|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.
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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