The kinematic flow pattern in slow deformation of a model dense granular medium is studied at high resolution using in situ imaging, coupled with particle tracking. The deformation configuration is indentation by a flat punch under macroscopic plane-strain conditions. Using a general analysis method, velocity gradients and deformation fields are obtained from the disordered grain arrangement, enabling flow characteristics to be quantified. The key observations are the formation of a stagnation zone, as in dilute granular flow past obstacles; occurrence of vortices in the flow immediately underneath the punch; and formation of distinct shear bands adjoining the stagnation zone. The transient and steady state stagnation zone geometry, as well as the strength of the vortices and strain rates in the shear bands, are obtained from the experimental data. All of these results are well-reproduced in exact-scale non-smooth contact dynamics simulations. Full 3D numerical particle positions from the simulations allow extraction of flow features that are extremely difficult to obtain from experiments. Three examples of these, namely material free surface evolution, deformation of a grain column below the punch and resolution of velocities inside the primary shear band, are highlighted. The variety of flow features observed in this model problem also illustrates the difficulty involved in formulating a complete micromechanical analytical description of the deformation.
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This work was supported in part by US Army Research Office Grant W911NF-12-1-0012 and NSF Grant CMMI 1234961 (Purdue); Department of Science and Technology (DST, India) Grant No. SR-CE-0057-2010 (to T.G.M., Indian Institute of Science); and a Bilsland Dissertation Fellowship (to K. V., Purdue). Use of codes made available by D. Blair (Georgetown U), E. Dufresne (Yale) and A. Donev (NYU) is gratefully acknowledged.
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Viswanathan, K., Mahato, A., Murthy, T.G. et al. Kinematic flow patterns in slow deformation of a dense granular material. Granular Matter 17, 553–565 (2015). https://doi.org/10.1007/s10035-015-0576-y
- Dense flow
- Shear bands
- Pattern formation