Quantifying Interparticle Forces and Heterogeneity in 3D Granular Materials

Hierarchical Supramolecular Aggregation of Molecular Nanoparticles for Granular Materials with Ultra High-Speed Impact-Resistance

The high-speed impact-resistanct materials are of great significance while their development is hindered by the intrinsic tradeoff between mechanical strength and energy dissipation capability. Herein, the new chemical system of molecular granular material (MGM) is developed for the design of impact-resistant materials from the supramolecular complexation of sub-nm molecular clusters (MCs) and hyper-branched polyelectrolytes. Their hierarchical aggregation provides the origin of the decoupling of mechanical strengths and structural relaxation dynamics. The MCs' intrinsic fast dynamics afford excellent high-speed impact-resistance, up to 5600 s-1 impact in a typical split-Hopkinson pressure bar test while only tiny boundary cracks can be observed even under 7200 s-1 impact. The high loadings of MCs and their hierarchical aggregates provide high-density sacrificial bonding for the effective dissipation of the impact energy, enabling the protection of fragile devices from the direct impact of over 200 m s-1 bullet. Moreover, the MGMs can be conveniently processed into protective coatings or films with promising recyclability due to the supramolecular interaction feature. The research not only reveals the unique relaxation dynamics and mechanical properties of MGMs in comparison with polymers and colloids, but also develops new chemical systems for the fabrication of high-speed impact-resistant materials.

Micromechanics of contact-bound cohesive granular materials in confined compression

The mechanical behavior of granular materials results from interparticle interactions, which are predominantly frictional. With the presence of even very small amounts of cohesion this frictional interparticle behavior significantly changes. In this study, we introduce trace amounts of cohesive binder between the intergranular contacts in a sample of quartz particles and apply one-dimensional (1D) compression loading. X-ray computed tomography is performed in situ during 1D compression. We make observations at three different length scales. At the macroscopic or ensemble scale, we track the evolution of the porosity, particle size and the stress-strain response during this compression. At the microstructure or interparticle scale, we compute the directional distribution of contacts and the particles. We also track the evolution of the fabric chains with continued compression. We also evaluate particle rotations, displacements, contact twist, rotation, and sliding. We show through our experiments that even a small amount of cohesion (as low as 1% by weight) significantly changes the response at multiple length scales. This interparticle cohesion suppresses the fragmentation of grains, alters force transmission and changes the structure of the ensemble.

Dynamic imaging of force chains in 3D granular media

Granular media constitute the most abundant form of solid matter on Earth and beyond. When external forces are applied to a granular medium, the forces are transmitted through it via chains of contacts among grains-force chains. Understanding the spatial structure and temporal evolution of force chains constitutes a fundamental goal of granular mechanics. Here, we introduce an experimental technique, interference optical projection tomography, to study force chains in three-dimensional (3D) granular packs under triaxial shear loads and illustrate the technique with random assemblies of spheres and icosahedra. We find that, in response to an increasing vertical load, the pack of spheres forms intensifying vertical force chains, while the pack of icosahedra forms more interconnected force-chain networks. This provides microscopic insights into why particles with more angularity are more resistant to shear failure-the interconnected force-chain network is stronger (that is, more resilient to topological collapse) than the isolated force chains in round particles. The longer force chains with less branching in the pack of round particles are more likely to buckle, which leads to the macroscopic failure of the pack. This work paves the way for understanding the grain-scale underpinning of localized failure of 3D granular media, such as shear localization in landslides and stick-slip frictional motion in tectonic and induced earthquakes.

Stress-activated friction in sheared suspensions probed with piezoelectric nanoparticles

A hallmark of concentrated suspensions is non-Newtonian behavior, whereby the viscosity increases dramatically once a characteristic shear rate or stress is exceeded. Such strong shear thickening is thought to originate from a network of frictional particle-particle contact forces, which forms under sufficiently large stress, evolves dynamically, and adapts to changing loads. While there is much evidence from simulations for the emergence of this network during shear thickening, experimental confirmation has been difficult. Here, we use suspensions of piezoelectric nanoparticles and exploit the strong local stress focusing within the network to activate charge generation. This charging can then be detected in the measured ac conductance and serve as a signature of frictional contact formation. The direct link between stress-activated frictional particle interactions and piezoelectric suspension response is further demonstrated by tracking the emergence of structural memory in the contact network under oscillatory shear and by showing how stress-activated friction can drive mechano-transduction of chemical reactions with nonlinear reaction kinetics. Taken together, this makes the ac conductance of piezoelectric suspensions a sensitive in-situ reporter of the micromechanics associated with frictional interactions.

