Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and real-world granular materials with large size dispersity. Here, invoking a recently developed neighbor binning algorithm, we generate mechanically stable jammed packings of frictionless spheres with power-law size distributions containing up to nearly 4 000 000 particles with size ratios up to 1:100. By systematically varying the width and exponent of the underlying power laws, we analyze the role of particle size distributions on the structure of jammed packings. The densest packings are obtained for size distributions that balance the relative abundance of large-large and small-small particle contacts. Although the proportion of rattler particles and mean coordination number strongly depend on the size distribution, the mean coordination of nonrattler particles attains the frictionless isostatic value of six in all cases. The size distribution of nonrattler particles that participate in the load-bearing network exhibits no dependence on the width of the total particle size distribution beyond a critical particle size for low-magnitude exponent power laws. This signifies that only particles with sizes greater than the critical particle size contribute to the mechanical stability. However, for high-magnitude exponent power laws, all particle sizes participate in the mechanical stability of the packing.
The peridynamic theory of solid mechanics is applied to modeling the deformation and fracture of micrometer-sized particles made of organic crystalline material. A new peridynamic material model is proposed to reproduce the elastic–plastic response, creep, and fracture that are observed in experiments. The model is implemented in a three-dimensional, meshless Lagrangian simulation code. In the small deformation, elastic regime, the model agrees well with classical Hertzian contact analysis for a sphere compressed between rigid plates. Under higher load, material and geometrical nonlinearity is predicted, leading to fracture. The material parameters for the energetic material CL-20 are evaluated from nanoindentation test data on the cyclic compression and failure of micrometer-sized grains.
This Laboratory Directed Research and Development project developed and applied closely coupled experimental and computational tools to investigate powder compaction across multiple length scales. The primary motivation for this work is to provide connections between powder feedstock characteristics, processing conditions, and powder pellet properties in the context of powder-based energetic components manufacturing. We have focused our efforts on multicrystalline cellulose, a molecular crystalline surrogate material that is mechanically similar to several energetic materials of interest, but provides several advantages for fundamental investigations. We report extensive experimental characterization ranging in length scale from nanometers to macroscopic, bulk behavior. Experiments included nanoindentation of well-controlled, micron-scale pillar geometries milled into the surface of individual particles, single-particle crushing experiments, in-situ optical and computed tomography imaging of the compaction of multiple particles in different geometries, and bulk powder compaction. In order to capture the large plastic deformation and fracture of particles in computational models, we have advanced two distinct meshfree Lagrangian simulation techniques: 1.) bonded particle methods, which extend existing discrete element method capabilities in the Sandia-developed , open-source LAMMPS code to capture particle deformation and fracture and 2.) extensions of peridynamics for application to mesoscale powder compaction, including a novel material model that includes plasticity and creep. We have demonstrated both methods for simulations of single-particle crushing as well as mesoscale multi-particle compaction, with favorable comparisons to experimental data. We have used small-scale, mechanical characterization data to inform material models, and in-situ imaging of mesoscale particle structures to provide initial conditions for simulations. Both mesostructure porosity characteristics and overall stress-strain behavior were found to be in good agreement between simulations and experiments. We have thus demonstrated a novel multi-scale, closely coupled experimental and computational approach to the study of powder compaction. This enables a wide range of possible investigations into feedstock-process-structure relationships in powder-based materials, with immediate applications in energetic component manufacturing, as well as other particle-based components and processes.
Microstructures and corresponding properties of compacted powders ultimately depend on the mechanical response of individual particles. In principle, computational simulations can predict the results of powder compaction processes, but the selection of appropriate models for both particle–particle interactions and particle deformations across all relevant length scales remain nontrivial tasks, especially in material systems lacking detailed mechanical property information. The work presented here addresses these issues by conducting uniaxial compressions in situ inside of a scanning electron microscope to characterize the mechanical response of individual micron-sized particles of a molecular crystal, hexanitrohexaazaisowurtzitane (CL-20). This experimental approach enabled the collection of quantitative force and displacement data alongside simultaneous imaging to capture morphology changes. The results reveal information about elastic deformation, yield, plastic deformation, creep, and fracture phenomena. Accordingly, this work demonstrates a generalizable approach for assessing the mechanical response of individual micron-sized molecular crystal particles and utilizing those responses in particle-level models. Graphic abstract: [Figure not available: see fulltext.].
