Static Granular Packings: Contact Forces and Geometry by Experiment and Model Anthony D. Dinsmore, University of Massachusetts Amherst, DMR Soft random solids are common in our everyday experience, but a fundamental understanding of their response to applied load is often elusive. Still, though these materials are far from equilibrium and have no crystalline order, experiments reveal many properties that arise commonly. In random piles of granular particles, for example, the strongest inter-particle forces are concentrated in chain-like regions of the sample. Motivated by experiments in 2D and 3D, we have developed a straightforward statistical model to test the effects of physical parameters on the formation of force chains. Our model predicts, among other things, that the strong contact forces tend to align parallel (180 o apart on a particle), giving rise to force chains (see figure). Adding friction (increasing  ), however, suppresses alignment and the formation of force chains. The effects of 2D vs. 3D packing and anisotropic loading were also studied. A map of measured contact forces shows that spatial patterns can arise even when the particles themselves are randomly arranged. This image shows the chains formed by contact forces that are much stronger than the average. A map of all contact forces in the sample reveals no such chains. t = 190 s The predicted probability of finding the angle  between two contact forces on a particle. Dashed curves show that the angles between any two contacts are nearly randomly distributed. The solid curves show that the angle between the two strongest contact forces on a given particle is likely to be near 180 o.

Static Granular Packings: Contact Forces and Geometry by Experiment and Model Anthony D. Dinsmore, University of Massachusetts Amherst, DMR Education: Jing Zhou and Timothy Prisk contributed to this work. Dr. Zhou has now received his Ph.D. and joined the research staff at the Xerox Innovation Group. Mr. Prisk obtained his B.S. degree and enrolled in graduate school in Another student supported by this project (John Savage) is now a postdoctoral Fellow at Cornell. This NSF project currently supports graduate students Liquan Pei and Hao Wang. Undergraduate student Ellie Radue is partially supported by a collaboration with Xerox that grew out of the work described here. The PI has incorporated these and other topics in soft condensed matter physics into a graduate course and the 2008 UMass Summer School in Complex Fluids and Soft Solids. Societal Impact: We have developed a powerful model system that allows us to probe the behavior of random granular solids. These materials are very common in everyday life, with examples including powders and sand piles. The results are expected to lead to advances in applications such as toner deposition and our fundamental understanding of non-equilibrium systems in general. The students involved in this project receive a comprehensive training in optics, computer analysis and condensed matter physics, suitable for jobs in industry or academia. Students also benefit from a collaboration with Xerox on questions of technological relevance.