Dense granular materials, such as sand, grains in a silo, and pharmaceutical powders, exhibit a unique class of material behavior: they behave as solids under static loading; but upon the initiation of instability, they flow like liquids. Accurate modeling of such materials remains a pressing challenge to both engineers and scientists studying natural or industrial flow phenomena such as landslides, segregation in industrial processing, and clogging in silo flow, to name a few. A characteristic feature in any stressed granular material is the generation of "force chains" or grain columns, the buildup of which resists flow and the collapse of which induces flow. In the context of shear banding (the localization of deformation into narrow zones of intense shearing) in sands, in particular, these columns exhibit characteristic lengths, resulting in length-scale dependency in material behavior. The understanding of the kinematic behavior of these force chains is critical. for the development of accurate predictive models.
We deform specimens of dense sand or glass beads in plane strain. The specimen base rests on a lowfriction, linear bearing "sled", which provides the kinematic freedom for formation of a single, persistent shear band. Throughout shearing, digital images of in plane deformations are collected at regular intervals. The technique of Digital Image Correlation (DIC) is used to measure grain-scale displacements within shear bands. The DIC method derives displacements by mapping subsets of pixels at many points across the specimen surface, and provides a nearly temporally continuous representation of grain-scale surface motion. From the dense DIC data arrays, we calculate various strain and kinematic quantities and examine patterns throughout softening and critical state.
At the softening-critical state transition, a systematic pattern in various kinematic quantities consistently appears along the shear band length, marking the existence of a collective, multi-force chain buckling event of the force chains that initially comprise the shear band upon its formation at peak stress. We observe rotational vortices centered at the peaks (absolute value) in kinematic rotation. The spatial peaks in rotational strain denote locations where a force chain is in the process of buckling. While the force chains are in the process of buckling throughout softening, it is only at the softening-critical state transition where vortices first appear, suggesting that the vortices are a consequence of the force chain collapse process. We also observe the presence of counter-rotating "wakes" along the shear band boundary. A preliminary assessment of the spatial periodicity of such patterns has been performed to glimpse the nature of an underlying length scale for granular material deformation. While shear band thickness and spacing between vortices increase as median grain size increases, neither vortex spacing nor shear band thickness exhibit a consistent relationship to grains diameter.
Much of the previous research on grain- and mesoscale behavior of granular systems has been derived from simulations or experiments on idealized particles. Our results represent one of the first findings on a real material. Characterization of the nature of statistical variations of grain-scale motions in granular systems is an ongoing effort in the development of thermodynamic-based models for granular materials, for which the methods here will play a key role.
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