A genus-tuning design on minimal surfaces for open-cell mechanical metamaterials

Mechanical metamaterials based on triply periodic minimal surfaces (TPMS) offer unprecedented opportunities for tailoring mechanical properties through their mathematically defined open-cell architecture. Although existing studies have examined the intrinsic properties, multi-physical applications, and geometric designs of TPMS metamaterials, a systematic approach for broad mechanical tunability remains underdeveloped. Here, we introduce a genus-tuning strategy as a novel geometric degree of freedom for systematically designing TPMS-based mechanical metamaterials. Through integrated numerical and theoretical analyses, we demonstrate that increasing genus induces a structural evolution that changes the Gaussian curvature distribution while preserving zero mean curvature. The Gaussian curvature distribution on newly generated TPMS metamaterials plays a pivotal role in modulating the stress distribution, thereby enabling flexible tuning of stiffness and energy absorption across a wide range. Notably, the specific Young's moduli increased by up to 47% on average within a relative density range of 0.04–0.12, and reached 177% of the Hashin-Shtrikman upper bound for maximum values, while specific shear moduli improved by up to 84.0%. Directional genus-tuning enabled TPMS metamaterials to attain nearly 94% of the stiffness of honeycombs under uniaxial load. A pronounced increase in specific energy absorption is demonstrated by 3D printed TPMS metamaterials, rising from 1.77 J·g⁻¹ to 6.93 J·g⁻¹, as the genus level is increased. Overall, this work establishes genus as a fundamental topological descriptor for mechanical performance and provides a powerful design paradigm for developing lightweight, highly customizable metamaterials.