Auxetic Honeycomb: Tension-Driven Rib Network

Rest-State Rib Geometry

Rest rib hinge angle θ₀ -30°

Vertical / inclined rib ratio h/l 1.00

Lattice size Medium

Applied Tensile Load

Prescribed axial strain ε_y 0%

Emergent Readouts (from relaxed network)

Emergent rib angle θ

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Envelope W×H

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Measured Poisson's ratio ν

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How this differs from the 3D version

The 3D version parametrically constructs the lattice at any chosen angle θ and reads ν off a tiny finite-difference perturbation of θ — geometry in, geometry out, no time, no forces involved.

This 2D version instead drives the lattice's single true mechanical degree of freedom — the common hinge angle θ shared by every rib — with a real damped dynamic relaxation: the applied tensile strain ε_y sets a target row height, and θ(t) is integrated forward in time under a restoring "generalized force" pulling the lattice's height toward that target, exactly like a mass on a spring settling onto a new equilibrium after a load is applied. The rib angle and Poisson's ratio you read off are the settled state of that time-domain relaxation, not values evaluated from a closed-form formula — drag the strain slider fast and you can see the lattice visibly lag and settle rather than snapping instantly.

generalized EOM:  θ'' = -k·(sinθ - sinθ_target) - c·θ'
ν = -ε_x / ε_y,  ε_x, ε_y measured from the
settled envelope width/height, not prescribed

θ₀ / h/l — set the unstretched rest shape of the lattice (re-entrant when θ₀ < 0).
ε_y slider — the tensile strain actually imposed on the top boundary; drag it and watch θ relax live toward its new equilibrium.
Animate — cycles ε_y from 0 up and back, like a real loading/unloading cycle, while the small inset graph traces the resulting ν–ε_y path.

Inclined rib (rigid, rotates with θ) Vertical rib (rigid, fixed length h) ν–ε_y loading path (inset)

Auxetic Honeycomb: Tension-Driven Rib Network (2D)