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Stress Response of Granular Systems

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Abstract

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of contact forces between constituent grains on a given, disordered, contact network, to external perturbations. By mapping this response to the spectral properties of the graph Laplacian corresponding to the underlying contact network, we show that this naturally leads to spatial localization of forces. We present numerical evidence for localization using exact diagonalization studies of network Laplacians of soft disk packings. Finally, we discuss the role of other constraints, such as torque balance, in determining the stability of a granular packing to external perturbations.

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Acknowledgements

This work has been supported by NSF-DMR 1409093 and the W. M. Keck Foundation.

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  1. Martin Fisher School of Physics, Brandeis University, Waltham, MA, 02453, USA

    Kabir Ramola & Bulbul Chakraborty

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  1. Kabir Ramola
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  2. Bulbul Chakraborty
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Correspondence to Kabir Ramola.

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Ramola, K., Chakraborty, B. Stress Response of Granular Systems. J Stat Phys 169, 1–17 (2017). https://doi.org/10.1007/s10955-017-1857-0

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