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Forces and Fluctuations in Dense Granular MaterialsR.P. Behringer, Dept. of Physics, Duke University
Discussant: C.S. O’Hern, SEAS, Dept. of Physics, Yale University
Quantitative characterization of force chains!
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Where it all began…
Duke University1994
Temporal fluctuations
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Spatial fluctuations
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Anisotropy
Isotropiccompression
Shear
•How does anisotropy affectthe ‘isotropic’ jamming picture?
•New critical points, related criticalpoints, controlled by point J,…?
•What is the coupling between friction and anisotropy, e.g. more anisotropic fabrics?
fabric
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What are the differences between isotropic and anisotropic jammed systems?
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Difference I
Different contact networks or fabrics
Isotropiccompression
Shear
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ShearIsotropic Compression
•Broad normal force distributions
Difference II
Snoeier et al. PRL 92, 054302 (2004)Tighe et al. Phys. Rev. E, 72, 031306 (2005)
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Difference III
Shear Compression
Chain direction
Direction normalTo chains
Both directions equivalent
•Local ‘pressure’ correlations are anisotropic longer ranged
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Difference III
Pq P
q P
q P
q
Simulations of Jammed Packings
Isotropic compression Pure shear
Chakraborty, Henkes, Lois, O’Hern, Majmudar, Behringer, 2008
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Difference IV
•Distribution of jamming onsets P(JA) changes,
e.g. shear dilation
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V
Quasistatic shear atconstant =0.85
Quasistatic shear atconstant ‘pressure = 0’
1 4 7
V
Dynamics from one jammed state to another
Dynamics from one inherent structure to another
1’ 3’ 3’ 5’
1 3 5
1’ 3’ 5’ Associated jammed states
ri
ri
Two ways to measure distribution P(JA)
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distribution of jamming onsets
shear
JA
•Distribution of jammingonsets shifts, i.e. shear dilation
Quasistatic shear at constant =0.85
N~100
shear
no shear
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V=0
strain
Shear at constant ‘Pressure=0’
•Number of jamming onsetsdepends on shear because fabrics are different
•Does packing fraction even matterat all? Or is the family or fabricthe more important variable even if 0?
family/fabric
JA
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1/
Point J
Point J is not really a single point?
jammedunjammed
• For frictionless isotropic jammed packings, there is an infinite number of J-points, but they all have same J when N and similar fabrics
• For frictionless anisotropic jammed packings, there is a different infinite set of JA-points with possibly different J
A that depend on the fabric. What happens
when N ?
•For frictional jammed packings, there is an infinite set of jammed
packings over a finite range RLP to RCP when N.
Point JA
1 N?
Points JAF
RCP-RLP
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1. How do we understand anisotropy?
2. Do anisotropic ‘critical’ points exist that ‘control’ response of anisotropic systems to deformation, and how do they relate to ‘isotropic’ jamming framework?
3. What is the density of states as a function of the fabric?
Questions
Gao, Lois, O’Hern, 2008.