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Rattler wedging and force chain buckling: metastable attractor dynamics of local grain rearrangements underlie globally bistable shear banding regime

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Abstract

Grain rearrangements govern the mechanical response of granular materials under load. A comprehensive time series analysis of macroscopic stress, previously undertaken for the persistent shear banding regime, uncovered a bistable dynamical system with two interconnected attractor basins—one tied to jamming, the other to unjamming. Here we examine the state space of local fabric of a 3D granular material to uncover the underlying grain rearrangements which induce the system to switch basins and manifest macroscopic quasistationary dynamics. The fabric state space comprises metastable attractors organized according to structural determinacy: hypostatic, isostatic and hyperstatic. Although trajectories overwhelmingly favor identity transitions which preserve local fabric, rare nonidentity transitions hold the key to basin switching. Jamming basin dynamics is governed by force chain transitions in the hyperstatic region: here redundant constraints enable force reconfigurations with little to no change in the local fabric. But as force chains become overloaded, they buckle. Buckling and attendant dilatancy push grains to the isostatic region. This in turn triggers unjamming and ensuant transitions to the hypostatic region where rattlers, though few, dominate dynamics. Rattlers provide wedge-like supports to unstable misaligned particle columns, promoting force chain formation and return to the hyperstatic region. The lateral reinforcement of an isostatically constrained grain in a trimer by the addition of a contact and/or a 3-cycle is the most probable nonidentity transition during nascent force chain evolution.

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Acknowledgements

We thank David M. Walker and Michael Small for useful discussions and our two anonymous reviewers whose insightful comments have improved the manuscript.

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  1. School of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia

    Sebastian Pucilowski & Antoinette Tordesillas

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  1. Sebastian Pucilowski
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  2. Antoinette Tordesillas
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Correspondence to Antoinette Tordesillas.

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This article is part of the Topical Collection: In Memoriam of Robert P. Behringer.

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Pucilowski, S., Tordesillas, A. Rattler wedging and force chain buckling: metastable attractor dynamics of local grain rearrangements underlie globally bistable shear banding regime. Granular Matter 22, 18 (2020). https://doi.org/10.1007/s10035-019-0979-2

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