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!

Where it all began…

Duke University1994

Temporal fluctuations

Spatial fluctuations

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

What are the differences between isotropic and anisotropic jammed systems?

Difference I

Different contact networks or fabrics

Isotropiccompression

Shear

ShearIsotropic Compression

•Broad normal force distributions

Difference II

Snoeier et al. PRL 92, 054302 (2004)Tighe et al. Phys. Rev. E, 72, 031306 (2005)

Difference III

Shear Compression

Chain direction

Direction normalTo chains

Both directions equivalent

•Local ‘pressure’ correlations are anisotropic longer ranged

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

Difference IV

•Distribution of jamming onsets P(JA) changes,

e.g. shear dilation

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)

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

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

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

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.