By generalizing a geometric argument for frictionless spheres, a model is proposed for the jamming density φJ of mechanically stable packings of bidisperse, frictional spheres. The monodisperse, μs-dependent jamming density φJmono(μs) is the only input required in the model, where μs is the coefficient of friction. The predictions of the model are validated by robust estimates of φJ obtained from computer simulations of up to 107 particles for a wide range of μs, and size ratios up to 40:1. Although φJ varies nonmonotonically with the volume fraction of small spheres fs for all μs, its maximum value φJ,max at an optimal fmaxs are both μs dependent. The optimal fmaxs is characterized by a sharp transition in the fraction of small rattler particles.
Two key mechanical processes exist in the formation of powder compacts. These include the complex kinematics of particle rearrangement as the powder is densified and particle deformation leading to mechanical failure and fragmentation. Experiments measuring the time varying forces across a densifying powder bed have been performed in powders of microcrystalline cellulose with mean particle sizes between 0.4 and 1.2 mm. In these experiments, diagnostics measured the applied and transmitted loads and the bulk powder density. Any insight into the particle behavior must be inferred from deviations in the smoothly increasing stress-density compaction relationship. By incorporating a window in the compaction die body, simultaneous images of particle rearrangement and fracture at the confining window are captured. The images are post-processed in MATLAB® to track individual particle motion during compression. Complimentary discrete element method (DEM) simulations are presented and compared to experiment. The comparison provides insight into applying DEM methods for simulating large or permanent particle deformation and suggests areas for future study.
Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning or twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and average coordination numbers as low as 0.53 and 2.5, respectively, when the particles experience high resistance to sliding, rolling, and twisting. Only when the particle model includes rolling and twisting friction were experimental volume fractions reproduced.
Particle characteristics can drastically influence the process-structure-property-performance aspects of granular materials in compression. We aim to computationally simulate the mechanical processes of stress redistribution in compacts including the kinematics of particle rearrangement during densification and particle deformation leading to fragmentation. Confined compression experiments are conducted with three sets of commercial microcrystalline cellulose particles nearly spherical in shape with different mean particle size. Experimentally measured compression curves from tall powder columns are fitted with the Kenkre et al. (J. of American Chemical Society, Vol. 79, No. 12) model. This model provides a basis to derive several common two-parameter literature models and as a framework to incorporate statistical representations of critical particle behaviors. We focus on the low-stress compression data and the model comparisons typically not discussed in the literature. Additional single particle compressions report fracture strength with particle size for comparison to the apparent particle strength extracted from bulk compression data.
Using random walk analyses we explore diffusive transport on networks obtained from contacts between isotropically compressed, monodisperse, frictionless sphere packings generated over a range of pressures in the vicinity of the jamming transition p→0. For conductive particles in an insulating medium, conduction is determined by the particle contact network with nodes representing particle centers and edges contacts between particles. The transition rate is not homogeneous, but is distributed inhomogeneously due to the randomness of packing and concomitant disorder of the contact network, e.g., the distribution of the coordination number. A narrow escape time scale is used to write a Markov process for random walks on the particle contact network. This stochastic process is analyzed in terms of spectral density of the random, sparse, Euclidean and real, symmetric, positive, semidefinite transition rate matrix. Results show network structures derived from jammed particles have properties similar to ordered, euclidean lattices but also some unique properties that distinguish them from other structures that are in some sense more homogeneous. In particular, the distribution of eigenvalues of the transition rate matrix follow a power law with spectral dimension 3. However, quantitative details of the statistics of the eigenvectors show subtle differences with homogeneous lattices and allow us to distinguish between topological and geometric sources of disorder in the network.
