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Key persornel in the Mechanics of Granular Materials (MGM) experiment include Khalid Alshibli, project scientist at NASA's Marshall Space Flight Center (MSFC). Sand and soil grains have faces that can cause friction as they roll and slide against each other, or even cause sticking and form small voids between grains. This complex behavior can cause soil to behave like a liquid under certain conditions such as earthquakes or when powders are handled in industrial processes. MGM experiments aboard the Space Shuttle use the microgravity of space to simulate this behavior under conditions that cannot be achieved in laboratory tests on Earth. MGM is shedding light on the behavior of fine-grain materials under low effective stresses. Applications include earthquake engineering, granular flow technologies (such as powder feed systems for pharmaceuticals and fertilizers), and terrestrial and planetary geology. Nine MGM specimens have flown on two Space Shuttle flights. Another three are scheduled to fly on STS-107. The principal investigator is Stein Sture of the University of Colorado at Boulder. (Credit: MSFC).

Key persornel in the Mechanics of Granular Materials (MGM) experiment are Mark Lankton (Program Manager at University Colorado at Boulder), Susan Batiste (research assistance, UCB), and Stein Sture (principal investigator). Sand and soil grains have faces that can cause friction as they roll and slide against each other, or even cause sticking and form small voids between grains. This complex behavior can cause soil to behave like a liquid under certain conditions such as earthquakes or when powders are handled in industrial processes. MGM experiments aboard the Space Shuttle use the microgravity of space to simulate this behavior under conditions that cannot be achieved in laboratory tests on Earth. MGM is shedding light on the behavior of fine-grain materials under low effective stresses. Applications include earthquake engineering, granular flow technologies (such as powder feed systems for pharmaceuticals and fertilizers), and terrestrial and planetary geology. Nine MGM specimens have flown on two Space Shuttle flights. Another three are scheduled to fly on STS-107. The principal investigator is Stein Sture of the University of Colorado at Boulder. (Credit: University of Colorado at Boulder).

We study, using simulations the dynamical properties of complex ferromagnetic granular materials. The system of grains is modeled by a disordered two-dimensional lattice in which the grains are embedded, while the magnitude and direction of the easy axis are random. Using the monte-carlo method we track the dynamics of the magnetic moments of the grains. We observe a transition of the system from a macroscopic blocked (ferromagnetic) phase at low temperature in which the grain's magnetic moment do not flip to the other direction to an unblocked (superparamagnetic) phase at high temperature in which the magnetic moment is free to rotate. Our results suggest that this transition exhibits the characteristics of a second order phase transition such as the appearance of a giant cluster of unblocked grains which is fractal at the critical temperature, a peak in the size of the second largest cluster at the same temperature and a power law distribution of cluster sizes near the criticality.

We attempt to describe the stress distributions of granular packings using lattice-based layer-by-layer stochastic models that satisfy the constraints of force and torque balance and non-tensile forces at each site. The inherent asymmetry in the layer-by-layer approach appears to lead to an asymmetric force distribution, in disagreement with both experiments and general symmetry considerations. The vertical force component probability distribution is robust and in agreement with predictions of the scalar q model while the distribution of horizontal force components is qualitatively different and depends on the details of implementation.

We show that a mixture of two species of granular particles with equal sizes but differing densities can be either segregated or mixed by adjusting the granular temperature gradient and the magnitude of the gravitational force. In the absence of gravity, the dense, heavy particles move to the colder regions. If the temperature gradient is put into a gravitational field with the colder regions above the hotter, a uniform mixture of light and heavy particles can be attained. This situation can be realized in a container of finite height with a vibrating bottom, placed in a gravitational field. We present a relation between the height of the container, the particle properties, and the strength of gravity required to minimize segregation.

The static as well as the dynamic behaviour of granular material are determined by dynamic {\it and} static friction. There are well known methods to include static friction in molecular dynamics simulations using scarcely understood forces. We propose an Ansatz based on the geometrical shape of nonspherical particles which does not involve an explicit expression for static friction. It is shown that the simulations based on this model are close to experimental results.

