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G. William Baxter - Stress Chains in a Granular Material 

Granular materials (including sand, seed, pharmaceutical powders, coal, powdered metals, soil, etc) have radically different properties from either solids or liquids. These properties result in a number of fundamental scientific and technological problems. Problems of current scientific interest include: causes of failure in granular media, constitutive relations for granular materials, model earthquake systems, fractal properties of materials, and transmission of force in granular materials. Technological problems include stability problems related to controlling failure or motion in a granular material. For example, in powder metallurgy and the transport of seeds and coal, it is important that the material fail easily in order for it to flow without blockage. However, the granular material should be rigid in construction situations such as buildings on soil foundations or pilings in a sea bed. In either case, successful manipulation of these materials requires an understanding of the fundamental physics and causes of stability for granular media. 

Unlike fluid mechanics where the continuum equations of motion of an incompressible fluid are the well-known Navier-Stokes equations, the continuum equations describing a granular material are the subject of considerable speculation. The missing ingredient for granular materials is a constitutive relation which describes how a material responds to applied stress. 

One reason that a constitutive relation for granular materials has been so hard to obtain becomes apparent when one looks at the internal stress distribution of such a material. In a granular material the stresses are distributed along branching chains of grains as shown below. 
Bill Baxter Example of granular stress chains 

Grains within chains may be under a large stress, while grains not in chains may be under no stress at all. This is in sharp contrast to the case in simple fluids where the stress is everywhere uniform. Stress chains support the granular material in much the same way that girders support a bridge. When they are unable to support the load, then the material fails and the grains rearrange to form a new stress chain structure. These stress chains are likely to determine when and where within the material failure occurs as well as the motion of the grains during deformation. 

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