16 January, 2010
Statistical Approaches to Jamming and Stress transmission in Granular materials
Abstract
A jammed material is defined as one that is structurally disordered but, unlike a fluid, possesses a yield stress. In the field of traditional condensed matter physics, such a material would be called an amorphous solid. The broader use of “jammed” extends this concept to non-traditional materials such as granular systems, foams and colloids, which have many microscopic, metastable states that are macroscopically equivalent. The major difficulty encountered in constructing a theoretical description of stress propagation, and phenomena such as Reynolds dilatancy is a robust, statistical treatment of the metastable states. In these lectures, I will review the ideas behind entropic descriptions of jammed, and quasistatically driven granular packings, and describe in detail the Edwards ensemble, the force-network ensemble, and the recently-developed stress ensemble, is based on a conservation principle. I will present recent tests and applications of these statistical ensembles.
References and suggested reading
- J. P. Bouchaud, “Nonequilibrium Dynamics in Granular Media: Some Ideas from Statistical Physics” in Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter, edited by J.-L. Barrat, J. Dalibard, M. Feigelman, and J. Kurchan (Springer, Berlin, 2003)
- S. F. Edwards and R. Blumenfeld, “The thermodynamics of Granular Media”, in Physics of Granular Materials, edited by A. Mehta (Cambridge Univ. Press, Cambridge, 2007)
- Sean McNamara et al, “Measurement of Granular Entropy”, Phys. Rev. E (2009)
- Snoeijer J, van Hecke M, Somfai E, van Saarloos W, “Force and weight distributions in granular media: Effects of contact geometry”, Phys Rev E 67, 030302 (2003)
- S. Henkes and B. Chakraborty, “Statistical mechanics framework for static granular matter”, Phys. Rev. E. 79, 0610301 (2009).