We have recently developed some simple continuum models of static granular media which display "fragile" behaviour: they predict that the medium is unable to support certain types of infinitesimal load (which we call "incompatible" loads) without plastic rearrangement. We argue that a fragile description may be appropriate when the mechanical integrity of the medium arises adaptively, in response to a load, through an internal jamming process. We hypothesize that a network of force chains (or "granular skeleton") evolves until it can just support the applied load, at which point it comes to rest; it then remains intact so long as no incompatible load is applied. Our fragile models exhibits unusual mechanical responses involving hyperbolic equations for stress propagation along fixed characteristics through the material. These characteristics represent force chains; their arrangement expressly depends on the construction history. Thus, for example, we predict a large difference in the stress pattern beneath two conical piles of sand, one poured from a point source and one created by sieving.

A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyze plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap $H$ when the latter is large compared to the grain diameter $d_p$. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as $(H/d_p)^{1/3}$ in the limit $(H/d_p) \gg 1$, for plane shear under gravity and cylindrical Couette flow.

We present experimental results on the shape of arches that block the outlet of a two dimensional silo. For a range of outlet sizes, we measure some properties of the arches such as the number of particles involved, the span, the aspect ratio, and the angles between mutually stabilizing particles. These measurements shed light on the role of frictional tangential forces in arching. In addition, we find that arches tend to adopt an aspect ratio (the quotient between height and half the span) close to one, suggesting an isotropic load. The comparison of the experimental results with data from numerical models of the arches formed in the bulk of a granular column reveals the similarities of both, as well as some limitations in the few existing models.

The effect of the anisotropy on the elastoplastic response of two dimensional packed samples of polygons is investigated here, using molecular dynamics simulation. We show a correlation between fabric coefficients, characterizing the anisotropy of the granular skeleton, and the anisotropy of the elastic response. We also study the anisotropy induced by shearing on the subnetwork of the sliding contacts. This anisotropy provides an explanation to some features of the plastic deformation of granular media.

The effect of the anisotropy on the elastoplastic response of two dimensional packed samples of polygons is investigated here, using molecular dynamics simulation. We show a correlation between fabric coefficients, characterizing the anisotropy of the granular skeleton, and the anisotropy of the elastic response. We also study the anisotropy induced by shearing on the subnetwork of the sliding contacts. This anisotropy provides an explanation to some features of the plastic deformation of granular media.

This report describes an investigation into one-dimensional stress wave propagation in granular materials with microstructure. The study employs the distributed body concept advanced by Goodman and the associated wave propagation studies conducted by Nuniziato, Walsh, et al. A one-dimensional computer program, referred to as MIC1D, has been developed for studying wave propagation in granular materials due to airblast loading. This program allows for: (1) arbitrary surface airblast loading, (2) depth-dependent volume distribution function simulating gravity effects in a granular mass, and (3) treatment of grain size and local porosity as random variables. It incorporates three forms of depth-dependent volume distribution functions, i.e., a periodic form, and exponential form, and a combined periodic-exponential formulation. The user can select any of these forms for the particular application at hand. The probabilistic treatment of grain size and local porosity is accomplished by using a moment-generating procedure due to Rosenblueth. The computer program calculates the expected value and the variance of the output quantities, such as stress and particle motion, due to the randomness in these variables. Application of the computer program is demonstrated by presenting the results of a series of parametric calculations dealing with propagation of acceleration waves in granular media. Documentation of MIC1D is provided in an Appendix.

We perform molecular dynamic (MD) simulations of frictional non-thermal particles driven by an externally applied shear stress. After the system jams following a transient flow, we probe its mechanical response in order to clarify whether the resulting solid is 'fragile'. We find the system to respond elastically and isotropically to small perturbations of the shear stress, suggesting absence of fragility. These results are interpreted in terms of the energy landscape of dissipative systems. For the same values of the control parameters, we check the behaviour of the system during a stress cycle. Increasing the maximum stress value, a crossover from a visco-elastic to a plastic regime is observed.

The vibrational properties of a face-centered cubic granular crystal of monodisperse particles are predicted using a discrete model as well as two micropolar models, first the classical Cosserat and second an enhanced Cosserat-type model, that properly takes into account all degrees of freedom at the contacts between the particles. The continuum models are derived from the discrete model via a micro-macro transition of the discrete relative displacements and particle rotations to the respective continuum field variables. Next, only the long wavelength approximations of the models are compared and, considering the discrete model as reference, the Cosserat model shows inconsistent predictions of the bulk wave dispersion relations. This can be explained by an insufficient modeling of sliding mode of particle interactions in the Cosserat model. An enhanced micropolar model is proposed including only one new elastic tensor from the more complete second order gradient micropolar theory. This enhanced micropolar model then involves the minimum number of elastic constants to consistently predict the dispersion relations in the long wavelength limit.

