Mesoscopic properties of dense granular materials: An overview

Abstract

A granular material is a conglomeration of discrete solid particles. It is intrinsically athermal because its dynamics always occur far from equilibrium. In highly excited gaseous states, it can safely be assumed that only binary interactions occur and a number of kinetic theories have been successfully applied. However, for granular flows and solid-like states, the theory is still poorly understood because of the internally correlated structures, such as particle clusters and force networks. The current theory is that the mesoscale characteristics define the key differences between granular materials and homogeneous solid materials. Widespread interest in granular materials has arisen among physicists, and significant progress has been made, especially in understanding the jamming phase diagram and the characteristics of the jammed phase. In this paper, the underlying physics of the mesoscale structure is discussed in detail. A multiscale framework is then proposed for dense granular materials.

Keywords

granular matter / macroscopic structure / jamming phase transition

References

[1] Jaeger H M, Nagel S E, Behringer R P. Granular solids, liquids, and gases. Reviews of Modern Physics, 1996, 68(4): 1259-1273

[2] Sun Q, Jin F, Liu J, Zhang G. Understanding force chains in dense granular materials. International Journal of Modern Physics B, 2010, 24(29): 5743-5759

[3] Song C, Wang P, Makse H A. A phase diagram for jammed matter. Nature, 2008, 453(7195): 629-632

[4] Liu A J, Nagel S R. Jamming is not just cool any more. Nature, 1998, 396(6706): 21-22

[5] Edwards S F, Oakeshott R B S. Theory of powders. Physica A, 1989, 157(3): 1080-1090

[6] Goldhirsch I. Introduction to granular temperature. Powder Technology, 2008, 182(2): 130-136

[7] Kondic L, Behringer R P. Elastic energy, fluctuations and temperature for granular materials. Europhysics Letters, 2004, 67(2): 205-211

[8] Sun Q, Song S, Jin F, Bi Z. Elastic energy and relaxation in triaxial compressions. Granular Matter, 2011, 13(6): 743-750

[9] Sun Q, Song S, Jin F, Jiang Y. Entropy productions in granular materials. Theoretical and Applied Mechanics Letters, 2012, 2(2): 021002

[10] Trappe V, Prasad V, Cipelletti L, Segre P N, Weitz D A. Jamming phase diagram for attractive particles. Nature, 2001, 411(6839): 772-775

[11] Durian D J. Foam mechanics at the bubble scale. Physical Review Letters, 1995, 75(26): 4780-4783

[12] Brujic J, Song C, Wang P, Briscoe C, Marty G, Makse H A. Impact of a projectile on a granular medium described by a collision model. Physical Review Letters, 2007, 98: 248001

[13] O'Hern C S, Silbert L E, Liu A J, Nagel S R. Jamming at zero temperature and zero applied stress: The epitome of disorder. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2003, 68(1): 011306

[14] Abate A R, Durian D J. Approach to jamming in an air-fluidized granular bed. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2006, 74(3): 031308

[15] Keys A S, Abate A R, Glotzer S C, Durian D J. Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material. Nature Physics, 2007, 3(4): 260-264

[16] Zhang Z, Xu N, Chen D T N, Yunker P, Alsayed A M, Aptowicz K B, Habdas P, Liu A J, Nagel S R, Yodh A G. Thermal vestige of the zero-temperature jamming transition. Nature, 2009, 459(7244): 230-233

[17] van Hecke M. Jamming of soft particles: geometry, mechanics, scaling and isostaticity. Journal of Physics Condensed Matter, 2010, 22(3): 033101

[18] Somfai E., van Hecke M., Ellenbroek W. G., Shundyak K., van Saarloos W.Critical and noncritical jamming of frictional grains. Physical Review E, 2007, 75(2): 020301(R)

[19] Zeravcic Z, Xu N, Liu A J, Nagel S R, Van Saarloos W. Excitations of ellipsoid packings near jamming. Europhysics Letters, 2009, 87(2): 26001

Acknowledgments

The authors acknowledge the support of the National Basic Research Program of China (Grant No. 2010CB731504), and the National Natural Science Foundation of China (Grant No. 51239006, 11272048).

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg