A unified spatial Poisson’s ratio design method (SPRDM) for 3D Poisson’s ratio metamaterials based on a minimal chiral structure

Abstract

Poisson’s ratio metamaterials exhibit unconventional deformation behaviors enabled by architected internal geometries. While numerous planar auxetic and related designs have been reported, the systematic generation and classification of spatial Poisson’s ratio metamaterials remains limited. In this work, we introduce the Spatial Poisson’s Ratio Design Method (SPRDM), a unified geometric framework that extends a previously established planar design approach to three-dimensional architectures. The SPRDM is built on two minimal kinematic bases, a planar and a spatial chiral structure and eight symmetry-based topological transformations that enable controlled manipulation of dimensionality and chirality. The method systematically generates 1.5D, 2D, 2.5D, and 3D metamaterial families, reproducing known auxetic, anepirretic, and meiotic architectures as well as enabling the design of previously unreported spatial and superchiral structures. A consistent classification scheme and naming protocol are introduced to organize the resulting design space, together with a unit-cell construction strategy supporting planar tessellations and three-dimensional honeycombs. Representative examples demonstrate the versatility of the method, including spatial auxetic and anepirretic architectures with tunable deformation mechanisms. Volume strain is employed as a general metric to characterize compressibility beyond directional Poisson’s ratios. The SPRDM provides a systematic foundation for the design of spatial Poisson’s ratio metamaterials with broad relevance to architected materials research.