We investigate the role of friction in compaction and segregation of granular materials by combining Edwards' thermodynamic hypothesis with a simple mechanical model and mean-field based geometrical calculations. Systems of single species with large friction coefficients are found to compact less. Binary mixtures of grains differing in frictional properties are found to segregate at high compactivities, in contrary to granular mixtures differing in size, which segregate at low compactivities. A phase diagram for segregation vs. friction coefficients of the two species is generated. Finally, the characteristics of segregation are related directly to the volume fraction without the explicit use of the yet unclear notion of compactivity.

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference $\delta$ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time $\tau$ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when $\delta$ is an integer part of $\pi$. Introduction of fluctuations of $\delta$ supresses the singularities of $\tau(\delta)$ and smoothes the dependence $\tau(\delta)$.

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference $\delta$ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time $\tau$ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when $\delta$ is an integer part of $\pi$. Introduction of fluctuations of $\delta$ supresses the singularities of $\tau(\delta)$ and smoothes the dependence $\tau(\delta)$.

A system of inelastic hard disks in a thin pipe capped by hot walls is studied with the aim of investigating velocity correlations between particles. Two effects lead to such correlations: inelastic collisions help to build localized correlations, while momentum conservation and diffusion produce long ranged correlations. In the quasi-elastic limit, the velocity correlation is weak, but it is still important since it is of the same order as the deviation from uniformity. For system with stronger inelasticity, the pipe contains a clump of particles in highly correlated motion. A theory with empirical parameters is developed. This theory is composed of equations similar to the usual hydrodynamic laws of conservation of particles, energy, and momentum. Numerical results show that the theory describes the dynamics satisfactorily in the quasi-elastic limit, however only qualitatively for stronger inelasticity.

Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches.

Refraction and deflection of shear zones in layered granular materials was studied experimentally and numerically. We show, that (i) according to a recent theoretical prediction [T. Unger, Phys. Rev. Lett. 98, 018301 (2007)] shear zones refract in layered systems in analogy with light refraction, (ii) zone refraction obeys Snell's law known from geometric optics and (iii) under natural pressure conditions (i.e. in the presence of gravity) the zone can also be deflected by the interface so that the deformation of the high friction material is avoided.

Granular materials are inherently heterogeneous, leading to challenges in formulating accurate models of sound propagation. In order to quantify acoustic responses in space and time, we perform experiments in a photoelastic granular material in which the internal stress pattern (in the form of force chains) is visible. We utilize two complementary methods, high-speed imaging and piezoelectric transduction, to provide particle-scale measurements of both the amplitude and speed of an acoustic wave in the near-field regime. We observe that the wave amplitude is on average largest within particles experiencing the largest forces, particularly in those chains radiating away from the source, with the force-dependence of this amplitude in qualitative agreement with a simple Hertzian-like model of particle contact area. In addition, we are able to directly observe rare transient force chains formed by the opening and closing of contacts during propagation. The speed of the leading edge of the pulse is in quantitative agreement with predictions for one-dimensional chains, while the slower speed of the peak response suggests that it contains waves which have travelled over multiple paths even within just this near-field region. These effects highlight the importance of particle-scale behaviors in determining the acoustical properties of granular materials.

We examine the "transmissibility" of a simulated two-dimensional pack of frictionless disks formed by confining dilute disks in a shrinking, periodic box to the point of mechanical stability. Two opposite boundaries are then removed, thus allowing a set of free motions. Small free displacements on one boundary then induce proportional displacements on the opposite boundary. Transmissibility is the ability to distinguish different perturbations by their distant responses. We assess transmissibility by successively identifying free orthonormal modes of motion that have the {\em smallest} distant responses. The last modes to be identified in this "pessimistic" basis are the most transmissive. The transmitted amplitudes of these most transmissive modes fall off exponentially with mode number. Similar exponential falloff is seen in a simple elastic medium, though the responsible modes differ greatly in structure in the two systems. Thus the marginal pack's transmissibility is qualitatively similar to that of a simple elastic medium. We compare our results with recent findings based on the projection of the space of free motion onto interior sites.

