Non-affine response: Jammed packings vs. spring networks

¹  Department of Physics and Astronomy, University of Pennsylvania - Philadelphia, PA 19104-6396, USA
²  Instituut-Lorentz, Universiteit Leiden - Postbus 9506, 2300 RA Leiden, The Netherlands
³  Kamerlingh Onnes Lab, Universiteit Leiden - Postbus 9504, 2300 RA Leiden, The Netherlands

Corresponding author: wouterel@sas.upenn.edu

Received: 12 May 2009
Accepted: 27 July 2009

Abstract

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.