Expanding Elastic Moduli Bounds in Solid-Void Metamaterials: Poisson's Ratio Dependence and Optimal Design

Abstract Two-phase solid-void mechanical metamaterials achieve exceptional properties through microstructural adjustments, including any isotropic Poisson’s ratio (−1 to 1 in two dimensions, −1 to 0.5 in three dimensions). Establishing theoretical bounds on these properties is essential for optimising material performance. However, as demonstrated herein, current research often overlooks isotropy constraints, limiting the upper bounds of elastic moduli to a narrow range of Poisson's ratios. In this study, we extend these bounds, revealing significant variability contingent on Poisson's ratio. Through the analysis of five truss lattice materials, each approaching these new bounds in specific Poisson's ratio ranges, we elucidate the interrelationships among deformation mechanisms, elastic moduli, and Poisson's ratio. Notably, we present the first stretching-dominated, isotropic, two-dimensional lattice materials that approach the upper elastic moduli limits as Poisson's ratio approaches -1. These findings provide valuable guidance for designing lightweight, stiff metamaterials across the entire Poisson's ratio spectrum.