Creep mechanisms in uniaxially compressed 3D granular solids comprised of faceted frictionless grains are studied numerically using a constant pressure and constant stress simulation method. Rapid uniaxial compression followed by slow dilation is predicted on the basis of a logarithmic creep phenomenon. Micromechanical analysis indicates the existence of a correlation between granular creep and grain-scale deformations. Localized regions of large strain appear during creep and grow in magnitude and size with time. Furthermore, the accumulation of non-affine granular displacements increases linearly with local strain, thereby providing insights into the origins of plastic dissipation during stress-driven creep evolution. The prediction of slow logarithmic dynamics in the absence of friction indicates a universality in the role of plastic dissipation during the creep of granular solids.

Granular materials transmit stress via a network of force chains. Despite the importance of these chains to characterizing the stress state and dynamics of the system, there is no common framework for quantifying their their properties. Recently, attention has turned to the tools of network science as a promising route to such a description. In this paper, we apply community detection techniques to numerically-generated packings of spheres over a range of interparticle friction coefficients and confining pressures. In order to extract chain-like features, we use a modularity maximization with a recently-developed geographical null model \cite{Bassett2015}, and optimize the technique to detect branched structures by minimizing the normalized convex hull of the detected communities. We characterize the force chain communities by their size (number of particles), network strength (internal forces), and normalized convex hull ratio (sparseness). We find the that the first two exhibit an approximately linear correlation and are therefore largely redundant. For both pressure $P$ and interparticle friction $\mu$, we observe crossovers in behavior. For $\mu \lesssim 0.1$, the packings exhibit more sensitivity to pressure. In addition, we identify a crossover pressure where the frictional dependence switches from having more large/strong communities at low $\mu$ vs. high $\mu$. We explain these phenomena by comparison to the spatial distribution of communities along the vertical axis of the system. These results provide new tools for considering the mesoscale structure of a granular system and pave the way for reduced descriptions based on the force chain structure.

The evolution of wide shear zones (or shear bands) was investigated experimentally and numerically for quasistatic dry granular flows in split bottom shear cells. We compare the behavior of materials consisting of beads, irregular grains (e.g. sand) and elongated particles. Shearing an initially random sample, the zone width was found to significantly decrease in the first stage of the process. The characteristic shear strain associated with this decrease is about unity and it is systematically increasing with shape anisotropy, i.e. when the grain shape changes from spherical to irregular (e.g. sand) and becomes elongated (pegs). The strongly decreasing tendency of the zone width is followed by a slight increase which is more pronounced for rod like particles than for grains with smaller shape anisotropy (beads or irregular particles). The evolution of the zone width is connected to shear induced density change and for nonspherical particles it also involves grain reorientation effects. The final zone width is significantly smaller for irregular grains than for spherical beads.

We apply the statistical mechanical approach based on the ``flat'' measure proposed by Edwards and coworkers to the parking lot model, a model that reproduces the main features of the phenomenology of vibrated granular materials. We first build the flat measure for the case of vanishingly small tapping strength and then generalize the approach to finite tapping strengths by introducing a new ``thermodynamic'' parameter, the available volume for particle insertion, in addition to the particle density. This description is able to take into account the various memory effects observed in vibrated granular media. Although not exact, the approach gives a good description of the behavior of the parking-lot model in the regime of slow compaction.

We apply the statistical mechanical approach based on the ``flat'' measure proposed by Edwards and coworkers to the parking lot model, a model that reproduces the main features of the phenomenology of vibrated granular materials. We first build the flat measure for the case of vanishingly small tapping strength and then generalize the approach to finite tapping strengths by introducing a new ``thermodynamic'' parameter, the available volume for particle insertion, in addition to the particle density. This description is able to take into account the various memory effects observed in vibrated granular media. Although not exact, the approach gives a good description of the behavior of the parking-lot model in the regime of slow compaction.

