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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.
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.
Mail suggestions and complaints regarding subject material to
"gwb@shahrazad.bd.psu.edu".
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This page was created and is maintained by Isaac Hagenbuch
Updated February 10, 1999
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