Granular shear flows at the elastic limit

2002 ◽  
Vol 465 ◽  
pp. 261-291 ◽  
Author(s):  
CHARLES S. CAMPBELL
Keyword(s):  
Stress Reduction ◽  
Particle Surface ◽  
Surface Friction ◽  
Internal Force ◽  
Force Chains ◽  
Rheological Parameter ◽  
Nonlinear Behaviour ◽  
Static Regime ◽  
Computer Simulation Studies ◽  
Inertial Regime

This paper describes computer simulation studies of granular materials under dense conditions where particles are in persistent contact with their neighbours and the elasticity of the material becomes an important rheological parameter. There are two regimes at this limit, one for which the stresses scale with both elastic and inertial properties (called the elastic–inertial regime), and a non-inertial quasi-static regime in which the stresses scale purely elastically (elastic–quasi-static). In these elastic regimes, the forces are generated by internal force chains. Reducing the concentration slightly causes a transition from an elastic to a purely inertial behaviour. This transition occurs so abruptly that a 2% concentration reduction can be accompanied by nearly three orders of magnitude of stress reduction. This indicates that granular flows near this limit are prone to instabilities such as those commonly observed in shear cells. Unexpectedly, there is no path between inertial (rapid) flow and quasi-static flow by varying the shear rate at a fixed concentration; only by reducing the concentration can one cause a transition from quasi-static to inertial flow. The solid concentrations at which this transition occurs as well as the magnitude of the stresses in the elastic regimes are strong functions of the particle surface friction, because the surface friction strongly affects the strength of the force chains. A parametric analysis of the elastic regime generated flowmaps showing the various regimes that might be realized in practice. Many common materials such as sand require such large shear rates to reach the elastic–inertial regime that it is unattainable for all practical purposes; such materials will demonstrate either an elastic–quasi-static behaviour or a pure inertial behaviour depending on the concentration – with many orders of magnitude of stress change between them. Finally, the effects of nonlinear contacts are investigated and an appropriate scaling is proposed that accounts for the nonlinear behaviour in the elastic–quasi-static regime.

Clusters in dense-inertial granular flows

2011 ◽  
Vol 687 ◽  
pp. 341-359 ◽  
Author(s):  
Charles S. Campbell
Keyword(s):  
Granular Flow ◽  
Significant Contribution ◽  
Cluster Formation ◽  
Particle Surface ◽  
Surface Friction ◽  
Momentum Transport ◽  
Cluster Development ◽  
Hard Sphere Models ◽  
Rate Limiting ◽  
Inertial Regime

AbstractIn the dense-inertial regime of granular flow, the stresses scale inertially, but the flow is dominated by clusters of particles. This paper describes observations of cluster development in this regime. Clusters were seen to form for both elastic and inelastic reasons: elastic when the shear rate pushes the particles together faster than the contacts can elastically disperse them, and inelastic as large energy dissipation leads to cluster formation. Furthermore, large particle surface friction leads to cluster formation both for structural reasons, because it generates stronger clusters, and for energetic reasons, as friction dissipates energy. However, the most intriguing result of this work is that clusters appear to have little effect on the rheology of the dense inertial regime, which suggests that one can model the dense inertial regime with entirely collisional hard sphere models, and not have to worry about the complexities of modelling clusters. But at the same time it presents a physical puzzle, as one would normally expect the rheology to be strongly dependent on microstructural features such as clusters, particularly as they present an elastic pathway for internal momentum transport. There is no completely satisfying explanation for why the clusters can be ignored, but two possibilities suggest themselves. Because the clusters are short-lived, it is possible that they do not survive long enough to make a significant contribution to the momentum transport. And it is also possible for the granular temperature that governs transport between clusters to act as a rate-limiting bottleneck that is in overall control of the momentum transport rate.

