Rigidity Loss in Disordered Systems: Three Scenarios

Wouter G. Ellenbroek, Varda F. Hagh, Avishek Kumar, M. F. Thorpe, and Martin van Hecke

Phys. Rev. Lett. 114, 135501 – Published 1 April 2015

Abstract

We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, whereas the effect on stress-relieved networks is more local and limited. These differences are also reflected in the linear elastic properties and point to the highly effective and unusual role of global self-organization in jammed sphere packings.

Received 28 November 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.135501

Authors & Affiliations

Wouter G. Ellenbroek¹, Varda F. Hagh², Avishek Kumar², M. F. Thorpe^2,3, and Martin van Hecke^4,5

¹Department of Applied Physics and Institute for Complex Molecular Systems, Eindhoven University of Technology, Postbus 513, NL-5600 MB Eindhoven, The Netherlands
²Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA
³Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, England
⁴Huygens-Kamerlingh Onnes Lab, Universiteit Leiden, P.O. Box 9504, NL-2300 RA Leiden, The Netherlands
⁵FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands