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Related Experiment Videos

Stress propagation through frictionless granular material.

A V Tkachenko1, T A Witten

  • 1The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary
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We found that forces in static granular materials transmit unidirectionally, like a wave. This applies to colloidal glasses and macroscopic granular materials, even with friction.

Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Static assemblies of hard, frictionless spherical beads, like colloidal glasses, are minimally connected.
  • Bead positions in finite subregions are underdetermined, requiring external forces for equilibrium.

Purpose of the Study:

  • To examine the network of forces in static assemblies of spherical beads.
  • To understand force transmission and stress propagation in granular materials.

Main Methods:

  • Analyzing the ratio of constraint equations to contact forces in large assemblies.
  • Deriving equations for stress transmission averaged over bead scales.
  • Applying an ansatz that force fluctuations are independent of contact geometry fluctuations.

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Main Results:

  • Force transmission is argued to be unidirectional, unlike in elastic materials.
  • Forces on buried beads can be uniquely specified by forces from subsequently added beads.
  • Stress fields are expressed using vector fields, and wave-like propagation is demonstrated in 2D and higher dimensions.

Conclusions:

  • The derived equations for stress transmission are generalizable to nonsequential packings.
  • Wave-like stress propagation is observed in granular materials, supporting existing postulates.
  • The approach is potentially applicable to macroscopic granular materials despite friction and non-sequential packing.