Granular Packing — Jamming Transition
Force chains, Z = 2d isostatic point, packing fraction φ
Controls
Number of discs N
80
Packing fraction φ
0.70
Size polydispersity
0.2
↺ Repack
Force Chains
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)