A parameterized microstructure spanning the bounds of extremal elastic property space

Planar microstructures with extreme elastic properties are two-dimensional architected material structures whose effective behavior is close to theoretical bounds. They are valuable for applications including mechanical cloaking, wave-guiding devices, bio-medical implants, and extreme stiffness-to-mass ratios for light-weighting. Existing single-scale designs are scattered within the theoretical bounds and lack a unified representation that enables continuous and low-dimensional control of their effective properties, requiring case-by-case design generation and limiting their use in applications with smooth spatial variations in target behavior. This study presents one simple parameterized planar microstructure, represented by only seven geometric parameters and their continuous variations, that continuously spans the isotropic elastic property space close to the extreme bounds. The microstructure is inspired by foregoing density-based topology optimization studies. The geometry parameters are first optimized for a small set of points along the elastic property bounds and then interpolated to rapidly generate smoothly varying, near-isotropic microstructures along the bounds. Fabricated prototypes and mechanical testing validate the predicted extreme properties. The presented microstructure parameterization provides fundamental understanding of the geometric origins of extreme elastic behavior across the complete admissible property space. Furthermore, the proposed parametric representation facilitates accelerated design of extreme-property microstructures, enabling smooth property grading for various engineering applications.