Granular Packing — Jamming Transition

Force chains, Z = 2d isostatic point, packing fraction φ

Controls

Packing φ: 0.70
Mean contacts Z:
Isostatic Z*: 4.00 (2d)
Status:
Jamming transition at φ_J ≈ 0.64 (random close packing) for monodisperse 2D discs.

Maxwell criterion: Z* = 2d = 4 in 2D.
Below: floppy (unjammed). Above: rigid (jammed).

Force chains carry stress anisotropically — bright lines show contact forces proportional to overlap.
φ_J ≈ 0.64 (2D random)
φ_max = π/(2√3) ≈ 0.906 (hexagonal close-packing)