Shaping Synthetic Multicellular and Complex Multimaterial Tissues via Embedded Extrusion-Volumetric Printing of Microgels

In living tissues, cells express their functions following complex signals from their surrounding microenvironment. Capturing both hierarchical architectures at the micro- and macroscale, and anisotropic cell patterning remains a major challenge in bioprinting, and a bottleneck toward creating physiologically-relevant models. Addressing this limitation, a novel technique is introduced, termed Embedded Extrusion-Volumetric Printing (EmVP), converging extrusion-bioprinting and layer-less, ultra-fast volumetric bioprinting, allowing spatially pattern multiple inks/cell types. Light-responsive microgels are developed for the first time as bioresins (µResins) for light-based volumetric bioprinting, providing a microporous environment permissive for cell homing and self-organization. Tuning the mechanical and optical properties of gelatin-based microparticles enables their use as support bath for suspended extrusion printing, in which features containing high cell densities can be easily introduced. µResins can be sculpted within seconds with tomographic light projections into centimeter-scale, granular hydrogel-based, convoluted constructs. Interstitial microvoids enhanced differentiation of multiple stem/progenitor cells (vascular, mesenchymal, neural), otherwise not possible with conventional bulk hydrogels. As proof-of-concept, EmVP is applied to create complex synthetic biology-inspired intercellular communication models, where adipocyte differentiation is regulated by optogenetic-engineered pancreatic cells. Overall, EmVP offers new avenues for producing regenerative grafts with biological functionality, and for developing engineered living systems and (metabolic) disease models.

X-ray 3D imaging-based microunderstanding of granular mixtures: Stiffness enhancement by adding small fractions of soft particles

This research focuses on performing ultrasound propagation measurements and micro-X-ray computed tomography (µXRCT) imaging on prestressed granular packings prepared with biphasic mixtures of monodisperse glass and rubber particles at different compositions/fractions. Ultrasound experiments employing piezoelectric transducers, mounted in an oedometric cell (complementing earlier triaxial cell experiments), are used to excite and detect longitudinal ultrasound waves through randomly prepared mixtures of monodisperse stiff/soft particles. While the fraction of the soft particles is increasing linearly from zero, the effective macroscopic stiffness of the granular packings transits nonlinearly and nonmonotonically toward the soft limit, remarkably via an interesting stiffer regime for small rubber fractions between 0.1 ≲ ν ≲ 0.2. The contact network of dense packings, as accessed from µXRCT, plays a key role in understanding this phenomenon, considering the structure of the network, the chain length, the grain contacts, and the particle coordination. While the maximum stiffness is due to surprisingly shortened chains, the sudden drop in elastic stiffness of the mixture packings, at ν ≈ 0.4, is associated with chains of particles that include both glass and rubber particles (soft chains); for ν ≲ 0.3, the dominant chains include only glass particles (hard chains). At the drop, ν ≈ 0.4, the coordination number of glass and rubber networks is approximately four and three, respectively, i.e., neither of the networks are jammed, and the chains need to include particles from another species to propagate information.

