http://www.flyingcircusofphysics.html
Jearl Walker, March 2007
What is something you really enjoyed as a child but now find utterly boring? Among many possible answers is playing with sand. Building sandpiles was loads of fun years ago but not now. Many physicists are still fascinated by sandpiles and have managed to build their careers on them. The reason is that a sandpile is a treasure trove of puzzles that figure into the general science of granular flow (that is the flow of grains of anything from powder to apples, in environments from the cosmetic industry to the dunes on a desert). Here is one puzzle.
If you were measuring the stress (or pressure) under a sandpile from the outer edge to the center, you would expect that stress to be greatest under the highest point, where the supporting surface must support the most weight. Measurements show that although the stress increases toward the center of the pile, it actually decreases in the region of the highest point. That decrease is called the stress dip.
As explained in The Flying Circus of Physics, the stress dip is most likely due to the formation of arcs of sand grains that are produced when the sand is poured to make the pile. Such arcing creates force chains, which are lines of support among the grains that form a skeletal structure hidden from view within the pile. This generation of force chains shifts support away from the center of the pile.
Recently, I. Zuriguel and T. Mullin of the University of Manchester and J. M. Rotter of the University of Edinburgh described a method to make the force chains visible in a two-dimensional granular pile. The "grains" are cut from a photoelastic polymer layer that is birefringent. That is, if the layer is placed between polarizing sheets, the stress in the polymer material shows up as a pattern.
A narrow rectangular container was made to hold the grains. The front and back were made of Perspex plates that were held 7 millimeters apart. The grains were carefully poured into the container. A polarizing sheet was mounted on the rear Perspex and a second sheet was mounted on the front Perspex, with the polarizing directions of the sheets perpendicular to each other. When light is sent through the apparatus, the light becomes polarized by the first sheet and would not nomally be passed by the second sheet because of the perpendicular arrangement. The stressed regions in the polymer grains rotate the polarization of the light, so that in some regions the light gets through the second polarizing sheet, revealing where the grains are stressed.
When the polymer grains are a mixture of circular grains with two different diameters, the grain pile has a slight stress dip under the highest section. When the grains are elliptical and identical, the pile has a dramatic stress dip under the highest section. Presumably, the elliptical shape naturally forms the supporting arcs that shift support away from the center.