In my 2D granular piston, described here, we examine the stress patterns within the bulk of the material. Since the particles themselves are birefringent under stress, placing them between "crossed" polarizers allows light to pass through only where the system is under stress. This is described many places in our group web pages.
Arrayed below is a series of images depicting average photoelastic reponse of a granular layer over many different realizations (typically >65) under the specified conditions. All images are normalized so that the full intensity scale (bottom of the image) is used. The actual area represented here is 25 cm by 18 cm, or about 35 particles across by 25 particles down.
In the ``hysdrostatic head'' image, this is the average stress pattern from allowing all the particles to come to rest in the piston by falling in bulk. Literally, the particles are thrown uniformly into the air and allowed to come to rest. Curiously, the pressure does not build linearly with depth as in a standard incompressible fluid, but instead is maximal about 1/4 and 3/4 of the way across the bottom, and minimal in the corners and at the bottom.
In the other 5 images, a uniform load is placed across the top of the granular layer by lowering aweighted bar (slowly) until it just rests on the top. The background image is subtracted, leaving just the response. One thing that becomes obvious is that the the load is not spread uniformly through the layer but instead is often transmitted along the walls -- evidenced by the stress spikes going down each side.
In the following cases, we
took an average in the picture space over an area about the size
of a particle. Hence a particle located at this position
exhibits -- on average -- the following responses. For the
first picture, we show an average of the typical hydrostatic
pressure due solely to the weight of the particles themselves.
(The picture is normalized so that the full intensity range,
0-255, is used.) Note the clear local minima of stress at the
midpoint and at the corners of the bottom row of particles.
(Click on the image for a larger version -- it has been pre-loaded and will take no extra time to load)
Here we show the average
response to a 178.9 g load placed uniformly across the top of
the cell. Again, the background has subtracted, so this shows
the average stress transmittance through the granular layer.
Note how the stress is transmitted largely along the walls, with
only some of the weight being supported by the bulk of the
material in the middle of the cell.
(Again, you can click on the image for a larger version -- it has been pre-loaded and will take no extra time to load)
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