Particle fraction is a bioactive cue in granular scaffolds

Microporous annealed particle (MAP) hydrogels are porous 3D scaffolds generated by interlinking randomly packed microgels (µgels). Particle fraction, hydrogel stiffness, microparticle shape, and crosslinking chemistry are paramount to the microstructure that microgels make within MAP scaffolds. Of these parameters, control over the particle fraction in MAP scaffolds varies greatly by user and drying technique, leading to inconsistent microarchitectures. These inconsistencies have biological ramifications, as the particle fraction of MAP scaffolds determines the void space within the material which strongly impacts cell growth. Here, we describe a method of freeze-drying microgels that leads to consistent and user-defined particle fractions by weighing the dried microgel powder and reconstituting at known volumes. Though freeze-drying hydrogels typically leads to ice crystal and cryogel formation, we report on mediums that result in freeze-dried microgels that retain their original properties when rehydrated. By rehydrating lyophilized microgels to form MAP scaffolds, we demonstrate that particle fraction controls the bulk scaffold stiffness, but not local microgel stiffness. Further, the particle fraction in MAP scaffolds directly affects cell growth and macromolecular diffusion. Using controlled particle fractions in MAP scaffolds, we can now reproducibly assess mechanical properties, diffusion of macromolecules, and cell responses within user-defined microarchitectures. STATEMENT OF SIGNIFICANCE: The porosity of biomaterials is one key characteristic that influences cell infiltration and growth. Granular hydrogels are a class of biomaterials that are comprised of small, building block components that boast a porous architecture in the void space between the particles. Controlling the composition of these granular materials is key to guiding cell responses. In this work, we demonstrate methods for controlling the fraction of the material containing hydrogel versus void space. As a result, we can now reproducibly study the effect of particle fraction on cell responses, mechanical properties, and mass transport in granular hydrogels.

A versatile microtomography system to study in situ the failure and fragmentation in geomaterials

This article describes a microtomography experimental platform enabling in situ micro-mechanical study of failure and fragmentation in geomaterials. The system is based on an original high-pressure triaxial flow cell, which is fully integrated into a custom built microtomography scanner equipped with a laboratory x-ray source. The design of the high-precision mechanical apparatus was informed by the concurrent development of advanced tomographic reconstruction methods based on helical scanning and of algorithms correcting for hardware inaccuracies. This experimental system produces very high-quality 3D images of microstructural changes occurring in rocks undergoing mechanical failure and substantial fragmentation. We present the results of two experiments as case studies to demonstrate the capabilities and versatility of this instrumental platform. These experiments tackle various questions related to the onset of rock failure, the hydromechanical coupling and relaxation mechanisms in fractured rocks, or the fragmentation process in geomaterials such as copper ores.

Force inference in granular materials: Uncertainty analysis and application to three-dimensional experiment design

Interparticle forces are known to influence mechanical and physical properties of granular materials. A method for inferring forces in two-dimensional and three-dimensional experiments has recently been developed and applied to the problem of examining force statistics, energy dissipation, fracture mechanics, and force-property relations. However, a systematic analysis of uncertainties in the forces inferred through this method has not been undertaken. In this paper, our goal is therefore to perform such a systematic analysis. We first review and modify the force inference technique to eliminate its sensitivity to the choice of units and coordinate system origin. We then use discrete-element method simulations to perform a systematic study of how experimental uncertainties and data-processing errors lead to errors in inferred forces. For the considered experiments and simulations, we find that (1) errors in inferred force magnitudes and orientations increase as the ratio between particle stress uncertainties and a measure of stress imposed on the system increases, but remain small in the largest forces in a material; (2) the absence of a moderate number of particle stress tensors in the force inference procedure leads to negligible errors in inferred force magnitudes and orientations; and (3) particle stress tensors that cannot be directly measured during experiments can be "recovered" through the force inference procedure. Based on our results, we make recommendations for future experiment design to reduce uncertainties in inferred forces.

Quantifying local rearrangements in three-dimensional granular materials: Rearrangement measures, correlations, and relationship to stresses

Quantifying the ways in which local particle rearrangements contribute to macroscopic plasticity is one of the fundamental pursuits of granular mechanics and soft matter physics. Here we examine local rearrangements that occur naturally during the deformation of three samples of 3D granular materials subjected to distinct boundary conditions by employing in situ x-ray measurements of particle-resolved structure and stress. We focus on five distinct rearrangement measures, their statistics, interrelationships, contributions to macroscopic deformation, repeatability, and dependence on local structure and stress. Our most significant findings are that local rearrangements (1) are correlated on a scale of three to four particle diameters, (2) exhibit volumetric strain-shear strain and nonaffine displacement-rotation coupling, (3) exhibit correlations that suggest either rearrangement repeatability or that rearrangements span multiple steps of incremental sample strain, and (4) show little dependence on local stress but correlate with quantities describing local structure, such as porosity. Our results are presented in the context of relevant plasticity theories and are consistent with recent findings suggesting that local structure may play at least as important of a role as local stress in determining the nature of local rearrangements.

