Curvature modulation of TPMS-based lattices: from geometric design to enhanced mechanical responses

The performance optimisation of Triply Periodic Minimal Surfaces (TPMS) structures currently faces a critical bottleneck involving a transition from a density-driven to a geometry-driven paradigm. Traditional design strategies for TPMS lattices are commonly interpreted using the Gibson-Ashby framework, which effectively describes density-dependent mechanical scaling. However, this framework does not explicitly distinguish the effects of local geometric parameters on mechanical properties. Concurrently, constrained by their inherent mathematical frameworks, existing TPMS-based structures struggle to achieve precise customisation of local curvature, which significantly limits the potential for optimisation of TPMS-based structures in high-performance, lightweight design applications. Here, we propose a TPMS-based design method that achieves controlled local curvature modulation through discrete geometric reconstruction in Gyroid lattices, and establish a Curvature-Volume Fraction (CV) model that quantitatively correlates curvature with mechanical properties. To validate this, we fabricated curvature-modulated Gyroid scaffolds using WE43 magnesium alloy via laser powder bed fusion (LPBF). The results demonstrate that curvature modulation reconfigures failure modes from shear band failure to layer-by-layer failure, achieving a ∼33% increase in yield strength and ∼29% increase in elastic modulus compared to standard Gyroids. This work establishes curvature as a design dimension for TPMS-based lattice architectures, opening new avenues for the customisation of additively manufactured lattices.