Non-affine response: Jammed packings vs. spring networks

We compare the elastic response of spring networks whose contact geometry is derived from real packings of frictionless discs, to networks obtained by randomly cutting bonds in a highly connected network derived from a well-compressed packing. We find that the shear response of packing-derived networks, and both the shear and compression response of randomly cut networks, are all similar: the elastic moduli vanish linearly near jamming, and distributions characterizing the local geometry of the response scale with distance to jamming. Compression of packing-derived networks is exceptional: the elastic modulus remains constant and the geometrical distributions do not exhibit simple scaling. We conclude that the compression response of jammed packings is anomalous, rather than the shear response.

[1]  L Mahadevan,et al.  Elasticity of floppy and stiff random networks. , 2008, Physical review letters.

[2]  Hernan A. Makse,et al.  Why Effective Medium Theory Fails in Granular Materials , 1999 .

[3]  Jacco H Snoeijer,et al.  Ensemble theory for force networks in hyperstatic granular matter. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  T. Vlugt,et al.  Force network ensemble: a new approach to static granular matter. , 2003, Physical review letters.

[5]  Critical scaling in linear response of frictionless granular packings near jamming. , 2006, Physical review letters.

[6]  Sheared force networks: anisotropies, yielding, and geometry. , 2005, Physical review letters.

[7]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[8]  Jean-Noël Roux,et al.  Wave propagation in confined granular systems , 2004 .

[9]  Critical and noncritical jamming of frictional grains. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Bulbul Chakraborty,et al.  Jamming in systems composed of frictionless ellipse-shaped particles. , 2008, Physical review letters.