Directed force propagation in semiflexible networks

We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory. We find the distribution of force within the network is highly heterogeneous, with a small number of fibers supporting a significant fraction of the applied load over distances of multiple mesh sizes surrounding the point of force application. We suggest that these structures may be thought of as tensile force chains, whose structure we explore via simulation. We develop self-consistent calculations of the point-force response function and introduce a transfer matrix approach to explore the decay of tension (into bending) energy and the branching of tensile force chains in the network.

Evolution of texture and internal stresses within polycrystalline rock salt using in situ 3D synchrotron computed tomography and 3D X-ray diffraction

Rock salt caverns have been extensively used as reliable repositories for hazardous waste such as nuclear waste, oil or compressed gases. Undisturbed rock salt deposits in nature are usually impermeable and have very low porosity. However, rock salt formations under excavation stresses can develop crack networks, which increase their porosities; and in the case of a connected crack network within the media, rock salt may become permeable. Although the relationship between the permeability of rock salt and the applied stresses has been reported in the literature, a microscopic study that investigates the properties influencing this relationship, such as the evolution of texture and internal stresses, has yet to be conducted. This study employs in situ 3D synchrotron micro-computed tomography and 3D X-ray diffraction (3DXRD) on two small-scale polycrystalline rock salt specimens to investigate the evolution of the texture and internal stresses within the specimens. The 3DXRD technique measures the 3D crystal structure and lattice strains within rock salt grains. The specimens were prepared under 1D compression conditions and have shown an initial {111} preferred texture, a dominant {110}〈110〉 slip system and no fully connected crack network. The {111} preferred texture under the unconfined compression experiment became stronger, while the {111}〈110〉 slip system became more prominent. The specimens did not have a fully connected crack network until applied axial stresses reached about 30 MPa, at a point where the impermeability of the material becomes compromised due to the development of multiple major cracks.

Intrusion into Granular Media Beyond the Quasistatic Regime

The drag force exerted on an object intruding into granular media is typically assumed to arise from additive velocity and depth dependent contributions. We test this with intrusion experiments and molecular dynamics simulations at constant speed over four orders of magnitude, well beyond the quasistatic regime. For a vertical cylindrical rod we find velocity dependence only right after impact, followed by a crossover to a common, purely depth-dependent behavior for all intrusion speeds. The crossover is set by the timescale for material, forced to well up at impact, to subsequently settle under gravity. These results challenge current models of granular drag.

Stress and force measurement uncertainties in 3D granular materials

We have developed and employed a 3D particle stress tensor and contact force inference technique that employs synchrotron X-ray tomography and diffraction with an optimization algorithm. We have used this technique to study stress and force heterogeneity, particle fracture mechanics, contact-level energy dissipation, and the origin of wave phenomena in 3D granular media for the past five years. Here, we review the technique, describe experimental and numerical sources of uncertainty, and use experimental data and discrete element method simulations to study the method’s accuracy. We find that inferred forces in the strong force network of a 3D granular material are accurately determined even in the presence of noisy stress measurements.

Microscopic origin of shear banding as a localized driven glass transition in compressed colloidal pillars

Here we report on compression experiments of colloidal pillars in which the evolution of a shear band can be followed at the particle level during deformation. Quasistatic deformation results in dilation and anisotropic changes in coordination in a localized band of material. Additionally, a transition from solid- to liquidlike mechanical response accompanies the structural change in the band, as evidenced by saturation of the packing fraction at the glass transition point, a diminishing ability to host anelastic strains, and a rapid decay in the long-range strain correlations. Overall, our results suggest that shear banding quantitatively resembles a localized, driven glass transition.