UNDERSTANDING FORCE CHAINS IN DENSE GRANULAR MATERIALS

2010 ◽  
Vol 24 (29) ◽  
pp. 5743-5759 ◽  
Author(s):  
QICHENG SUN ◽  
FENG JIN ◽  
JIANGUO LIU ◽  
GUOHUA ZHANG
Keyword(s):  
Particle Surface ◽  
Length Distribution ◽  
Surface Friction ◽  
Contact Forces ◽  
Force Chains ◽  
Compression Tests ◽  
Physical Processes ◽  
Dimensionless Numbers ◽  
Chain Length Distribution ◽  
Insight Into

When a load is applied to a dense granular material, the stress is largely transmitted by relatively rigid, heavily stressed chains of particles forming a sparse network of larger contact forces. Force chains act as the key determinant of mechanical properties such as stability, elasticity and flowability. To understand the structure and evolution of force chains, related physical processes and three corresponding characteristic time scales are analyzed in this study. We also propose three dimensionless numbers for the measurement of the relative importance of force chains. To solely study the effect of particle surface friction on force chains, uniaxial compression tests of 11,000 equal-sized particles in 2D were numerically simulated using the discrete element method. By proposing three conditions to define a force chain, the chain length distribution is found in the form of a power law. The exponent of 1.744 is independent of the surface friction. Although these results were obtained from partially crystallized jammed packings, they provide new insight into the physical processes and the structure of force chains, and thus will be helpful in the interpretation of force chains in other dense granular systems.

Microscopic Study of Pressure-Transfer Characteristics in the Solid Granule Medium Forming

2011 ◽  
Vol 183-185 ◽  
pp. 1752-1756 ◽  
Author(s):  
Miao Yan Cao ◽  
Chang Cai Zhao ◽  
Hong Xiao
Keyword(s):  
Pressure Coefficient ◽  
Internal Force ◽  
Force Chains ◽  
Forming Process ◽  
Compression Process ◽  
Transfer Characteristics ◽  
Steel Balls ◽  
Granule Medium ◽  
Axial Compression Experiment ◽  
Solid Granule

To reveal the pressure-transfer characteristics of the granular materials in the Solid Granule Medium Forming process, the stainless steel balls with diameter of 1 mm were selected as medium to conduct the axial compression experiment. The particle compression process was simulated by discrete element method, and then the variation law of the microstructure was analyzed from the perspective of force chain. The results showed that: In the gradual compression process of granule medium, its force chains distribution changes from the initial circular shape to the elliptical shape. As the stress increases, the force chains get denser and denser. In addition, the lateral pressure coefficient changes in power law with the compressive stress and it tends to be constant when the internal force chains structure gets stable.

A non-local rheology for dense granular flows

2009 ◽  
Vol 367 (1909) ◽  
pp. 5091-5107 ◽  
Author(s):  
Olivier Pouliquen ◽  
Yoel Forterre
Keyword(s):  
Granular Flows ◽  
Constitutive Law ◽  
Local Theory ◽  
Plane Shear ◽  
Static Regime ◽  
Entire Flow ◽  
Non Local ◽  
Inclined Planes ◽  
Inertial Regime ◽  
Dense Granular Flows

A non-local theory is proposed to model dense granular flows. The idea is to describe the rearrangements occurring when a granular material is sheared as a self-activated process. A rearrangement at one position is triggered by the stress fluctuations induced by rearrangements elsewhere in the material. Within this framework, the constitutive law, which gives the relation between the shear rate and the stress distribution, is written as an integral over the entire flow. Taking into account the finite time of local rearrangements, the model is applicable from the quasi-static regime up to the inertial regime. We have checked the prediction of the model in two different configurations, namely granular flows down inclined planes and plane shear under gravity, and we show that many of the experimental observations are predicted within the self-activated model.

