Search results

There are very few individuals who have studied the question of weights and measures who do not most strongly favour the decimal system. The disadvantages of the weights and measures at present in use in the United Kingdom are indeed manifold. At the very commencement of life the schoolboy is expected to commit to memory the conglomerate mass of facts and figures which he usually refers to as “Tables,” and in this way the greater part of twelve months is absorbed. And when he has so learned them, what is the result? Immediately he leaves school he forgets the whole of them, unless he happens to enter a business‐house in which some of them are still in use; and it ought to be plain that the case would be very different were all our weights and measures divided or multiplied decimally. Instead of wasting twelve months, the pupil would almost be taught to understand the decimal system in two or three lessons, and so simple is the explanation that he would never be likely to forget it. There is perhaps no more interesting, ingenious and useful example of the decimal system than that in use in France. There the standard of length is the metre, the standard of capacity the cubic decimetre or the litre, while one cubic centimetre of distilled water weighs exactly one gramme, the standard of weight. Thus the measures of length, capacity and weight are most closely and usefully related. In the present English system there is absolutely no relationship between these weights and measures. Frequently a weight or measure bearing the same name has a different value for different bodies. Take, for instance, the stone; for dead meat its value is 8 pounds, for live meat 14 pounds; and other instances will occur to anyone who happens to remember his “Tables.” How much simpler for the business man to reckon in multiples of ten for everything than in the present confusing jumble. Mental arithmetic in matters of buying and selling would become much easier, undoubtedly more accurate, and the possibility of petty fraud be far more remote, because even the most dense could rapidly calculate by using the decimal system.

Granular materials possess multiscale structures, i.e. micro-scales involving atoms and molecules in a solid particle, meso-scales involving individual particles and their correlated structure, and macroscopic assembly. Strong and abundant dissipations are exhibited due to mesoscopic unsteady motion of individual grains, and evolution of underlying structures (e.g. force chains, vortex, etc.), which defines the key differences between granular materials and ordinary objects. The purpose of this paper is to introduce the major studies have been conducted in recent two decades.

The main properties at individual scale are introduced, including the coordination number, pair-correlation function, force and mean stress distribution functions, and the dynamic correlation function. The relationship between meso- and macro-scales is analyzed, such as between contact force and stress, the elastic modulus, and bulk friction in granular flows. At macroscales, conventional engineering models (i.e. elasto-plastic and hypo-plastic ones) are introduced. In particular, the so-called granular hydrodynamics theory, derived from thermodynamics principles, is explained.

On the basis of recent study the authors conducted, the multiscales (both spatial and temporal) in granular materials are first explained, and a multiscale framework is presented for the mechanics of granular materials.

It would provide a paramount view on the multiscale studies of granular materials.

Granular lubrication can solve some lubrication problems under many extreme operating conditions. Meanwhile, the flow constitutive relation is one of its unsolved problems in fully understanding its rheological mechanism.

In this paper, a plane shear cell under granular lubrication is established by the discrete element method to study the flow constitutive relation and its mechanical mechanism of the hard granular lubricants.

Research results show that the flow regimes in granular flow lubrication strongly rely on the dimensionless parameter I, in which it is called the inertial coefficient. When the inertial coefficient I increase, the flow regimes of the granular lubricants also evolve from a quasi-static state to a collisional state accordingly. Comparing to the influence of the restitution coefficient, the friction coefficient of the hard granular lubricants has a strong influence on its constitutive relation of the granular flow lubrication. Finally, it is shows that the dimensionless parameter I has strong influence on the contacts and flow states of this granular lubrication system than the influence of the dimensionless parameter R.

These findings reveal the constitutive relation and mechanical mechanism of granular lubrication and can also offer the helpful reference for the design of the new granular lubrication bearing.

The purpose of this paper is to show that there are some underlying principles of granular media that can be derived from statistical mechanics and that could be useful when considered in the context of computer simulations.

The fundamentals of statistical mechanics are presented and they are revised in order to set up a suitable approach for jammed static granular media. After a conceptual discussion about the entropy of granular matter, some specific statistical mechanics approaches that have been used for granular media are reviewed. Finally, a numerical simulation, conducted using an open source molecular dynamics code, is included as an illustrative example.

It is shown qualitatively how statistical mechanics can be used to analytically compute the expected statistical distribution of some quantities in numerical simulations.

The computation of entropy from histograms and the establishment of the constraints of the ensembles in simulations are still open issues.

Considering the entropy could set up new computational techniques. Initial arrangements could be analyzed in terms of their probability of occurrence and of their “distance” to the most probable state.

The paper includes the distribution of the mean force‐moment tensor component of a fast cyclic quasi isotropic compression process of a simple granular media. Results show how the system tends to an equilibrium state.

Granular flow lubrication is developed in recent years as a new lubrication method which can be used in extreme environments, while the stick-slip mechanisms of granular flow lubrication are an urgent obstacle remains unsolved in fully establishing the granular flow lubrication theory.

A granular flow lubrication research model is constructed by the discrete element method. Using this numerical model, the mesoscopic and macroscopic responses of stick-slip that influenced by the shear velocity, and the influence of the shear velocity and the normal pressure on the vertical displacement are studied.

