Journal
PHILOSOPHICAL MAGAZINE
Volume 92, Issue 36, Pages 4547-4587Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/14786435.2012.715766
Keywords
granular materials; diffuse failure; force chain buckling; contact cycles; complex networks
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Funding
- US Army Research Office [DAAD-W911NF1110175]
- Australian Research Council [DP0986876, DP120104759]
- Melbourne Energy Institute
- Gilbert Riggs PhD Scholarship
- Australian Research Council [DP0986876] Funding Source: Australian Research Council
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We study the evolution of structure inside a deforming, cohesionless granular material undergoing failure in the absence of strain localisation so-called diffuse failure. The spatio-temporal evolution of the basic building blocks for self-organisation (i.e. force chains and minimal contact cycles) reveals direct insights into the structural origins of failure. Irrespective of failure mode, self-organisation is governed by the cooperative behaviour of truss-like 3-cycles providing lateral support to column-like force chains. The 3-cycles, which are initially in scarce supply, form a minority subset of the minimal contact cycle bases. At large length-scales (i.e. sample size), these structures are randomly dispersed, and remain as such while their population progressively falls as loading proceeds. Bereft of redundant constraints from the 3-cycles, the force chains are initially just above the isostatic state, a condition that progressively worsens as the sample dilates. This diminishing capacity for redistribution of forces without incurring physical rearrangements of member particles renders the force chains highly prone to buckling. A multiscale analysis of the spatial patterns of force chain buckling reveals no clustering or localisation with respect to the macroscopic scale. Temporal patterns of birth-and-death of 3-cycles and 3-force chains provide unambiguous evidence that significant structural reorganisations among these building blocks drive rheological behaviour at all stages of the loading history. The near-total collapse of all structural building blocks and the spatially random distribution of force chain buckling and 3-cycles hint at a possible signature of diffuse failure.
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