Reversibility and force behavior for cyclic shear of a granular material
Jie Ren, Joshua Dijksman, Robert P. Behringer
Department of Physics, Duke University, Durham, NC
Introduction
2D granular system
γ
We experimentally investigate the diffusion
and contact forces in a two-dimensional
granular system, an array of disks, exposed
to oscillatory, linear shear. By comparison,
slow viscous fluid flow is governed by timereversible evolution equations. This
reversibility breaks down for even quite
dilute suspensions, as was recently
shown[1]. The breakdown is abrupt and
occurs at finite strain amplitude, as
evidenced by a marked increase in particle
diffusivity. We seek an understanding of the
properties of this reversibility-irreversibility
for granular systems. We study the
reversibility of particle motion as a function
of the volume fraction of disks and the shear
amplitude. We find anomalous spatial and
rotational diffusion and a sudden increase of
the diffusivity around a particular volume
fraction. Our data suggests that the
reversibility transition observed by Pine et al
can also be observed in dry granular media.
Cyclic shear
φ
60 cm
Polarizer
γ
Unsheared,
unjammed
------
Sheared,
shear-jamming
101
102
Diffusivity significantly
increases around this
region -Reversibility-irreversibility
transition!
‹∆θ2› (T = 100) (rad2)
101
γ=4.5%
100
noise level?
10-1
10-2
0.45
φ
0.55
0.65
0.75
0.85
But NO forces visible in
the packings at the same
region
Forces
10-1
γ=4.5%
10-3
Time [cycles]
101
102
sheared phase
unsheared phase
>
8
8
0
φ
0.81
γ = 2.7%
Time [cycles]
102
101
1000
1000
16
0.79
transient time t
0
2
4
6
γ [%]
0
100
100
10
10
1
0.77
φ
0.79
0.81
0
2
0.55
φ
0.65
0.75
0.85
4
6
γ[%]
0
γ=4.5%
0.45
16
0.77
7
3
-- Shear-Jamming!
<
transient time t
100
103
φ = 0.802
γ=4.5%
11
Force [AU]
100
10-2
Force evolution of unsheared (blue) and
sheared (red) phases: transient behavior
On increasing ϕ and γ, we
observe:
-- Increase of force value
-- Growing timescale of force
dynamics
in systems below jamming point,
where one would expect only
unjammed states to exist [2].
1.6
φ
10-4 0
10
103
Rotation
Position
Transient time t [cycles]
Time [cycles]
Mean-squared
Rotation: Superdiffusive
101
Average Force [AU]
γ=4.5%
Unsheared Phase
~1000 particles:
Photo-elastic disks
Bi-disperse
Radius ratio:
1:1.25
Number ratio:
3:1
Time-averaged fore [AU]
10-2
100
t
Force behavior: shear-jamming
‹∆θ2› (rad2)
‹∆x2›/d2
Mean-squared
Displacement: Subdiffusive
0.8
10-4
Time
0
Slats
Polarizer
102
10-3
γ
Panel Light
100
φ
Sheared Phase
Particles
Diffusion & reversible-irreversible transition
10-1
Shear Strain
Camera
100~500 Shear Cycles
References:
[1] D. J. Pine, J. P. Gollub, J. F. Brady and A. M. Leshansky, Nature, 438, 997 (2005)
[2] A. Liu and S. Nagel, Nature, 396, 21 (1998)
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