Most materials get thinner when stretched — pull a rubber band lengthwise and it narrows. Poisson's ratio ν quantifies this:
ν = -(transverse strain) / (axial strain)
= -ε_x / ε_y
Ordinary solids have ν between 0 and 0.5. An auxetic material has ν < 0: it gets wider when stretched. This isn't exotic chemistry — it's geometry. A re-entrant honeycomb is built from rigid ribs joined at hinges: a zig-zag of inclined ribs (length l, angle θ from horizontal) connected row-to-row by vertical ribs (length h). When θ is negative the cell walls point inward ("re-entrant" / bow-tie shape) instead of bulging outward like a normal hexagon.
Pulling the lattice vertically rotates the inclined ribs toward horizontal (θ increases toward 0). That rotation simultaneously pushes the whole row outward in x — so the lattice expands in both directions at once. This simulator builds the exact rib node grid at the current θ and h/l, then perturbs θ by a small step to measure the resulting strains directly from the geometry — the ν value shown is not a canned formula, it's read off the actual lattice, the same way you'd measure it on a real specimen.
- θ slider — negative = re-entrant (auxetic) cells, positive = a conventional convex honeycomb for comparison. Crossing θ = 0 flips the sign of ν.
- h/l ratio — longer vertical ribs relative to the inclined ones make the auxetic effect stronger (more negative ν).
- Animate — cycles θ to visualize the lattice actually breathing in and out together, as it would under real tension/compression.
Real auxetic honeycombs like this (and 3D re-entrant foams, chiral lattices, and rotating-unit structures) are used in impact-absorbing padding, auxetic textiles, and expandable medical stents — the negative ν makes them densify under impact and dome into curved shapes instead of buckling flat.