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Research Papers

Length Scale for Transmission of Rotations in Dense Granular Materials

[+] Author and Article Information
Jagan M. Padbidri

 George W. Woodruff School of Mechanical Engineering,  Georgia Institute of Technology, Atlanta, GA, 30332 e-mail: jagan.padbidri@me.gatech.edu

Carly M. Hansen

 Texas Lutheran University, Seguin, TX, 78155 e-mail: cmhansen@tlu.edu

Sinisa Dj. Mesarovic1

Associate Professor,  School of Mechanical and Materials Engineering,  Washington State University, Pullman, WA, 99164 e-mail: mesarovic@mme.wsu.edu

Balasingam Muhunthan

Professor,Department of Civil and Environmental Engineering,  Washington State University, Pullman, WA, 99164 e-mail: muhuntha@wsu.edu

1

Corresponding author.

J. Appl. Mech 79(3), 031011 (Apr 05, 2012) (9 pages) doi:10.1115/1.4005887 History: Received July 08, 2011; Revised January 16, 2012; Posted February 06, 2012; Published April 04, 2012; Online April 05, 2012

Deformation of granular materials is often characterized by strain localization in the form of shear bands, which exhibit a characteristic width of about 10–20 particle diameters. Much of the relative motion of particles within a shear band is accompanied by rolling, as opposed to sliding, since the latter requires more dissipative work. However, in a densely packed assembly, rolling cannot be accomplished without some sliding. This dissipative constraint implies a characteristic rotation transmission distance, i.e., the distance to which the information about rotation of a particle propagates. Here, we use the discrete element method to investigate this length and its directional dependence as function of the force chain network. We found that the rotation transmission distance correlates with the shear band width observed in experiments and previous numerical simulations. It is strongly dependent on the particle size distribution and the coefficient of interparticle friction, and weakly dependent on pressure. Moreover, the transmission of rotations is strongly directionally dependent following the pattern of force chains. To describe this dependence, we define a nonlocal tensorial description of force chain directionality.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Necessity of sliding in a cluster of particles. The centers of three particles A, B and C are fixed and the particles are in contact with each other. Impose the counterclockwise rotation on particle A, as shown. Relative sliding is defined by nonzero relative velocities of the contact points. To avoid sliding with respect to A, both B and C must rotate in the clockwise direction. But this will result in sliding on the B-C contact. Thus, even in a three particle cluster, rolling without sliding cannot be accomplished, unless one of the contacts is disengaged.

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Figure 2

Force nework of a pressurized assembly of particles. Let ⟨f⟩ be the average contact force. The four different line widths, represent the relative magnitude of forces: f<⟨f⟩, ⟨f⟩<f<2⟨f⟩, 2⟨f⟩<f<4⟨f⟩ and f>4⟨f⟩.

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Figure 3

Evolution of angular velocity with distance for particle assemblies with ɛ0=6.647×10-4 and μ = 0.5. (a) σ/σRR=0.115, (b) σ/σRR=0.1925, (c) σ/σRR=0.2727.

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Figure 4

Evolution of angular velocity with distance for particle assemblies with ɛ0=6.647×10-4 and μ = 0.9. (a) σ/σRR=0.115, (b) σ/σRR=0.1925, (c) σ/σRR=0.2727.

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Figure 5

Evolution of angular velocity with distance for particle assemblies with ɛ0=1.944×10-3 and μ = 0.5. (a) σ/σRR=0.115, (b) σ/σRR=0.1925, (c) σ/σRR=0.2727.

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Figure 6

Evolution of angular velocity with distance for particle assemblies with ɛ0=1.944×10-3 and μ = 0.9. (a) σ/σRR=0.115, (b) σ/σRR=0.1925, (c) σ/σRR=0.2727.

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Figure 7

Definition of contact in the neighborhood of a particle, used to define the nonlocal force chain fabric tensor (Eq. 11)

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Figure 8

Force chain structure (left) and the corresponding rose plot of W(θ,Δθ) (right) indicating the strength of force chains as function of direction. Shown in red are the eigenvectors of the symmetric portion of T.

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Figure 9

Propagation of angular velocities from the forced particle shown as color-coded contours and the rose plot of W(θ,π/π2020) in blue with eigenvectors of the symmetric part of T in red, and the rose plot for ω(θ,π/π2020) in green for R¯=14R, ɛ0=6.647×10-4 and μ = 0.5. (a) σ/σRR=0.1925, (b) σ/σRR=0.2727. The forced particle is colored black.

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Figure 10

Propagation of angular velocities from the forced particle shown as color-coded contours and the rose plot of W(θ,π/π2020) in blue with eigenvectors of the symmetric part of T in red, and the rose plot for ω(θ,π/π2020) in green for R¯=14R, ɛ0=6.647×10-4 and μ = 0.9. (a) σ/σRR=0.1925, (b) σ/σRR=0.2727. The forced particle is colored black.

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Figure A1

Variation of pressure and friction with non-dimensional time to obtain the initial configuration. The time is non-dimensionalized following Ref. [21].

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