On the Rigidity and Mechanical Behavior of Triply Periodic Minimal Surfaces-Based Lattices: Insights from Extensive Experiments and Simulations

Triply Periodic Minimal Surfaces (TPMS)-based lattices are gaining attention for their multifunctional properties. Current studies have largely focused on limited cases, characterizing the mechanical properties of only a few TPMS architectures and often applying classification systems (e.g., stretching- or bending-dominated behavior) developed for slender beam-based lattices. However, TPMS structures are far frombeing slender beams, and the validity of such classifications has not been rigorously confirmed for their case. This study bridges these gaps by analyzing 36 distinct TPMS lattice architectures, covering both elastic and plastic regimes. We critically assess theapplicability of Gibson-Ashby scaling laws, the rigidity classification, and the stretching-bending paradigm to TPMS structures-none of which have been rigorously validated for TPMS lattices. Using experiments and numerical simulations, we investigate the strength and stiffness scaling in TPMS lattices, identifying rigid, compliant, and mixed architectures. Our findings show that TPMS rigidity depends on the alignment of surface members with load directions and the presence of solid regions that prevent rotation. We reveal that top-performing geometries include so far unexplored TPMS such as P + CP (-), K (+), and Ss-Yssxxx (+), further expanding the design space, challenging prior assumptions and providing critical insights for selecting the optimal TPMS-based architecture for specific applications.