A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.
We generate a wide range of models of proppant-packed fractures using discrete element simulations, and measure fracture conductivity using finite element flow simulations. This allows for a controlled computational study of proppant structure and its relationship to fracture conductivity and stress in the proppant pack. For homogeneous multi-layered packings, we observe the expected increase in fracture conductivity with increasing fracture aperture, while the stress on the proppant pack remains nearly constant. This is consistent with the expected behavior in conventional proppant-packed fractures, but the present work offers a novel quantitative analysis with an explicit geometric representation of the proppant particles. In single-layered packings (i.e. proppant monolayers), there is a drastic increase in fracture conductivity as the proppant volume fraction decreases and open flow channels form. However, this also corresponds to a sharp increase in the mechanical stress on the proppant pack, as measured by the maximum normal stress relative to the side crushing strength of typical proppant particles. We also generate a variety of computational geometries that resemble highly heterogeneous proppant packings hypothesized to form during channel fracturing. In some cases, these heterogeneous packings show drastic improvements in conductivity with only moderate increase in the stress on the proppant particles, suggesting that in certain applications these structures are indeed optimal. We also compare our computer-generated structures to micro computed tomography imaging of a manually fractured laboratory-scale shale specimen, and find reasonable agreement in the geometric characteristics.
Electrical conductivity is key to the performance of thermal battery cathodes. In this work we present the effects of manufacturing and processing conditions on the electrical conductivity of Li/FeS2 thermal battery cathodes. We use finite element simulations to compute the conductivity of three-dimensional microcomputed tomography cathode microstructures and compare results to experimental impedance spectroscopy measurements. A regression analysis reveals a predictive relationship between composition, processing conditions, and electrical conductivity; a trend which is largely erased after thermally-induced deformation. The trend applies to both experimental and simulation results, although is not as apparent in simulations. This research is a step toward a more fundamental understanding of the effects of processing and composition on thermal battery component microstructure, properties, and performance.
Two of the central challenges in the mechanical design of components in nuclear systems are the dissipation of energy from external shocks and the localization of energy in energetic materials. This research seeks to address these problems by developing a patterned granular microstructure that can be optimized to direct or impede the transfer of energy carried by stress waves. Such structures require the development of a manufacturing technique that can yield perfectly ordered lattices. Two branches of research are detailed here: the development of a sphere-by-sphere additive manufacturing technique, and the development of a framework for modeling the technique in order to guide future improvements. Proof of concept of the method is demonstrated, and recommendations for future work are made.
The following details the implementation of an analytical elastic plastic contact model with strain hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of elastic loading followed by a period of mixed elastic plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the elastic/plastic model took 1.66x as long as similar runs using gran/hertz/history.
This report summarizes a project in which the authors sought to develop and deploy: (i) experimental techniques to elucidate the complex, multiscale nature of thermal transport in particle-based materials; and (ii) modeling approaches to address current challenges in predicting performance variability of materials (e.g., identifying and characterizing physical- chemical processes and their couplings across multiple length and time scales, modeling information transfer between scales, and statically and dynamically resolving material structure and its evolution during manufacturing and device performance). Experimentally, several capabilities were successfully advanced. As discussed in Chapter 2 a flash diffusivity capability for measuring homogeneous thermal conductivity of pyrotechnic powders (and beyond) was advanced; leading to enhanced characterization of pyrotechnic materials and properties impacting component development. Chapter 4 describes success for the first time, although preliminary, in resolving thermal fields at speeds and spatial scales relevant to energetic components. Chapter 7 summarizes the first ever (as far as the authors know) application of TDTR to actual pyrotechnic materials. This is the first attempt to actually characterize these materials at the interfacial scale. On the modeling side, new capabilities in image processing of experimental microstructures and direct numerical simulation on complicated structures were advanced (see Chapters 3 and 5). In addition, modeling work described in Chapter 8 led to improved prediction of interface thermal conductance from first principles calculations. Toward the second point, for a model system of packed particles, significant headway was made in implementing numerical algorithms and collecting data to justify the approach in terms of highlighting the phenomena at play and pointing the way forward in developing and informing the kind of modeling approach originally envisioned (see Chapter 6). In both cases much more remains to be accomplished.
