Auxetic behavior refers to lateral widening upon stretching.

We investigate planar periodic frameworks which can deform from a folded tiling configuration to a deployed configuration while maintaining an auxetic behavior at all times. Particular attention is given to a pair of framework structures, one with a single degree of freedom, the other with four degrees of freedom.

This complements our recent study [BS] of a related planar periodic framework with three degrees of freedom.

Reference:

[BS] Borcea, C.S. and Streinu, I.: Periodic tilings and auxetic deployments.

Mathematics and Mechanics of Solids, 2021, Vol. 26(2) 199–216.

DOI: 10.1177/1081286520948116