Research results show that movement states of granular flow lubrication medium gradually transform from the stick-slip state to the sliding state with increased shear velocity, in which these are closely related to the fluctuations of force chains and friction coefficients between granules. The stick-slip phenomenon comes up at lower shear velocity prior to the appearance of granular lift-off between the two friction pair, which comes up at higher shear velocity. Higher normal pressure restrains the dilatation of the granular flow lubrication medium, which in turn causes a decrease in the displacement.

These findings reveal the stick-slip mechanism of granular flow lubrication and can also offer the helpful reference for the design of the new granular lubrication bearing.

Granular lubrication is a new lubrication method and can be used in extreme working conditions; however, the obstacle of force transmission characteristics needs to be urgently solved to fully understand the mechanical and bearing mechanisms of granular lubrication.

A flat sliding friction cell is developed to study the force transmission behaviors of granules under shearing. Granular material, sliding velocity, granule size and granule humidity are considered in these experiments. The measured normal and shear force, which is transmitted from the bottom friction pair to the top friction pair via the granular lubrication medium, reveals the influence of these controlling parameters on the force transmission characteristics of granules.

Experimental results show that a low sliding velocity, a large granule size and a low granular humidity increase the measured normal force and shear force. Besides, a comparison experiment with other typical lubrication styles is also carried out. The force transmission under granular lubrication is mainly dependent on the force transmission path, which is closely related to the deconstruction and reconstruction of the force chains in the granule assembly.

These findings reveal the force transmission mechanism of granular lubrication and can also offer the helpful reference for the design of the new granular lubrication bearing.

We set up an original apparatus to measure the grain grain friction stress inside a granular medium composed of sodo‐silicate‐glass beads surrounded by a water vapor atmosphere.We analyze here the influence of the physico chemistry of water on our glass beads and its consequences on our shear experiment. We found two scales in the analysis of the shear stress signal. On the microscopic scale of one bead, the experimental results show a dependence on the size of beads, on the shear rate and on humidity for the resulting stick slip signal. On the macroscopic scale of the whole assembly of beads, the behavior of the total amplitude of the shear stress depends on the size of the beads and is humidity dependent only for relative humidity larger than 80%. For high degrees of humidity, on the microscopic scale, water lubricates the surface of the beads leading to a decrease in the microscopic resistance to shear while on the macroscopic scale the resistance to shear is increased: the assembly of very humid grains behaves as a rheothickening fluid.

A numerical analysis of the micromechanical behaviour of a granular material is described using a new program MASOM based on Cundall's discrete element method. In the analysis the individual grains which make up the material are taken to be deformable 2D polygons of arbitrary size and shape. Contact forces between the grains are calculated according to Mindlin's solution for frictional contact between elastic bodies. The material in each grain is taken to be linear elastic but limited by the fracture strength of the material. Fracture is permitted along any one of a number of candidate fracture planes if an associated compressive load tending to split the gain reaches a critical level. Fragments of fractured grains are carried until they become too small to track using the explicit time integration algorithm used to advance the solution. The MASOM program is able to consider a number of different classes of elements and different types of contact between the various classes. Thus, in addition to the granular material the program can also model containers and loading devices. The program is used to simulate uniaxial and triaxial compression tests for geological materials. The results are shown to give results for stress‐strain and stress difference versus pressure which are in qualitative agreement with test data. The numerical results reveal a very complex micromechanical behaviour in granular materials, including highly variable and rather unstable load paths and a very inhomogeneous load distribution within a representative sample of the material. A video of the response of a typical frictional material to applied loads shows an interesting localized effect near sample boundaries involving crowding together of grains which cannot be observed using conventional static field plots.

Granular material exhibits rich dynamical behaviors under impacting, and its impacting dynamical process is seriously influenced by many factors. The purpose of this paper is to explore the dynamical response of granular bed obliquely impacted by a rotational projectile, and the effect of density ratio and diameter ratio on its penetration depth is mainly considered.

In most experiments, as the angular velocity and the impact velocity always produce a coupling effect on the whole impact process, then it is quite difficult to separately distinguish the influence of angular velocity. Therefore, the discrete element method is used here to achieve this purpose. The authors vary one parameter and keep other parameter unchanged, and then discuss the effect of these parameters on penetration depth statistically.

The numerical model in this paper can effectively predict the dynamical process of granular medium under impacting. The projectile’s penetration depth exhibits a similar scaling with its angular velocity under different density ratios and diameter ratios, and the angular velocity exhibits an obvious criticality.

A DEM code and corresponding statistical approach are used to explore the complex dynamical process of a granular material obliquely impacted by a rotation projectile.

The purpose of this paper is to present large‐scale parallel direct numerical simulations of granular flow, using a novel, portable software program for discrete element method (DEM) simulations.

Since particle methods provide a unifying framework for both discrete and continuous systems, the program is based on the parallel particle mesh (PPM) library, which has already been demonstrated to provide transparent parallelization and state‐of‐the‐art parallel efficiency using particle methods for continuous systems.

By adapting PPM to discrete systems, results are reported from three‐dimensional simulations of a sand avalanche down an inclined plane.

The paper demonstrates the parallel performance and scalability of the new simulation program using up to 122 million particles on 192 processors, employing adaptive domain decomposition and load balancing techniques.