We present a review and critique of several methods for the simulation of the dynamics of colloidal suspensions at the mesoscale. We focus particularly on simulation techniques for hydrodynamic interactions, including implicit solvents (Fast Lubrication Dynamics, an approximation to Stokesian Dynamics) and explicit/particle-based solvents (Multi-Particle Collision Dynamics and Dissipative Particle Dynamics). Several variants of each method are compared quantitatively for the canonical system of monodisperse hard spheres, with a particular focus on diffusion characteristics, as well as shear rheology and microstructure. In all cases, we attempt to match the relevant properties of a well-characterized solvent, which turns out to be challenging for the explicit solvent models. Reasonable quantitative agreement is observed among all methods, but overall the Fast Lubrication Dynamics technique shows the best accuracy and performance. We also devote significant discussion to the extension of these methods to more complex situations of interest in industrial applications, including models for non-Newtonian solvent rheology, non-spherical particles, drying and curing of solvent and flows in complex geometries. This work identifies research challenges and motivates future efforts to develop techniques for quantitative, predictive simulations of industrially relevant colloidal suspension processes.
Active brazes have been used for many years to produce bonds between metal and ceramic objects. By including a relatively small of a reactive additive to the braze one seeks to improve the wetting and spreading behavior of the braze. The additive modifies the substrate, either by a chemical surface reaction or possibly by alloying. By its nature, the joining process with active brazes is a complex nonequilibrium non-steady state process that couples chemical reaction, reactant and product diffusion to the rheology and wetting behavior of the braze. Most of the these subprocesses are taking place in the interfacial region, most are difficult to access by experiment. To improve the control over the brazing process, one requires a better understanding of the melting of the active braze, rate of the chemical reaction, reactant and product diffusion rates, nonequilibrium composition-dependent surface tension as well as the viscosity. This report identifies ways in which modeling and theory can assist in improving our understanding.
This document summarizes a three year Laboratory Directed Research and Development (LDRD) program effort to improve our understanding of algal flocculation with a key to overcoming harvesting as a techno-economic barrier to algal biofuels. Flocculation is limited by the concentrations of deprotonated functional groups on the algal cell surface. Favorable charged groups on the surfaces of precipitates that form in solution and the interaction of both with ions in the water can favor flocculation. Measurements of algae cell-surface functional groups are reported and related to the quantity of flocculant required. Deprotonation of surface groups and complexation of surface groups with ions from the growth media are predicted in the context of PHREEQC. The understanding of surface chemistry is linked to boundaries of effective flocculation. We show that the phase-space of effective flocculation can be expanded by more frequent alga-alga or floc-floc collisions. The collision frequency is dependent on the floc structure, described in the fractal sense. The fractal floc structure is shown to depend on the rate of shear mixing. We present both experimental measurements of the floc structure variation and simulations using LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). Both show a densification of the flocs with increasing shear. The LAMMPS results show a combined change in the fractal dimension and a change in the coordination number leading to stronger flocs.
We present results of molecular dynamics simulations of the flocculation of model algae particles under shear. We study the evolution of the cluster size distribution as well as the steady-state distribution as a function of shear rates and algae interaction parameters. Algal interactions are modeled through a DLVO-type potential, a combination of a HS colloid potential (Everaers) and a yukawa/colloid electrostatic potential. The effect of hydrodynamic interactions on aggregation is explored. Cluster strucuture is determined from the algae-algae radial distribution function as well as the structure factor. DLVO parameters including size, salt concentration, surface potential, initial volume fraction, etc. are varied to model different species of algae under a variety of environmental conditions.
