Forces and Fluctuations in Dense Granular Materials R.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… Temporal fluctuations Duke University 1994

Spatial fluctuations

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

What are the differences between isotropic and anisotropic jammed systems?

Difference I Different contact networks or fabrics Isotropic compression Shear Different contact networks or fabrics

Difference II Broad normal force distributions Isotropic Compression Shear Broad normal force distributions Snoeier et al. PRL 92, 054302 (2004) Tighe et al. Phys. Rev. E, 72, 031306 (2005)

Difference III Shear Compression Both directions equivalent Chain direction Direction  normal To chains Local ‘pressure’ correlations are anisotropic longer ranged

Difference III Simulations of Jammed Packings Isotropic compression Pure shear Simulations of Jammed Packings Chakraborty, Henkes, Lois, O’Hern, Majmudar, Behringer, 2008

Difference IV Distribution of jamming onsets P(JA) changes, e.g. shear dilation

Two ways to measure distribution P(JA) V Quasistatic shear at constant =0.85 1’ 3’ 3’ 5’ 1 3 5 Dynamics from one inherent structure to another 1’ 3’ 5’ Associated jammed states V Quasistatic shear at constant ‘pressure = 0’ 1 4  7 Dynamics from one jammed state to another

Quasistatic shear at constant =0.85 distribution of jamming onsets N~100 no shear shear JA Distribution of jamming onsets shifts, i.e. shear dilation

Shear at constant ‘Pressure=0’ 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? V=0 strain JA  family/fabric

Point J is not really a single point? RCP-RLP ? unjammed jammed 1/ Points JAF Point JA Point J 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.

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, O’Hern, 2008.