Material Instability in Rapid Granular Shear Flow
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Material Instability in Rapid Granular Shear Flow1 J.D.Goddard Department of Mechanical and Aerospace Engineering University of California, San Diego La Jolla, CA 92093-0411 ABSTRACT This is a survey of recent theoretical work on shear flow instabilities of dry granular media in the Bagnold or "grain-inertia" régime. Attention is devoted to steady homogeneous unbounded simple shear, with the goal of identifying material (constitutive) instabilities arising from the coupling of stress to granular concentration and temperature fields. Such instabilities, the dissipative analogs of thermodynamic phase transitions, are familiar in numerous branches of the mechanics of materials. The current interest is motivated in part by the "dissipative clustering" found in various particledynamics ("DEM") simulations of granular systems. Since particle clustering may invalidate standard gas kinetic theory, it is pertinent to ask whether hydrodynamic models based on such theories may themselves exhibit clustering instability. The present article is based largely on a recent review (Goddard and Alam 1999), which provides a unified linear-stability treatment for rapid granular flow, as well for slow flow of mobile particles immersed in viscous liquids. The analysis is based on a "short-memory" response of various fluxes to perturbations on steady uniform states, a feature characteristic of the most popular constitutive models for granular flow. In the absence of gravity, previous theoretical analyses reveal transverse "layering" and spanwise "corrugations" as possible forms of material instability (Alam and Nott 1998) Based on current theoretical findings, further work is recommended, including the exploration of the effects of gravity and of stress relaxation, both of which are likely to be important in real granular flows. INTRODUCTION Particle clustering is found in various particle-dynamics simulations of dry granular media subject to rapid shearing (Hopkins and Louge, 1991). Other simulations (Goldhirsch and Zanetti, 1993; Tan and Goldhirsch, 1997) indicate that the density and extent of such clusters increase with collisional inelasticity, implicating microscale dissipation as the mechanism. Temporal stress fluctuations have also been found in several experiments and computer simulations of shear flow (Savage, 1992a; Miller et al., 1996). Savage's simulation of a particulate mass sheared between rough walls exhibit régimes of quasi-turbulent stress 1
Paper BB4.1, Materials Research Society, Spring Meeting, San Francisco, CA, April 24-28, 2000.
BB4.1.1 Downloaded from https://www.cambridge.org/core. The Librarian-Seeley Historical Library, on 03 Dec 2019 at 05:13:35, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1557/PROC-627-BB4.1
fluctuations with 1/f spectrum. Stress fluctuations have been observed experimentally by Behringer and Baxter (1991) in hopper flow and by Miller et al. in an annular shear cell. Clustering and stress fluctuations may cast doubt on v
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