Selective hinge removal strategy for architecting hierarchical auxetic metamaterials

Mechanical metamaterials are man-made structures capable of achieving different intended mechanical properties through their artificial, structural design. Specifically, metamaterials with negative Poisson's ratio, known as auxetics, have been of widespread interest to scientists. It is well-known that some pivotally interconnected polygons exhibit auxetic behaviour. While some hierarchical variations of these structures have been proposed, generalising such structures presents various complexities depending on the initial configuration of their basic module. Here, we report the development of pivotally interconnected polygons based on even-numbered modules, which, in contrast to odd-numbered ones, are not straightforward to generalize. Particularly, we propose a design method for such assemblies based on the selective removal of rotational hinges, resulting in fully-deployable structures, not achievable with previously known methods. Analytical and numerical analyses are performed to evaluate Poisson's ratio, verified by prototyping and experimentation. We anticipate this work to be a starting point for the further development of such metamaterials. Pivotally interconnected polygons are capable of auxetic behavior, but have not been fully explored. Here, a design method is demonstrated based on the selective removal of rotational hinges in pivotally interconnected polygons with even-numbered modules, leading to fully-deployable structures.