Bistable auxetic surface structures

A deployable material system that is flat-fabricated from an elastic sheet and deploys into a prescribed doubly curved surface that is stable by design. The sheet is tiled with bistable auxetic cells, each of which expands isotropically to a second stable state set by its geometry. A precomputed library of cells covers expansion factors from 1.13 to 1.78; a conformal flattening of the target surface gives the expansion required at every point, and the matching cells are tiled into the flat cut pattern. Laser-cut rubber prototypes - spherical caps, a seamed cylinder, and architectural freeform surfaces - deploy by hand and match their targets to within a few percent of the bounding-box diagonal.