Nonlinear Behaviour of Equivalent Stiffness of Plates Clamped by Bolted Joints Under Loading

2009 ◽  
Author(s):  
Tomohiro Naruse ◽  
Yoji Shibutani
Keyword(s):  
Axial Load ◽  
Bending Moment ◽  
Internal Force ◽  
Bolted Joints ◽  
Axial Stiffness ◽  
Nonlinear Behaviour ◽  
Equivalent Stiffness ◽  
Contact Conditions ◽  
Linear Behaviour ◽  
Load Displacement

The equivalent stiffness of clamped plates is needed not only to evaluate the strength of bolted joints but also to estimate the deformation and vibration characteristics of practical structures with many bolted joints. The axial stiffness and bending stiffness of clamped plates were estimated using finite element (FE) analyses while taking the contact conditions on bearing surfaces and between plates into account. We constructed FE models with an M10 bolt and plate thicknesses of 3.2, 4.5, 6.0, or 9.0 mm, and subjected them to an axial load and a bending moment. The axial compliance was estimated using the load-displacement relation obtained from the FE results. When the axial load was lower than 110% of the clamping force, the load-displacement relation showed linear behaviour and the axial compliance was almost constant. When the axial load was higher than that, the axial compliance varied nonlinearly with changes in the contact conditions between clamped plates. The compliances of the clamped plates were compared with those specified in the German engineering society code VDI 2230 (2003), in which equivalent conical compressive stress fields in the plates had been assumed. When the load-displacement relation behaves linearly, the axial and bending compliances obtained in FE analysis can basically be expressed by the VDI 2230 (2003) code. However, this code gives the slightly large axial stiffness, and thus the internal force borne to the bolt is predicted in a little bit unsafe estimation. In addition, the code is not suitable for application in the case of clamped plates with different thicknesses due to the assumptions it makes with respect to models.

Elastic Granular Flows

2004 ◽  
Vol 2 (1) ◽  
Author(s):  
Charles S Campbell
Keyword(s):  
Shear Rate ◽  
Friction Coefficient ◽  
Granular Flows ◽  
Force Chains ◽  
Long Duration ◽  
Rapid Flow ◽  
Induced Stresses ◽  
Quasistatic Regime ◽  
Inertial Regime ◽  
Effective Friction

Large scale landslide simulations provided the surprising result that the effective friction coefficient (the ratio of shear to normal forces at the base of the slide) increased with the shear rate. This might possibly explain the effect of slide volume on the runout of large landslides, but it also indicates that landslides operated in an entirely new and unexplored flow regime.Previously, granular flows had been divided into (1) the slow, quasistatic regime, in which the effective friction coefficient is taken to be a material property and thus constant, and (2) the fast, rapid-flow regime, where the particles interact collisionally, but which scales in such a way that the effective friction coefficient is independent of the shear rate. Both indicate that the effective friction coefficient is independent of the shear rate. Consequently the landslides operated in a separate intermediate regime.This talk will discuss detailed computer simulation studies into this intermediate regime and into the transitions between regimes. In this way, it is possible to draw the entire flowmap connecting the quasistatic and rapid-flow regimes. The key was to include the elastic properties of the solid material in the set of rheological parameters; in effect this put solid properties into the rheology of granular solids, properties that were unnecessary in previous theories as a result of the plasticity and kinetic theory formalisms on which quasistatic and rapid-flow theories are respectively based. Granular flows are then divided into two broad categories, the Elastic Regimes, in which the particles are locked in force chains and interact elastically over long duration contact with their neighbors and the Inertial regimes, where the particles have broken free of the force chains. The Elastic regimes can be further subdivided into the Elastic-Quasistatic regime (the old quasistatic regime) and the Elastic-Inertial regime. The Elastic-Inertial regime is the “new” regime observed in the landslide simulations, in which the inertially induced stresses are significant compared to the elastically induced stresses. The Inertial regime can also be sub-divided into an Inertial-Non-Collisional where the stresses scale inertially, but the particles interact through long duration contacts, and the Inertial-Collisional or the old rapid-flow regime.Finally, it will be shown that Stress-Controlled flows are rheologically different from Controlled-Volume flows. Physically, there is a range of dense concentrations (solid volume fractions between 0.5 and 0.6) in which it is possible to form force chains and thus to demonstrate elastically. But there are conditions under which force chains do not form at the same average concentrations. (In other words it is possible for the material to exhibit two different states at the same concentration.) By forcing the material to support an applied loads across force chains, Stress-Controlled flows generally behave elastically through this range of concentrations under the same conditions where Controlled-Volume flows behave inertially.

