The planar and spatial base structures as input to the design method, with the naming protocol and examples of existing and novel structures. • A chiral structure is proposed as a base for all spatial Poisson’s ratio metamaterials. • Poisson’s ratio metamaterials are named and classified by their achirality, chirality and superchirality order. • Eight topological transformations can generate all existing and create novel Poisson’s ratio structures. • The volume strain, linked to compressibility, is proposed as a general metric for Poisson’s ratio behavior. 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.
Roberjot et al. (Sun,) studied this question.