The study is on detonation characteristics of low-density granular materials. The purpose of the research under this and preceding contracts is to clarify the processes during initiation to detonation in propellants and explosives. Toward this end studies have been made of (a) the mechanisms of initiation and propagation in low-density NH4ClO4, (b) the properties of initiating shocks, (c) the loci of shocked states achieved in low-density granular aggregates, (d) hot spots in shocked granular NH4ClO4 and KC1, and (2) friction and jetting as possible causes of hot spots. The main conclusions are that shocks greater than about 5 kbar are reactive in granular NH4ClO4 at a density of 1.0 g/cu cm, that the reaction occurs from the time of shock entry and therefore is at least partially in the shock front, and that the likely sites of this shock-front reaction are hot spots which occur when the interstices collapse. These hot spots have been photographed at about 40 kbar.

The study is on detonation characteristics of low-density granular materials. The purpose of the research under this and preceding contracts is to clarify the processes during initiation to detonation in propellants and explosives. Toward this end studies have been made of (a) the mechanisms of initiation and propagation in low-density NH4ClO4, (b) the properties of initiating shocks, (c) the loci of shocked states achieved in low-density granular aggregates, (d) hot spots in shocked granular NH4ClO4 and KC1, and (2) friction and jetting as possible causes of hot spots. The main conclusions are that shocks greater than about 5 kbar are reactive in granular NH4ClO4 at a density of 1.0 g/cu cm, that the reaction occurs from the time of shock entry and therefore is at least partially in the shock front, and that the likely sites of this shock-front reaction are hot spots which occur when the interstices collapse. These hot spots have been photographed at about 40 kbar.

Bibliographical footnotes

Working with soil, sand, powders, ores, cement and sintered bricks, excavating, grading construction sites, driving off-road, transporting granules in chutes and pipes, sifting gravel, separating solids from gases, and using hoppers are so routine that it seems straightforward to do it on the Moon and Mars as we do it on Earth. This paper brings to the fore how little these processes are understood and the millennia-long trial-and-error practices that lead to today's massive over-design, high failure rate, and extensive incremental scaling up of industrial processes because of the inadequate predictive tools for design. We present a number of pragmatic scenarios where granular materials play a role, the risks involved, and what understanding is needed to greatly reduce the risks.

A lattice model is presented for investigating the fluctuations in static granular materials under gravitationally induced stress. The model is similar in spirit to the scalar q-model of Coppersmith et al., but ensures balance of all components of forces and torques at each site. The geometric randomness in real granular materials is modeled by choosing random variables at each site, consistent with the assumption of cohesionless grains. Configurations of the model can be generated rapidly, allowing the statistical study of relatively large systems. For a 2D system with rough walls, the model generates configurations consistent with continuum theories for the average stresses (unlike the q-model) without requiring the assumption of a constitutive relation. For a 2D system with periodic boundary conditions, the model generates single-grain force distributions similar to those obtained from the q-model with a singular distribution of q's.

We discuss the effect of virtual intermediate localized states on inter-grain tunneling that controls conduction in granular conductors on the insulating side of the metal-insulator transition. It is shown that intermediate states can substantially increase inter-grain tunneling transition probabilities and give rise to the conductivity temperature dependence of the form ln(sigma) ^ -(T(0)/T), where x approximately equal 0.4, and to a large enhancement of the conductivity.

This paper experimentally discusses events being relevant to the arching effect in granular materials by the developed trapdoor apparatus. A focus on the features of stable arch at two moments when an arch is on the verge of collapse in addition to the time after the collapse. The critical arch for a granular medium is the last stable arch belonging to a trapdoor with maximum possible width at a particular base angle. The maximum trapdoor width is observed 4.7 to 8.67 times the average particles diameter depending on the internal friction angle and base angle values. The critical arch has the maximum width in proportion to previous run, whereas its height not only increases but will get smaller. After arch collapses, particles remained in the test box, are approximately located on the horizontal rails symmetrical. Besides, their arrangement remains almost constant compared to early one.

This paper discusses the arching effect as the formation of a stable arch in granular materials. For this aim, a developed trapdoor apparatus is designed in order to investigate the arch dimensions in term of the internal friction angle, average size and base angle of materials. Observations show that for all tested granular ensembles, width and height of the arch increase with an increase in trapdoor width and a decrease in base angle. It is also found that the shape of the whole arches is governed by a parabola. In addition, for both constant values of trapdoor width and base angle, the increase in both the internal friction angle and density of granular materials leads to the increase in arch dimensions.

