Friction and relative energy dissipation in sheared granular materials

The oscillating cylinder of a low-frequency inverted torsion pendulum is immersed into layers of noncohesive granular materials, including fine sand and glass beads. The relative energy dissipation and relative modulus of the granular system versus the amplitude and immersed depth of the oscillating cylinder are measured. A rheological model based on a mesoscopic picture is presented. The experimental results and rheological model indicate that small slides in the inhomogeneous force chains are responsible for the energy dissipation of the system, and the friction of the grains plays two different roles in the mechanical response of sheared granular material: damping the energy and enhancing the elasticity.

Figure 1

Sketch of the forced torsion pendulum immersed into a granular medium. 1, suspension wires; 2, permanent magnet; 3, external coils; 4, mirror; 5, cylinder (made of aluminum alloy with inner radius $R$) covered or not by a fixed layer of granules; 6, optic source; 7, optic detector.

Figure 2

RED of a fine sand assembly, with the oscillating cylinder covered by a layer of grains. (a) $\eta$ vs $A_0$ for different immersed depths, as noted. The solid lines are fitted by $\eta =a\tanh \left(b{A}_0\right)+c$, where $a$, $b$, and $c$ are fitting parameters. Here only five lines are presented. (b) $\eta$ vs $L$ for different oscillating amplitudes $A_0$, as noted.

Figure 3

RED of a fine sand assembly, with a clean oscillating cylinder. (a) $\eta$ vs $A_0$ for different immersed depths, as noted. The solid lines are fitted by $\eta =a\tanh \left(b{A}_0\right)+c$. Here only five lines are presented. (b) $\eta$ vs $L$ for different oscillating amplitudes $A_0$, as noted.

Figure 4

RED of an assembly of glass beads, with the oscillating cylinder covered by a layer of grains. (a) $\eta$ vs $A_0$ for different immersed depths, as noted. (b) $\eta$ vs $L$ for different oscillating amplitudes $A_0$, as noted.

Figure 5

RED of an assembly of glass beads, with the clean oscillating cylinder. (a) $\eta$ vs $A_0$ for different immersed depths, as noted. (b) $\eta$ vs $L$ for different oscillating amplitudes $A_0$, as noted.

Figure 6

Relative modulus of a fine sand assembly, with the oscillating cylinder covered by a layer of grains. (a) $G_0$ vs $A_0$ for different immersed depth, as noted. (b) $G_0$ vs $L∕d$ for different oscillating amplitude $A_0$, as noted.

Figure 7

(a) Rheological model. The lower branch represents the granular medium, characterized by a slide unit of critical torque $T_c$ and a spring of torsion constant $G_g$. The upper branch represents the suspension wires of the pendulum, of torsion constant $G_p$. (b) The RED $\eta =Q∕2\pi W$ and (c) the modulus $G$ calculated from the rheological model, potted as a function of the normalized amplitude $A_0∕A_c$ for different $\chi$. The various curves correspond to an increasing $\chi$ of 0.2, 0.5, 1, 2, 5, 7, 10, and 14, respectively.

Figure 8

Schematic distribution of force chains opposing (a) the rotation of the pendulum and (b) the straight motion of an immersed object, where $L$ is the immersion depth. (c) The mesoscopic rheological model.

Figure 9

RED $\eta$ versus (a) torsion amplitude, for different immersed depths, as noted; and (b) immersed depth $L∕10d$, calculated from the rheological model based on the mesoscopic picture, for different torsion amplitudes, as noted.