Advances in ultramicrotomy for physical sciences applications

1993 ◽  
Vol 51 ◽  
pp. 710-711
Author(s):  
G. McMahon ◽  
T. Malis
Keyword(s):  
Particle Surface ◽  
Zeolite Catalysts ◽  
Physical Sciences ◽  
Pull Out ◽  
Large Particles ◽  
Novel Applications ◽  
Metal Wires ◽  
Frequent Problem ◽  
Specific Orientation ◽  
Diamond Knife

As with all techniques which are relatively new and therefore underutilized, diamond knife sectioning in the physical sciences continues to see both developments of the technique and novel applications.Technique Developments Development of specific orientation/embedding procedures for small pieces of awkward shape is exemplified by the work of Bradley et al on large, rather fragile particles of nuclear waste glass. At the same time, the frequent problem of pullout with large particles can be reduced by roughening of the particle surface, and a proven methodology using a commercial coupling agent developed for glasses has been utilized with good results on large zeolite catalysts. The same principle (using acid etches) should work for ceramic fibres or metal wires which may only partially pull out but result in unacceptably thick sections. Researchers from the life sciences continue to develop aspects of embedding media which may be applicable to certain cases in the physical sciences.

Structural Studies on the Eukaryotic Ribosome

1990 ◽  
Vol 48 (1) ◽  
pp. 256-257
Author(s):  
Adriana Verschoor ◽  
Ronald Milligan ◽  
Suman Srivastava ◽  
Joachim Frank
Keyword(s):  
Chick Embryo ◽  
3D Reconstruction ◽  
Single Particle ◽  
Mass Density ◽  
Particle Surface ◽  
Uranyl Acetate ◽  
Electron Microscopic ◽  
Eukaryotic Ribosome ◽  
Negative Stain ◽  
Reconstruction Methods

We have studied the eukaryotic ribosome from two vertebrate species (rabbit reticulocyte and chick embryo ribosomes) in several different electron microscopic preparations (Fig. 1a-d), and we have applied image processing methods to two of the types of images. Reticulocyte ribosomes were examined in both negative stain (0.5% uranyl acetate, in a double-carbon preparation) and frozen hydrated preparation as single-particle specimens. In addition, chick embryo ribosomes in tetrameric and crystalline assemblies in frozen hydrated preparation have been examined. 2D averaging, multivariate statistical analysis, and classification methods have been applied to the negatively stained single-particle micrographs and the frozen hydrated tetramer micrographs to obtain statistically well defined projection images of the ribosome (Fig. 2a,c). 3D reconstruction methods, the random conical reconstruction scheme and weighted back projection, were applied to the negative-stain data, and several closely related reconstructions were obtained. The principal 3D reconstruction (Fig. 2b), which has a resolution of 3.7 nm according to the differential phase residual criterion, can be compared to the images of individual ribosomes in a 2D tetramer average (Fig. 2c) at a similar resolution, and a good agreement of the general morphology and of many of the characteristic features is seen.Both data sets show the ribosome in roughly the same ’view’ or orientation, with respect to the adsorptive surface in the electron microscopic preparation, as judged by the agreement in both the projected form and the distribution of characteristic density features. The negative-stain reconstruction reveals details of the ribosome morphology; the 2D frozen-hydrated average provides projection information on the native mass-density distribution within the structure. The 40S subunit appears to have an elongate core of higher density, while the 60S subunit shows a more complex pattern of dense features, comprising a rather globular core, locally extending close to the particle surface.

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