Eur. Phys. J. E (2018) 41: 93
https://doi.org/10.1140/epje/i2018-11705-9

Regular Article

Quasilocalized states of self stress in packing-derived networks

Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands

^* e-mail: e.lerner@uva.nl

Received: 7 July 2017
Accepted: 24 July 2018
Published online: 21 August 2018

Abstract

States of self stress (SSS) are assignments of forces on the edges of a network that satisfy mechanical equilibrium in the absence of external forces. In this work we show that a particular class of quasilocalized SSS in packing-derived networks, first introduced by D.M. Sussman, C.P. Goodrich, A.J. Liu (Soft Matter 12, 3982 (2016)), are characterized by a decay length that diverges as , where is the mean connectivity of the network, and is the Maxwell threshold in two dimensions, at odds with previous claims. Our results verify the previously proposed analogy between quasilocalized SSS and the mechanical response to a local dipolar force in random networks of relaxed Hookean springs. We show that the normalization factor that distinguishes between quasilocalized SSS and the response to a local dipole constitutes a measure of the mechanical coupling of the forced spring to the elastic network in which it is embedded. We further demonstrate that the lengthscale that characterizes quasilocalized SSS does not depend on its associated degree of mechanical coupling, but instead only on the network connectivity.