The influence of packing structure and interparticle forces on ultrasound transmission in granular media

Ultrasound propagation through externally stressed, disordered granular materials was experimentally and numerically investigated. Experiments employed piezoelectric transducers to excite and detect longitudinal ultrasound waves of various frequencies traveling through randomly packed sapphire spheres subjected to uniaxial compression. The experiments featured in situ X-ray tomography and diffraction measurements of contact fabric, particle kinematics, average per-particle stress tensors, and interparticle forces. The experimentally measured packing configuration and inferred interparticle forces at different sample stresses were used to construct spring networks characterized by Hessian and damping matrices. The ultrasound responses of these network were simulated to investigate the origins of wave velocity, acoustic paths, dispersion, and attenuation. Results revealed that both packing structure and interparticle force heterogeneity played an important role in controlling wave velocity and dispersion, while packing structure alone quantitatively explained most of the observed wave attenuation. This research provides insight into time- and frequency-domain features of wave propagation in randomly packed granular materials, shedding light on the fundamental mechanisms controlling wave velocities, dispersion, and attenuation in such systems.

The helical motions of roots are linked to avoidance of particle forces in soil

Limitation to root growth results from forces required to overcome soil resistance to deformation. The variations in individual particle forces affects root development and often deflects the growth trajectory. We have developed transparent soil and optical projection tomography microscopy systems where measurements of growth trajectory and particle forces can be acquired in a granular medium at a range of confining pressures. We developed image-processing pipelines to analyse patterns in root trajectories and a stochastic-mechanical theory to establish how root deflections relate to particle forces and thickening of the root. Root thickening compensates for the increase in mean particle forces but does not prevent deflections from 5% of most extreme individual particle forces causing root deflection. The magnitude of deflections increases with pressure but they assemble into helices of conserved wavelength in response linked to gravitropism. The study reveals mechanisms for the understanding of root growth in mechanically impeding soil conditions and provides insights relevant to breeding of drought-resistant crops.

Hydrogel microparticles for biomedical applications

Hydrogel microparticles (HMPs) are promising for biomedical applications, ranging from the therapeutic delivery of cells and drugs to the production of scaffolds for tissue repair and bioinks for 3D printing. Biologics (cells and drugs) can be encapsulated into HMPs of predefined shapes and sizes using a variety of fabrication techniques (batch emulsion, microfluidics, lithography, electrohydrodynamic (EHD) spraying and mechanical fragmentation). HMPs can be formulated in suspensions to deliver therapeutics, as aggregates of particles (granular hydrogels) to form microporous scaffolds that promote cell infiltration or embedded within a bulk hydrogel to obtain multiscale behaviours. HMP suspensions and granular hydrogels can be injected for minimally invasive delivery of biologics, and they exhibit modular properties when comprised of mixtures of distinct HMP populations. In this Review, we discuss the fabrication techniques that are available for fabricating HMPs, as well as the multiscale behaviours of HMP systems and their functional properties, highlighting their advantages over traditional bulk hydrogels. Furthermore, we discuss applications of HMPs in the fields of cell delivery, drug delivery, scaffold design and biofabrication.

Reversibility of granular rotations and translations

We analyze reversibility of displacements and rotations of spherical grains in three-dimensional compression experiments. Using transparent acrylic beads with cylindrical holes and index matching techniques, we are not only capable of tracking displacements but also analyzing reversibility of rotations. We observe that for moderate compression amplitudes, up to one bead diameter, the translational displacements of the beads after each cycle become mostly reversible after an initial transient. By contrast, granular rotations are largely irreversible. We find a weak correlation between translational and rotational displacements, indicating that rotational reversibility depends on more subtle changes in contact distributions and contact forces between grains compared with displacement reversibility. Three-dimensional rotations in dense granular systems are particularly important, since frictional losses associated with rotations are the dominant mechanism for energy dissipation. As such our work provides a first step toward a thorough study of rotations and tangential forces to understand the granular dynamics in dense systems.

