle level, such as force chains and slow cage breaking. Here, we analyze large-scale Discrete-Element Method (DEM) simulations of different granular flows and show that a "granular element" can indeed be defined at the scale of dynamical correlations, roughly three to five particle diameters. Its rheology is rather subtle, combining liquid-like dependence on deformation rate and solid-like dependence on strain. Our results confirm some aspects of classical plasticity theory (e.g., coaxiality of stress and deformation rate), while contradicting others (i.e., incipient yield), and can guide the development of more realistic continuum models.