Supplementary material from "Fractal-inspired auxetic metamaterial from hierarchical and recursively self-similar interconnected hexagons and triangles"
Year: 2026
Type: supplementary-materials
Abstract: An auxetic metamaterial is proposed based on a hierarchical assembly of self-similar rigid hexagons interconnected by rotating triangular units. The architecture incorporates both intra- and inter-generational connectors to ensure kinematic compatibility across scales, thereby preserving the overall hexagonal form during deformation and yielding an in-plane Poisson's ratio of −1 in all loading directions. Closed-form expressions are derived for the number of structural elements, displacement fields and inter-generational distances, enabling exact characterization of the deformation kinematics. Analytical formulations for the exact material area and the apparent enclosing area are obtained, both of which exhibit finite limits as the number of generations tends to infinity despite the exponential growth in structural complexity. The displacement paths of all constituent units are shown to follow bounded, self-similar trajectories, converging to limiting envelopes. The proposed design establishes a rigourous framework for auxetic metamaterials with tunable geometric and mechanical properties, offering potential for applications requiring shape-preserving expansion and hierarchical stiffness modulation.
Source: Figshare
Author: Teik-Cheng Lim
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214894475