Force networks and jamming in shear-deformed sphere packings

The emergence of rigidity upon changes of temperature, density, or applied stresses in disordered assemblies of particles is of interest in a wide range of soft matter, from glass formers, gels, foams, and granular matter. Shear jamming of frictional grains presents an interesting special case wherein the application of shear stress leads to rigidity rather than its loss. The formation of self-organized structures that resist shear deformation offers an appealing geometric picture of shear jamming, which nevertheless is incompletely developed, and not well integrated with ideas concerning rigidity in frictionless systems. Exploiting the observation that athermally sheared sphere assemblies develop structural features necessary for shear jamming even in the absence of friction [H. A. Vinutha and S. Sastry, Nature Physics 12, 578 (2016)1745-247310.1038/nphys3658], we analyze conditions for jamming in such assemblies computationally. Solving force and torque balance conditions for their contact geometry, we show, and validate with frictional simulations, that the mean contact number Z equals D+1 (for spatial dimension D=2,3) at jamming for both finite and infinite friction, above the "random loose packing" limit density, at variance with previous analyses of frictional jamming. We show that the shear jamming threshold satisfies the marginal stability condition recently proposed for jamming in frictionless systems. Along lines explored in studying covalent glasses, we perform rigidity percolation analysis for D=2 and find that rigidity percolation precedes shear jamming, which, however, coincides with the percolation of over-constrained regions, leading to the identification of a regime analogous to the intermediate phase observed in covalent glasses. Together, these results provide a geometric description of shear jamming that relate closely with analyses of jamming, rigidity, and the glass transition in frictionless systems, and thus help develop a unified description of jamming phenomenology in diverse disordered matter.

Simultaneous X-ray radioscopy/tomography and energy-dispersive diffraction applied to liquid aluminium alloy foams

High-speed X-ray imaging in two dimensions (radioscopy) and three dimensions (tomography) is combined with fast X-ray diffraction in a new experimental setup at the synchrotron radiation source BESSY II. It allows for in situ studies of time-dependent phenomena in complex systems. As a first application, the foaming process of an aluminium alloy was studied in three different experiments. Radioscopy, optical expansion measurements and diffraction were used to correlate the change of foam morphology to the various phases formed during heating of an AlMg15Cu10 alloy to 620°C in the first experiment. Radioscopy was then replaced by tomography. Acquiring tomograms and diffraction data at 2 Hz allows even more details of foam evolution to be captured, for example, bubble size distribution. In a third experiment, 4 Hz tomography yields dynamic insights into fast phenomena in evolving metal foam.

Reduction of the bulk modulus with polydispersity in noncohesive granular solids

We study the effect of grain polydispersity on the bulk modulus in noncohesive two-dimensional granular solids. Molecular dynamics simulations in two dimensions are used to describe polydisperse samples that reach a stationary limit after a number of hysteresis cycles. For stationary samples, we obtain that the packing with the highest polydispersity has the lowest bulk modulus. We compute the correlation between normal and tangential forces with grain size using the concept of branch vector or contact length. Classifying the contact lengths and forces by their size compared to the average length and average force, respectively, we find that strong normal and tangential forces are carried by large contact lengths, generally composed of at least one large grain. This behavior is more dominant as polydispersity increases, making force networks more anisotropic and removing the support, from small grains, in the loading direction thus reducing the bulk modulus of the granular pack. Our results for two dimensions describe qualitatively the results of three-dimensional experiments.

Characterization of the crystal structure, kinematics, stresses and rotations in angular granular quartz during compaction

Three-dimensional X-ray diffraction and X-ray computed tomography are used to study the grain-scale response of angular granular materials to understand grain kinematics, stresses and rotations during compaction and to compare the responses of angular grains with those of spherical grains.

Three-dimensional X-ray diffraction (3DXRD), a method for quantifying the position, orientation and elastic strain of large ensembles of single crystals, has recently emerged as an important tool for studying the mechanical response of granular materials during compaction. Applications have demonstrated the utility of 3DXRD and X-ray computed tomography (XRCT) for assessing strains, particle stresses and orientations, inter-particle contacts and forces, particle fracture mechanics, and porosity evolution in situ. Although past studies employing 3DXRD and XRCT have elucidated the mechanics of spherical particle packings and angular particle packings with a small number of particles, there has been limited effort to date in studying angular particle packings with a large number of particles and in comparing the mechanics of these packings with those composed of a large number of spherical particles. Therefore, the focus of the present paper is on the mechanics of several hundred angular particles during compaction using in situ 3DXRD to study the crystal structure, kinematics, stresses and rotations of angular quartz grains. Comparisons are also made between the compaction response of angular grains and that of spherical grains, and stress-induced twinning within individual grains is discussed.

