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.

Phys. Rev. Lett.
Mechanical Metamaterials

Ellenbroek, W. G., Hagh, V. F., Kumar, A., Thorpe, M. F., & van Hecke, M. (2015). Rigidity loss in disordered systems : three scenarios. Phys.Rev.Lett., 114(Article number: 135501), 1–5. doi:10.1103/PhysRevLett.114.135501