In this report a model for simulating aerosol cluster impact with rigid walls is presented. The model is based on JKR adhesion theory and is implemented as an enhancement to the granular (DEM) package within the LAMMPS code. The theory behind the model is outlined and preliminary results are shown. Modeling the interactions of small particles is relevant to a number of applications (e.g., soils, powders, colloidal suspensions, etc.). Modeling the behavior of aerosol particles during agglomeration and cluster dynamics upon impact with a wall is of particular interest. In this report we describe preliminary efforts to develop and implement physical models for aerosol particle interactions. Future work will consist of deploying these models to simulate aerosol cluster behavior upon impact with a rigid wall for the purpose of developing relationships for impact speed and probability of stick/bounce/break-up as well as to assess the distribution of cluster sizes if break-up occurs. These relationships will be developed consistent with the need for inputs into system-level codes. Section 2 gives background and details on the physical model as well as implementations issues. Section 3 presents some preliminary results which lead to discussion in Section 4 of future plans.
The most feasible way to disperse particles in a bulk material or control their packing at a substrate is through fluidization in a carrier that can be processed with well-known techniques such as spin, drip and spray coating, fiber drawing, and casting. The next stage in the processing is often solidification involving drying by solvent evaporation. While there has been significant progress in the past few years in developing discrete element numerical methods to model dense nanoparticle dispersion/suspension rheology which properly treat the hydrodynamic interactions of the solvent, these methods cannot at present account for the volume reduction of the suspension due to solvent evaporation. As part of LDRD project FY-101285 we have developed and implemented methods in the current suite of discrete element methods to remove solvent particles and volume, and hence solvent mass from the liquid/vapor interface of a suspension to account for volume reduction (solvent drying) effects. To validate the methods large scale molecular dynamics simulations have been carried out to follow the evaporation process at the microscopic scale.
Understanding the interaction of aerosol particle clusters/flocs with surfaces is an area of interest for a number of processes in chemical, pharmaceutical, and powder manufacturing as well as in steam-tube rupture in nuclear power plants. Developing predictive capabilities for these applications involves coupled phenomena on multiple length and timescales from the process macroscopic scale ({approx}1m) to the multi-cluster interaction scale (1mm-0.1m) to the single cluster scale ({approx}1000 - 10000 particles) to the particle scale (10nm-10{micro}m) interactions, and on down to the sub-particle, atomic scale interactions. The focus of this report is on the single cluster scale; although work directed toward developing better models of particle-particle interactions by considering sub-particle scale interactions and phenomena is also described. In particular, results of mesoscale (i.e., particle to single cluster scale) discrete element method (DEM) simulations for aerosol cluster impact with rigid walls are presented. The particle-particle interaction model is based on JKR adhesion theory and is implemented as an enhancement to the granular package in the LAMMPS code. The theory behind the model is outlined and preliminary results are shown. Additionally, as mentioned, results from atomistic classical molecular dynamics simulations are also described as a means of developing higher fidelity models of particle-particle interactions. Ultimately, the results from these and other studies at various scales must be collated to provide systems level models with accurate 'sub-grid' information for design, analysis and control of the underlying systems processes.
In this presentation we examine the accuracy and performance of a suite of discrete-element-modeling approaches to predicting equilibrium and dynamic rheological properties of polystyrene suspensions. What distinguishes each approach presented is the methodology of handling the solvent hydrodynamics. Specifically, we compare stochastic rotation dynamics (SRD), fast lubrication dynamics (FLD) and dissipative particle dynamics (DPD). Method-to-method comparisons are made as well as comparisons with experimental data. Quantities examined are equilibrium structure properties (e.g. pair-distribution function), equilibrium dynamic properties (e.g. short- and long-time diffusivities), and dynamic response (e.g. steady shear viscosity). In all approaches we deploy the DLVO potential for colloid-colloid interactions. Comparisons are made over a range of volume fractions and salt concentrations. Our results reveal the utility of such methods for long-time diffusivity prediction can be dubious in certain ranges of volume fraction, and other discoveries regarding the best formulation to use in predicting rheological response.
