Topological hybridization of constant-mean-curvature metamaterials for ultimate structural efficiency

Architected materials gain stiffness from beams, plates or minimal-surface shells, yet beam lattices lose efficiency to bending and nodal stress concentration and closed-cell lattices are difficult to manufacture and to clear of powder or resin. Open-cell minimal-surface shells print readily, but their zero mean curvature suppresses the stretching needed for hydrostatic load transfer. We make mean curvature the central design parameter and offset the limits of any single cubic constant-mean-curvature family by hybridization. Here we introduce an open-cell hybrid shell metamaterial combining four such families with differing wall spans and non-redundant load paths, Schwarz Primitive (SP), Schwarz Diamond (SD), Schoen I-graph wrapped polyhedron (IWP) and Schoen F-graph rhombic dodecahedron (FRD), whose non-zero curvature carries load by stretching rather than bending. A Bayesian surrogate search over 116 high-fidelity simulations identifies the optimal hybrid. At volume fraction 0.45 it reaches 97.3% of the isotropic Hashin-Shtrikman bulk-modulus reference for a porous solid, staying within 7% across 0.25 ≤ v ≤ 0.55 with only weak cubic anisotropy. Carbon-fiber-reinforced nylon specimens printed by desktop fused-deposition modeling reproduce the ranking and recover 82-89% of the corresponding specimen-scale predictions, with stiffness 28.8-35.5 GPa and peak compressive stress 205-231 MPa across printing and in-plane directions, 40% and 48% above the strongest single-family baseline in the printing direction. Static finite-element integration into a virtual-reality headset and smartwatch case indicates 45% and 63.5% mass reductions at matched stiffness or strength. Curvature-guided hybridization thus offers a manufacturable route to open-cell shell metamaterials approaching a declared isotropic Hashin-Shtrikman hydrostatic reference.