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Fluctuations in granular media.

Daniel W. Howell¹, R. P. Behringer, C. T. Veje

¹Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305.

Chaos (Woodbury, N.Y.)

|June 5, 2003

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Dense granular materials exhibit significant force fluctuations along "force chains." Experiments in 2D and 3D reveal how packing fraction influences these force distributions, identifying a critical transition point.

Area of Science:

Physics of granular materials
Soft condensed matter physics
Statistical mechanics

Background:

Dense granular materials display substantial force fluctuations despite weak spatial disorder.
Forces are primarily transmitted through networks of aligned grains known as force chains.
Previous research has focused on understanding the nature of these stress fluctuations.

Purpose of the Study:

To experimentally characterize force fluctuations in slowly sheared granular systems in 2D and 3D.
To investigate the influence of mean packing fraction on force distributions.
To explore the relationship between granular motion, stress chains, and critical transitions.

Main Methods:

Conducted experiments using photoelastic disks in 2D to visualize internal force structures.

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Performed 3D experiments to analyze stress fluctuations and force distributions.

Measured particle kinematics, including velocities and rotations, and analyzed stress time series power spectra.

Main Results:

Observed strong temporal fluctuations in local stress/force with length scales up to 100 grains.
Force distributions varied with packing fraction: exponential at dense, Gaussian at higher, and power-law at lower packing.
Discovered a continuous critical transition (strengthening/softening) controlled by packing fraction, where grain motion becomes intermittent and stress chains lengthen.

Conclusions:

Force distributions in granular materials are sensitive to packing fraction and grain deformability.
A critical point exists in granular systems, marked by changes in stress, motion, and force chain structure.
3D experiments confirm statistical rate invariance of stress and reveal distinct power-law behaviors in frequency spectra.