Negative Poisson's ratio in porous metamaterials inspired by hinged polygonal tessellations

Hinged structures, also known as hinged tessellations, are a class of idealized architecture metamaterials composed of rigid rotating units connected by pivoting hinges, which exhibit negative Poisson's ratios (auxetic behavior). While kirigami-based architectures provide a prominent physical realization of such mechanisms, translating these idealized concepts into manufacturable continuum materials remain a challenge. In particular, mechanism-like response can be approximated in porous engineered materials fabricated via additive manufacturing (AM), where deformation is governed by ligament elasticity rather than perfect hinges. In this work, we present new planar (2D) porous mechanical metamaterials with negative Poisson's ratios, inspired by hinged tessellations. First, we propose and analytically investigate two novel hinged structures based on convex (dual) polygons - namely, deltoidal and trapezoidal units - which exhibit a Poisson's ratio equal to -1. Second, building on these results, we propose the design and practical implementation of porous mechanical metamaterials featuring an array of patterned elongated voids. The metamaterials are generated by placing
ligaments at the vertices of the polygonal units in the original hinged frameworks. The elastic properties of different geometric variants are evaluated through Finite Element analysis. Numerical investigations show thatthe Poisson's ratio can be tuned from -0.12 up to nearly -1, accompanied by a wide range of elastic moduli controlled by adjusting the void size. The resulting designs span a porosity range of approximately 6% to 58%. In
addition, the metamaterials are provided with a moderate degree of anisotropy, with quasi-isotropic behavior observed for specific configurations. Finally, prototypes are fabricated through AM and experimentally tested, confirming the auxetic response of the proposed architectures.