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Analysis of stresses in two-dimensional isostatic granular systems

Author

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  • Gerritsen, Margot
  • Kreiss, Gunilla
  • Blumenfeld, Raphael

Abstract

We analyze a recently proposed continuous model for stress fields that develop in two-dimensional purely isostatic granular systems. We present a reformulation of the field equations, as a linear first-order hyperbolic system, and show that it is very convenient both for analysis and for numerical computations. Our analysis allows us to predict quantitatively the formation and directions of stress paths and, from these, trajectories and magnitudes of force chains, given the structure in terms of a particular fabric tensor. We further predict quantitatively changes of stresses along the paths, as well as leakage and branching of stress from the main paths into the cones that they make in terms of the fabric tensor. Numerical computations in both Cartesian and cylindrical coordinates verify the analytic results and illustrate the rich behavior discovered. All the phenomena predicted by our solutions have been observed experimentally, suggesting that stresses in isostatic systems can form a base model for a more developed stress theory in granular materials.

Suggested Citation

  • Gerritsen, Margot & Kreiss, Gunilla & Blumenfeld, Raphael, 2008. "Analysis of stresses in two-dimensional isostatic granular systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(25), pages 6263-6276.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:25:p:6263-6276
    DOI: 10.1016/j.physa.2008.06.057
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    Cited by:

    1. Zhang, Xinggang & Dai, Dan, 2020. "Governing equations for stress distribution in rhombic disk packings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).

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