Force-chain evolution in a two-dimensional granular packing compacted by vertical tappings

We experimentally study the statistics of force-chain evolution in a vertically-tapped two-dimensional granular packing by using photoelastic disks. In this experiment, the tapped granular packing is gradually compacted. During the compaction, the isotropy of grain configurations is quantified by measuring the deviator anisotropy derived from fabric tensor, and then the evolution of force-chain structure is quantified by measuring the interparticle forces and force-chain orientational order parameter. As packing fraction increases, the interparticle force increases and finally saturates to an asymptotic value. Moreover, the grain configurations and force-chain structures become isotropically random as the tapping-induced compaction proceeds. In contrast, the total length of force chains remains unchanged. From the correlations of those parameters, we find two relations: (i) a positive correlation between the isotropy of grain configurations and the disordering of force-chain orientations, and (ii) a negative correlation between the increasing of interparticle forces and the disordering of force-chain orientations. These relations are universally held regardless of the mode of particle motions with or without convection.

Sounds of Failure: Passive Acoustic Measurements of Excited Vibrational Modes

Granular materials can fail through spontaneous events like earthquakes or brittle fracture. However, measurements and analytic models which forecast failure in this class of materials, while of both fundamental and practical interest, remain elusive. Materials including numerical packings of spheres, colloidal glasses, and granular materials have been known to develop an excess of low-frequency vibrational modes as the confining pressure is reduced. Here, we report experiments on sheared granular materials in which we monitor the evolving density of excited modes via passive monitoring of acoustic emissions. We observe a broadening of the distribution of excited modes coincident with both bulk and local plasticity, and evolution in the shape of the distribution before and after bulk failure. These results provide a new interpretation of the changing state of the material on its approach to stick-slip failure.

Two sides of a fault: Grain-scale analysis of pore pressure control on fault slip

Pore fluid pressure in a fault zone can be altered by natural processes (e.g., mineral dehydration and thermal pressurization) and industrial operations involving subsurface fluid injection and extraction for the development of energy and water resources. However, the effect of pore pressure change on the stability and slip motion of a preexisting geologic fault remains poorly understood; yet, it is critical for the assessment of seismic hazard. Here, we develop a micromechanical model to investigate the effect of pore pressure on fault slip behavior. The model couples fluid flow on the network of pores with mechanical deformation of the skeleton of solid grains. Pore fluid exerts pressure force onto the grains, the motion of which is solved using the discrete element method. We conceptualize the fault zone as a gouge layer sandwiched between two blocks. We study fault stability in the presence of a pressure discontinuity across the gouge layer and compare it with the case of continuous (homogeneous) pore pressure. We focus on the onset of shear failure in the gouge layer and reproduce conditions where the failure plane is parallel to the fault. We show that when the pressure is discontinuous across the fault, the onset of slip occurs on the side with the higher pore pressure, and that this onset is controlled by the maximum pressure on both sides of the fault. The results shed new light on the use of the effective stress principle and the Coulomb failure criterion in evaluating the stability of a complex fault zone.

Linking initial microstructure and local response during quasistatic granular compaction

We performed experiments combining three-dimensional x-ray diffraction and x-ray computed tomography to explore the relationship between microstructure and local force and strain during quasistatic granular compaction. We found that initial void space around a grain and contact coordination number before compaction can be used to predict regions vulnerable to above-average local force and strain at later stages of compaction. We also found correlations between void space around a grain and coordination number, and between grain stress and maximum interparticle force, at all stages of compaction. Finally, we observed grains that fracture to have an above-average initial local void space and a below-average initial coordination number. Our findings provide (1) a detailed description of microstructure evolution during quasistatic granular compaction, (2) an approach for identifying regions vulnerable to large values of strain and interparticle force, and (3) methods for identifying regions of a material with large interparticle forces and coordination numbers from measurements of grain stress and local porosity.

