Auxetic Metamaterial
Re-entrant honeycomb with negative Poisson's ratio — expands when stretched
ν (Poisson ratio): –
ε_x: –
ε_y: –
Auxetic materials have negative Poisson's ratio: ν = -ε_lateral/ε_axial.
The re-entrant honeycomb achieves this through its geometry — angled ribs "unfold" outward when stretched.
ν depends on angle θ: ν = -(cos²θ·(h/l + sin θ)) / (sin θ · (h/l + sin θ)² / cos²θ ... see Gibson-Ashby model.
Regular honeycomb (θ > 0): ν ≈ +1. Re-entrant (θ < 0): ν < 0. At θ = -30°, ν ≈ -1.
Applications: protective armor, medical stents, shape-morphing structures.