Segregation and mixing of granular mixtures during heap formation have important consequences in industry and agriculture. This research investigates three different final particle configurations of bi-disperse granular mixtures -- stratified, segregated and mixed -- during filling of quasi-two dimensional silos. We consider a larger number and relatively wider range of control parameters than previous studies, including particle size ratio, flow rate, system size and heap rise velocity. The boundary between stratified and unstratified states is primarily controlled by the two-dimensional flow rate, with the critical flow rate for the transition depending weakly on particle size ratio and flowing layer length. In contrast, the transition from segregated to mixed states is controlled by the rise velocity of the heap, a control parameter not previously considered. The critical rise velocity for the transition depends strongly on the particle size ratio.

The heart of the MGM experiment is a set of six test cells, each containing a sleeve of 2.8 lbs. of Ottawa F-75 banding sand. Because Ottawa sand is widely used in the civil engineering experiments and evaluations, its use on MGM will allow results to be compared directly with results already obtained on Earth. The soil specimen is contained in a latex sleeve that is 0.3 mm thick and printed with a grid pattern so cameras can record changes in shape and position. Each specimen is contained in a test cell shaped like an equilateral prism and includes a Lexan jacket sandwiched between metal end plates cornected by guide rods. During the experiment, a test cell is held on a rigid observation pad mounted between an array of three CCD cameras and banks of small light-emitting diodes. The MGM video control system electronically interleaves the images for a video recorder. MGM was designed and developed by Sandia National Laboratories and the U.S. Department of Energy in Albuquerque, N.M.

The heart of the MGM experiment is a set of six test cells, each containing a sleeve of 2.8 lbs. of Ottawa F-75 banding sand. Because Ottawa sand is widely used in the civil engineering experiments and evaluations, its use on MGM will allow results to be compared directly with results already obtained on Earth. The soil specimen is contained in a latex sleeve that is 0.3 mm thick and printed with a grid pattern so cameras can record changes in shape and position. Each specimen is contained in a test cell shaped like an equilateral prism and includes a Lexan jacket sandwiched between metal end plates cornected by guide rods. During the experiment, a test cell is held on a rigid observation pad mounted between an array of three CCD cameras and banks of small light-emitting diodes. The MGM video control system electronically interleaves the images for a video recorder. MGM was designed and developed by Sandia National Laboratories and the U.S. Department of Energy in Albuquerque, N.M.

Balance laws for constituents of a mixture of a finite number of granular materials are given. It is shown that the resulting balance laws for the mixture as a whole generalize those previously given for a single granular material.

Phase transition of strongly excited granular materials in 2D pipe is investigated numerically. By changing the ratio between width of the pipe and the height of the granular bed, we observe the transition between the 1 dimensional like state and the actual 2 dimensional state. Moreover, it is found that the character of the transition changes when the magnitude of dissipation passes through a critical value.

A microstructural theory of dense granular materials is presented, based on two main ideas. Firstly, that macroscopic shear results form activated local rearrangements at a mesoscopic scale. Secondly, that the update frequency of microscopic processes is determined by granular temperature. In a shear cell, the resulting constitutive equations account for Bagnold's scaling and for the existence of a Coulomb criterion of yield. In the case of a granular flow down an inclined plane, they account for the rheology observed in recent experiments and for the temperature and velocity profiles measured numerically.

We propose a nonlinear hydrodynamical model of granular materials. We show how this model describes the formation of a sand pile from a homogeneous distribution of material under gravity, and then discuss a simulation of a rotating sandpile which shows, in qualitative agreement with experiment, a static and dynamic angle of repose.

A test cell for Mechanics of Granular Materials (MGM) experiment is tested for long-term storage with water in the system as plarned for STS-107. This view shows the compressed sand column with the protective water jacket removed. Sand and soil grains have faces that can cause friction as they roll and slide against each other, or even cause sticking and form small voids between grains. This complex behavior can cause soil to behave like a liquid under certain conditions such as earthquakes or when powders are handled in industrial processes. Mechanics of Granular Materials (MGM) experiments aboard the Space Shuttle use the microgravity of space to simulate this behavior under conditons that cannot be achieved in laboratory tests on Earth. MGM is shedding light on the behavior of fine-grain materials under low effective stresses. Applications include earthquake engineering, granular flow technologies (such as powder feed systems for pharmaceuticals and fertilizers), and terrestrial and planetary geology. Nine MGM specimens have flown on two Space Shuttle flights. Another three are scheduled to fly on STS-107. The principal investigator is Stein Sture of the University of Colorado at Boulder. Credit: University of Colorado at Boulder

Test cells comprise specimen sand contained in a latex membrane (with a grid pattern for CCD cameras) between metal end plates and housed in a water-filled Lexan jacket. Experiment flown on STS-79 and STS-89. Principal Investigator: Dr. Stein Sture.

