Stresses in Granular Materials

Sand dunes, agricultural grains in silos, pills or lumps of coal in bins, salt or sugar in boxes -- all of these are examples of granular materials. These are physical systems one encounters every day, made up of pieces that are usually big enough to see clearly and held in place by the familiar forces of gravity, elasticity, and friction. So it may seem surprising that the behavior of such materials is poorly understood compared to fluids and solids with intricate flow patterns or atomic structures. But physicists are only beginning to understand how the simple interactions between individual grains give rise to the dazzling array of behaviors observed in static and flowing granular materials.
Experimental image of plastic disks under stress viewed through crossed polarizers. From the lab of R. Behringer.
My work in this field focuses on static materials. Think of a pile of sand that is just sitting there. The microscopic stress field in a static granular material has an extraordinarily complex structure. (The figure at right shows an image showing the chains of strong stresses in a computer model of a granular material.) Some grains support lots of weight, others essentially none. The problem is to understand how stress is distributed in such a material and under what conditions it will support a load without collapsing or breaking its container.

I am currently working on theories for describing the force chain network in static granular materials. The key idea is to take the force chains themselves as fundamental objects and describe their interactions with each other. We are discovering a rich and subtle mathematical structure in this problem.

Average stress response as a function of depth (vertical axis) and horizontal position, computed from a theory of force chain structure in a granular material. The crossover from a single-peaked to double-peaked structure at large depths is an unexpected result.

Papers on this work:

Links are to the LANL cond-mat archive.
Last modified: 23-Oct-07