What Is Shaking in the Sandbox?
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MRS BULLETIN/MAY 1994
occur solely through nearest-neighbor contacts. The macroscopic (and microscopic) material properties of individual grains are typically well-known and it is the cooperative phenomena associated with the entire system that are of interest. As an example of what we might expect from vibration we consider the phenomenon of arching. We are familiar with arches used to build medieval bridges and churches. Without steel armatures or reinforced concrete, large open areas are created by placing stones in an arch, one on top of another, until at the uppermost level they are kept in position by the clever placement of a keystone. This stone distributes the weight in horizontal directions rather than letting it solely exert forces downward along the vertical. In a granular material, because individual grains are macroscopically large, thermal energies are negligible compared to gravitational ones. Thus any particular grain configuration in the material corresponds to a metastable state that will persist indefinitely until it is disturbed by some (nonthermal) means. As a consequence, granular materials exhibit arching, where disorder in the packing can lead to a large proportion of voids, held up by "keystones" in the packing. These keystones form nodes in a network of force chains that percolate through the grain assembly and take up both the self-weight of the material as well as additional loads placed on top, deflecting all forces toward the exterior of the packing. In this case, vibrations play the important role of rearranging the pile by displacing the keystone and destroying the arches. Since thermal motion is entirely negligible, only externally generated vibrations can let the pile escape from the metastable configurations and approach a more compact state. Another example of the importance of vibration is in the flow properties of a granular medium. While the densest
possible packing of monodisperse spheres in three dimensions is a close-packed hexagonal structure (volume fraction of spheres 17 = 0.74), in general, even after most arches have been relaxed by whatever means, a disordered packing will approach the random close-packed (RCP) limit 7} = 0.64. Conversely, the transition from a packing at rest to one exhibiting grain movement is necessarily connected with a volume expansion to allow grains to pass each other. This phenomenon is known as dilation and was first discussed by Reynolds in 1885.4 However, external vibrations can allow the sandpile to expand temporarily, so that the density decreases sufficiently for flow to occur. Thus vibrating a material can produce flow where it otherwise would not have occurred. We will describe a series of research activities that have investigated the effects of external vibrations on granular media. We will first discuss the behavior induced by the lowest amplitude vibrations which are the "elementary excitations" of the medium. This is the phenomenon of sound propagation. We will then look at what happens when the amplitude of the vibrations is r
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