Energy absorbing mechanisms in sand subjected to one-dimensional compression are reported. For pressures below crushing of the grains, a granular medium of equal radii elastic spheres in a face-centered cubic array is analyzed. Expressions are obtained for the axial stress-strain curve, constrained modulus, coefficient of earth pressure at rest, and relationship between absorbed energy and input energy for one cycle of loading. The energy absorbed as a result of crushing is considered by analyzing statistical relationships between changes in grain size distribution curves and the new surface areas created. An apparatus is described which has the capability of maintaining conditions at zero radial strain under in- creasing axial stress. The lateral stresses developed under these conditions are measured. Preliminary experimental results are presented for one sand which show the variation of the coefficient of earth pressure at rest and the stress- strain relationships with initial void ratio, over consolidation ratio, and strain rate. A correlation of theory and test results is presented.

Strain in granular materials in quasistatic conditions under varying stress originate in (I) contact deformation and (II) rearrangements of the contact network. Depending on sample history and applied load, either mechanism might dominate. One may thus define rheological regimes I and II accordingly. Their properties are presented and illustrated here with discrete numerical simulation results on sphere packings. Understanding the microscopic physical origin of strain enables one to clarify such issues as the existence of macroscopic elasticity, the approach to stress-strain relations in the large system limit and the sensitivity to noise.

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the equation. A line of nontrivial fixed point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively.

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the equation. A line of nontrivial fixed point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively.

The packing of particles can change radically during cyclic loading such as in an earthquake or when shaking a container to compact a powder. A large hole (1) is maintained by the particles sticking to each other. A small, counterclockwise strain (2) collapses the hole, and another large strain (3) forms more new holes which collapse when the strain reverses (4). Sand and soil grains have faces that can cause friction as they roll and slide against each other, or even cause sticking and form small voids between grains. This complex behavior can cause soil to behave like a liquid under certain conditions such as earthquakes or when powders are handled in industrial processes. MGM experiments aboard the Space Shuttle use the microgravity of space to simulate this behavior under conditions that carnot be achieved in laboratory tests on Earth. MGM is shedding light on the behavior of fine-grain materials under low effective stresses. Applications include earthquake engineering, granular flow technologies (such as powder feed systems for pharmaceuticals and fertilizers), and terrestrial and planetary geology. Nine MGM specimens have flown on two Space Shuttle flights. Another three are scheduled to fly on STS-107. The principal investigator is Stein Sture of the University of Colorado at Boulder. (after T.L. Youd, Packing Changes and Liquefaction Susceptibility, Journal of the Geotechnical Engieering Division, 103: GT8,918-922, 1977)(Credit: NASA/Marshall Space Flight Center.)(Credit: University of Colorado at Boulder).

The objective of this research is to obtain response and constitutive characterization for Concrete and mortar at strain rates up to 105/s, to analyze the evolution of load-carrying and energy absorption capacities, and to understand deformation and failure mechanisms under high pressures. The high rate failure mechanisms considered include fragmentation, comminution and granular flow. Our investigation has focused on (1) the dynamic response of the G-mix concrete under impact conditions; (2) the effect of composite microstructure and aggregate reinforcement on the material stress-carrying capacity; and (3) the failure wave phenomenon in mortar under uniaxial-strain impact loading. Experiments and numerical simulations have shown that while the quasistatic uniaxial strength for the concrete is approximately 30 MPa, the average compressive stresses carried by the concrete under the conditions of impact experiments involving elastic steel target plates and impact velocities between 290 - 330 /ma is on the order of 1600 MPa. The marked increase in stress is attributed to the effect of higher strain rates which are on the order of 104/s and to the effect of lateral confining stresses. Experiments also showed that the stresses carried by mortar (matrix phase in concrete) under the same conditions are approximately 1200 MPa or 75 % of that for the concrete (approximately 1600 MPa). Due to the composite microstructures and its relatively coarse aggregate size, the deformation and stresses are nonuniform inside the concrete.