The Physics of the Deformation of Densely Packed Granular Materials. M A C Koenders

       Chapter 1

       General Concepts

       1.1Introduction

      Granular materials play a role in nearly all human activities. Users of, for example, sand, from children in sandpits to sophisticated geotechnical engineers, know that it is a fascinating — and to some extent, unpredictable — material. Many groups are concerned professionally with granular materials: chemical engineers, pharmacists, food technologists, agriculturalists, biologists, geologists, geophysicists, astronomers even, are obliged to study their behaviour under a wide variety of circumstances. In addition to sand, which itself may be of many compositions, the types of materials include gravel, fine-particle aggregates as employed in cosmetics, pharmaceuticals, dust, crushed rock and granules that occur in a domestic environment, such as breakfast cereals, sugar, salt and (instant or ground) coffee granules.

      It is important to distinguish between the various states in which these materials may be encountered. The possible range of regimes is extensive. The delineation of regimes is accomplished by specifying first the packing density, second the grain-size, or size distribution and particle shape, then the type of medium in the interstices between the grains (fluid, gas, vacuum) and finally the stress and temperature environment. Depending on any combination of these factors, examples of phenomena that may take place come in a wide variety. A few celebrated ones are landslides, blocked silos and sewers, rubble asteroids breaking up, segregation effects in breakfast cereals, dust-storm propagation after a terrorist attack, the spreading of sun-cream over skin and the formation of dunes. The list is by no means exhaustive; not only do people continually invent new applications for granulates, they also discover new processes where these materials may be deployed. The sheer diversity of effects illustrates the range of professionals that may be engaged with the subject.

      The mechanical behaviour of an assembly of grains depends first and foremost on the interaction between the particles. For a low packing density the grains are fairly free to move and interactions may take place in a similar way to the molecules in a gas: the interactions are short-duration ‘events’. When, on the other hand, the material is densely packed the grains are locked in enduring interaction with each other. This does not preclude relative motion between the particles. In a dense slurry, for example, the interstitial fluid is the interactive medium. Particles may move, while the interactive strength varies with motion, but the interaction continues to be relevant for particles in close proximity. When the medium is dense and dry, on the other hand, particles must make contact. Their relative motion may be sliding, or even suffer a very slight indentation when two particles are being pressed together hard, but there is only a non-zero interaction while the contact endures.

      In order to describe the motion in various states, distinctly different branches of mechanics are required. For a dilute flow in which collisions are prevalent, for example, concepts of gas dynamics have to be invoked: a temperature field is needed to describe the velocity fluctuations while motion takes place. For dense (but not too dense) slurry flow in which a fluid mediates the interaction of the grains the relative velocity difference of the particles needs to be described. For very small particles Brownian motion will play a role too. For a dense packing, in which the grains are in enduring contact, the physics of the interaction is quite different. As this is the field of interest in the publication to hand a small study of the background of this subject is of use.

      It could be argued that the densely packed state is fairly boring, as the displacements tend to be so insignificant. Essentially, one might say, a densely packed granular material behaves like a solid. There are, however, certain features that relate to this régime that are quite unlike traditional solids. In fact, it is one of the most difficult to describe problems in materials science. The reason for this is that the material properties change dramatically under certain specific loading conditions.