Achieving Auxetic Metamaterials through Variations in the Reciprocal Space Topology of the Triangular Lattice

Auxetic metamaterials, renowned for their counterintuitive lateral expansion under tension and contraction under compression, present significant potential across diverse applications such as impact mitigation and fracture‐resistant systems. This study presents a mechanism‐driven design strategy for auxetic behavior by strategically modulating the reciprocal space topology of triangular lattice networks. Through systematic transitioning the triangle lattice component from acute to obtuse configurations, programmable control over the Poisson's ratio is achieved, enabling a continuous transition from positive to negative regimes and reaching the isotropic theoretical limit of −1. Theoretical analysis uncovers that the negative Poisson's ratio arises from a geometric inversion in momentum space, governed by a defined parameter ⅅ, which is the length difference between next‐nearest neighbor and nearest neighbor reciprocal lattice vectors. The proposed architecture exhibits exceptional mechanical stability due to its high coordination number ( z = 6), surpassing conventional auxetic designs. Experimental validation via 3D‐printed prototypes confirms the tunability across a spectrum of Poisson's ratio values, with auxetic behavior emerging in obtuse configurations. The design framework not only advances the understanding of auxetic mechanisms but also enables programmable metamaterials for various applications.