Non-affine response: jammed packings versus spring networks

TL;DR

This study compares the elastic responses of spring networks derived from real jammed packings and random cuts, revealing that shear responses are similar near jamming, but compression responses are notably different and anomalous.

Contribution

It demonstrates that the shear response of packing-derived and randomly cut networks are similar near jamming, while the compression response of packing-derived networks is uniquely anomalous.

Findings

Shear response vanishes linearly near jamming in both network types.

Distributions of local geometry scale with distance to jamming.

Compression response of packing-derived networks remains constant, unlike shear response.

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.