Trigonally and hexagonally symmetric TPMS metamaterials under compressive loading

• Novel, non-cubic, TPMS structures revealing new design freedoms • Triagonal/hexagonal TPMS exhibit in-plane isotropy and out-of-plane anisotropy • TPMS patch aspect ratio and topology tailors the mechanical properties • Design strategies for maximising energy absorption under compression Designing trigonally and hexagonally symmetric triply periodic minimal surface (TPMS) sheet structures offers a new approach for creating lightweight and multi-functional metamaterials. Unlike the extensively studied TPMS structures with cubic symmetries, the mechanical response of trigonally and hexagonally symmetric TPMS sheet structures is in-plane isotropic and yet the properties out-of-plane can remain highly anisotropic. These novel trigonally and hexagonally symmetric TPMS possess the same advantages of the conventional cubic TPMS in terms of continuous, smooth shells, providing large surface areas and interconnected internal channels. This study examines the mechanical properties and energy absorption capabilities of two trigonally symmetric (GW, H) and three hexagonally symmetric (H’-T, H’’-R, T’-R’) TPMS sheet structures, made from polylactic acid (PLA) using Fused Filament Fabrication (FFF) under compression loading. The study also investigates the mechanical performance with Finite Element Analysis (FEA), where the universal anisotropy index is used to characterise stiffness anisotropy. Experimental and numerical results show that a wide array of mechanical responses is attainable with trigonally and hexagonally symmetric TPMS sheet structures, with the universal anisotropy index spanning two orders of magnitude from near elastic isotropy to highly anisotropic unit cells. Finally, an energy absorption diagram is presented to provide a systematic approach for selecting the optimal relative densities, topology, and orientation of trigonally and hexagonally symmetric TPMS structures in energy absorption applications.