Forces and Fluctuations in Dense Granular Materials

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Forces and Fluctuations in Dense Granular
Materials
R.P. Behringer, Dept. of Physics, Duke University
Discussant C.S. OHern, SEAS, Dept. of Physics,
Yale University
Quantitative characterization of force chains!
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Where it all began
Temporal fluctuations
Duke University
1994
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Spatial fluctuations
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Anisotropy

• How does anisotropy affect
• the isotropic jamming picture?
• New critical points, related critical
• points, controlled by point J,?
• What is the coupling between
• friction and anisotropy, e.g. more
• anisotropic fabrics?

Isotropic compression
Shear
fabric
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What are the differences between isotropic and
anisotropic jammed systems?
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Difference I
Isotropic compression
Shear
Different contact networks or fabrics
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Difference II
Isotropic Compression
Shear

• Broad normal force distributions

Snoeier et al. PRL 92, 054302 (2004) Tighe et al.
Phys. Rev. E, 72, 031306 (2005)
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Difference III
Shear
Compression
Both directions equivalent
?Chain direction
Direction ? normal To chains

• Local pressure correlations are anisotropic
  longer ranged

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Difference III
Isotropic compression
Pure shear
Simulations of Jammed Packings
Chakraborty, Henkes, Lois, OHern, Majmudar,
Behringer, 2008
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Difference IV

• Distribution of jamming onsets P(?JA) changes,
• e.g. shear dilation

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Two ways to measure distribution P(?JA)
V
Quasistatic shear at constant ?0.85
1
3
5
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Dynamics from one inherent structure to another
1? 3? 5
1? 3? 5
Associated jammed states
V
Quasistatic shear at constant pressure 0
Dynamics from one jammed state to another
1? 4 ? 7
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Quasistatic shear at constant ?0.85
shear
distribution of jamming onsets
N100
no shear
shear
?JA

• Distribution of jamming
• onsets shifts, i.e. shear
• dilation

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Shear at constant Pressure0

• Number of jamming onsets
• depends on shear because
• fabrics are different
• Does packing fraction even matter
• at all? Or is the family or fabric
• the more important variable even
• if ???0?

V0
strain
?JA
??
family/fabric
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Point J is not really a single point?
?RCP-?RLP
?
jammed
unjammed
1/?
Points JAF
Point J
Point JA

• 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 ?JA 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??.

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Questions
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?
Gao, Lois, OHern, 2008.