A method is developed for modeling fluid transport in domains that do not conform to the finite element mesh. One or more level set functions are used to describe the fluid domain. A background, non-conformal mesh is decomposed into elements that conform to the level set interfaces. Enrichment takes place by adding nodes that lie on the interfaces. Unlike other enriched finite element methods, the proposed technique requires no changes to the underlying element assembly, element interpolation, or element quadrature. The complexity is entirely contained within the element decomposition routines. It is argued that the accuracy of the method is no less than that for eXtended Finite Element Methods (XFEM) with Heaviside enrichment. The accuracy is demonstrated using multiple numerical tests. In all cases, optimal rates of convergence are obtained for both volume and surface quantities. Jacobi preconditioning is shown to remove the ill-conditioning that may result from the nearly degenerate conformal elements.
Nanoparticles are now more than ever being used to tailor materials function and performance in differentiating technologies because of their profound effect on thermo-physical, mechanical and optical properties. The most feasible way to disperse particles in a bulk material or control their packing at a substrate is through fluidization in a carrier, followed by solidification through solvent evaporation/drying/curing/sintering. Unfortunately processing particles as concentrated, fluidized suspensions into useful products remains an art largely because the effect of particle shape and volume fraction on fluidic properties and suspension stability remains unexplored in a regime where particle-particle interaction mechanics is prevalent. To achieve a stronger scientific understanding of the factors that control nanoparticle dispersion and rheology we have developed a multiscale modeling approach to bridge scales between atomistic and molecular-level forces active in dense nanoparticle suspensions. At the largest length scale, two 'coarse-grained' numerical techniques have been developed and implemented to provide for high-fidelity numerical simulations of the rheological response and dispersion characteristics typical in a processing flow. The first is a coupled Navier-Stokes/discrete element method in which the background solvent is treated by finite element methods. The second is a particle based method known as stochastic rotational dynamics. These two methods provide a new capability representing a 'bridge' between the molecular scale and the engineering scale, allowing the study of fluid-nanoparticle systems over a wide range of length and timescales as well as particle concentrations. To validate these new methodologies, multi-million atoms simulations explicitly including the solvent have been carried out. These simulations have been vital in establishing the necessary 'subgrid' models for accurate prediction at a larger scale and refining the two coarse-grained methodologies.
The evolution of granular shear flow is investigated as a function of height in a split-bottom Couette cell. Using particle tracking, magnetic-resonance imaging, and large-scale simulations, we find a transition in the nature of the shear as a characteristic height H* is exceeded. Below H* there is a central stationary core; above H* we observe the onset of additional axial shear associated with torsional failure. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height, while the axial width remains narrow and fixed.
Slow, dense granular flows often exhibit thin, localized regions of particle motion, called shear bands, separating largely solid-like regions. Recent experiments using a split-bottom Couette cell found that the width of the shear zone grew as the pack height increased and the azimuthal velocities when rescaled fall on a universal curve regardless of the particle properties. Here we present large-scale Discrete Element simulations of a similar system for packs of varying height up to 180,000 monodisperse spheres. The onset and evolution of granular shear flow is investigated as a function of height. We find a transition in the nature of the shear as a characteristic height is exceeded. Below this height there is a central quasi-solid core; above this height we observe the onset of additional axial shear associated with a torsional failure mode of the inner core. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height while the axial width remains narrow and fixed.
Large-scale three dimensional Discrete Element simulations of granular flow in a modified split-bottom Couette cell for packs of up to 180,000 mono-disperse spheres are presented and compared with experiments. We find that the velocity profiles collapse onto a universal curve not only at the surface but also in the bulk of the pack until slip between layers becomes significant. In agreement with experiment, we find similar relations between the cell geometry and parameters involved in rescaling the velocities at the surface and in the bulk. Likewise, a change in the shape of the shear zone is observed as predicted for tall packs once the center of the shear zone is correctly defined; although the transition does not appear to be first order. Finally, the effect of cohesion is considered as a means to test the theoretical predictions.