Jamming Transition in Granular Packing

As packing fraction φ increases above φ_J ≈ 0.64, a granular material jams — particles become rigid and force chains emerge. At the transition, coordination number Z → 2d (isostatic point) and pressure P ~ (φ − φ_J)^α.

0.55
φ (packing)
0.00
Pressure
0.0
⟨Z⟩ contacts
-
State