Two-Dimensional Mechanical Metamaterials with Unusual Poisson Ratio Behavior

We design two-dimensional mechanical metamaterials that may be deformed substantially at little or no energy cost. Examples of such deformable structures include assemblies of rigid isosceles triangles hinged at their corners on the macroscale and polymerized phenanthrene molecules forming porous graphene on the nanoscale. In these and in a large class of related structures, the Poisson ratio ν diverges for particular strain values. It also changes its magnitude and sign, and displays a shape-memory effect.