Mechanical characterisation of stereolithography-printed TPMS scaffolds: geometry and density property relationships

Triply periodic minimal surface (TPMS) lattices were stereolithography‑printed to investigate how topology and relative density govern the elastic behaviour of sheet‑based architectures. Five TPMS—Gyroid, Diamond, Schwarz P, Lidinoid and Split‑P—were mechanically characterised in uniaxial tension and compression across multiple wall‑thickness levels. Mechanical properties were first obtained as net‑section quantities using the minimum resistant cross‑section; apparent (homogenised) moduli were then reconstructed via a strain‑preserving rescaling to the external cross‑section, ensuring compatibility with continuum‑level scaling. Relative density was defined purely volumetrically from the exact implicit geometry. Crucially, the solid resin modulus ES was measured experimentally on fully dense specimens with the same external gauge as the TPMS tensile samples, yielding a metrologically consistent normalisation E*/ES. Within this framework, linearised Gibson–Ashby fits reveal topology‑dependent scaling that is robust to the choice of ES: Diamond is closest to stretching‑assisted behaviour, Gyroid and Schwarz P are bending‑dominated, Split‑P lies near the bending limit, and Lidinoid exhibits an extreme bending‑controlled response with pronounced geometric inefficiencies. In terms of geometric efficiency, the prefactors rank Schwarz P > Gyroid > Lidinoid > Diamond > Split‑P, showing that density or wall‑thickness increases do not necessarily deliver proportional stiffness gains in sheet‑based TPMS. The study provides a traceable, topology‑centred methodology and design guidance that are directly transferable to other photopolymers and loading modes when the same volumetric‑density and strain‑preserving reconstruction principles are applied.