Force distribution in a granular medium under dynamic loading

Force distribution in a granular medium subjected to an impulse loading is investigated in experiment and computer simulations. An experimental technique is developed to measure forces acting on individual grains at the bottom of the granular sample consisting of steel balls. Discrete element method simulation also is performed under conditions mimicking those in experiment. Both theory and experiment display exponentially decaying maximum force distributions at the bottom of the sample in the range of large forces. In addition, the simulations also reveal exponential force distribution throughout the sample and uncover correlation properties of the interparticle forces during dynamic loading of the granular samples. Simulated time dependence of coordination number, orientational order parameter, correlation radius, and force distribution clearly demonstrates the nonequilibrium character of the deformation process in a granular medium under impulse loading.

Multi-scale mechanics of granular solids from grain-resolved X-ray measurements

This work discusses an experimental technique for studying the mechanics of three-dimensional (3D) granular solids. The approach combines 3D X-ray diffraction and X-ray computed tomography to measure grain-resolved strains, kinematics and contact fabric in the bulk of a granular solid, from which continuum strains, grain stresses, interparticle forces and coarse-grained elasto-plastic moduli can be determined. We demonstrate the experimental approach and analysis of selected results on a sample of 1099 stiff, frictional grains undergoing multiple uniaxial compression cycles. We investigate the inter-particle force network, elasto-plastic moduli and associated length scales, reversibility of mechanical responses during cyclic loading, the statistics of microscopic responses and microstructure-property relationships. This work serves to highlight both the fundamental insight into granular mechanics that is furnished by combined X-ray measurements and describes future directions in the field of granular materials that can be pursued with such approaches.

Time-of-Flight Three Dimensional Neutron Diffraction in Transmission Mode for Mapping Crystal Grain Structures

The physical properties of polycrystalline materials depend on their microstructure, which is the nano- to centimeter scale arrangement of phases and defects in their interior. Such microstructure depends on the shape, crystallographic phase and orientation, and interfacing of the grains constituting the material. This article presents a new non-destructive 3D technique to study centimeter-sized bulk samples with a spatial resolution of hundred micrometers: time-of-flight three-dimensional neutron diffraction (ToF 3DND). Compared to existing analogous X-ray diffraction techniques, ToF 3DND enables studies of samples that can be both larger in size and made of heavier elements. Moreover, ToF 3DND facilitates the use of complicated sample environments. The basic ToF 3DND setup, utilizing an imaging detector with high spatial and temporal resolution, can easily be implemented at a time-of-flight neutron beamline. The technique was developed and tested with data collected at the Materials and Life Science Experimental Facility of the Japan Proton Accelerator Complex (J-PARC) for an iron sample. We successfully reconstructed the shape of 108 grains and developed an indexing procedure. The reconstruction algorithms have been validated by reconstructing two stacked Co-Ni-Ga single crystals, and by comparison with a grain map obtained by post-mortem electron backscatter diffraction (EBSD).

Analyzing X-ray tomographies of granular packings

Starting from three-dimensional volume data of a granular packing, as, e.g., obtained by X-ray Computed Tomography, we discuss methods to first detect the individual particles in the sample and then analyze their properties. This analysis includes the pair correlation function, the volume and shape of the Voronoi cells, and the number and type of contacts formed between individual particles. We mainly focus on packings of monodisperse spheres, but we will also comment on other monoschematic particles such as ellipsoids and tetrahedra. This paper is accompanied by a package of free software containing all programs (including source code) and an example three-dimensional dataset which allows the reader to reproduce and modify all examples given.

Refractive index matched scanning and detection of soft particles

We describe here how to apply the three-dimensional imaging technique of refractive index matched scanning to hydrogel spheres. Hydrogels are water based materials with a low refractive index, which allows for index matching with water-based solvent mixtures. We discuss here various experimental techniques required to handle specifically hydrogel spheres as opposed to other transparent materials. The deformability of hydrogel spheres makes their identification in three-dimensional images non-trivial. We will also discuss numerical techniques that can be used in general to detect contacting, non-spherical particles in a three-dimensional image. The experimental and numerical techniques presented here give experimental access to the stress tensor of a packing of deformed particles.