Mechanics-guided optimization of hybrid periodic architectures

Lightweight architected materials require systematic design strategies to maximize stiffness-to-weight efficiency under realistic finite-domain loading conditions. However, optimization of hybrid triply periodic surface architectures remains challenging due to implicit geometric representations, high-dimensional parameter spaces, and the computational cost of mechanical evaluation. This study presents a mechanics-guided optimization framework for hybrid triply periodic surface architectures. An 18-dimensional coefficient representation based on linearly independent periodic basis functions enables continuous hybridization across canonical surface families within a unified design space. Candidate geometries are evaluated as finite 2×2×2 multi-cell specimens using voxel-based finite element analysis under uniaxial compression. Exploration of the high-dimensional space is performed using a Gaussian process surrogate with expected improvement, combined with connectivity screening to ensure structural feasibility. The surrogate-assisted Bayesian optimization achieves an effective modulus of E eff = 216 , 536 MPa, outperforming random search (10 seeds, equal budget) by 31.0%. The optimized hybrid design also exhibits approximately 112–114% higher effective stiffness than representative gyroid and Schwarz P structures evaluated under identical conditions. Gibson–Ashby scaling gives an exponent of n = 1.082 ± 0.015 ( R 2 = 0.999 ) , compared with n = 2.2 –3.4 for canonical TPMS surfaces, supporting a transition toward stretching-dominated load transfer. The improvement is associated with material reorganization into vertically continuous load paths that enhance axial force transmission and reduce bending-driven compliance. The proposed framework provides a computationally efficient and mechanically interpretable approach for high-dimensional design of periodic surface architectures under finite-domain constraints.