224 research outputs found

    Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume

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    Naturally-occurring granular materials often consist of angular particles whose shape and frictional characteristics may have important implications on macroscopic flow rheology. In this paper, we provide a theoretical account for the peculiar phenomenon of auto-acoustic compaction -- non-monotonic variation of shear band volume with shear rate in angular particles -- recently observed in experiments. Our approach is based on the notion that the volume of a granular material is determined by an effective-disorder temperature known as the compactivity. Noise sources in a driven granular material couple its various degrees of freedom and the environment, causing the flow of entropy between them. The grain-scale dynamics is described by the shear-transformation-zone (STZ) theory of granular flow, which accounts for irreversible plastic deformation in terms of localized flow defects whose density is governed by the state of configurational disorder. To model the effects of grain shape and frictional characteristics, we propose an Ising-like internal variable to account for nearest-neighbor grain interlocking and geometric frustration, and interpret the effect of friction as an acoustic noise strength. We show quantitative agreement between experimental measurements and theoretical predictions, and propose additional experiments that provide stringent tests on the new theoretical elements.Comment: 12 pages, 3 figure

    Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations

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    We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stick-slip behavior at intermediate shear rates, even if the material is rate-strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stick-slip amplitude, or suppress stick-slip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stick-slip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics, and thus produce useful information about a variety of granular phenomena including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing.Comment: 12 pages, 8 figure

    Discrete Half-Logistic Distribution: Statistical Properties, Estimation, and Application

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    This article presented a novel discrete distribution with one parameter derived by the discretization approach and called the discrete half-logistic distribution. Its probability mass function and hazard function have different shapes. A variety of its statistical properties, including moments, probability generating function, incomplete moments, and order statistics, were determined mathematically. Maximum likelihood, moments, and proportion estimation methods were used to estimate its parameter. A simulation study conducts to check the various estimating method’s performance. By using a real data set, its flexibility is assessed. Lastly, it can model count data sets in a way that is compared with other distributions that are already in the scientific literature
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