Curvature distribution modulates stiffness in hybrid TPMS-spinodal shell metamaterials

Shell-based architected materials can achieve exceptional specific stiffness by combining smooth curvature with stretch-dominated load paths, yet simple design rules that link curvature distribution, topological disorder, and elastic properties are still lacking. We investigate a controlled family of hybrid shell architectures that continuously interpolates between periodic triply periodic minimal surface (TPMS) shells (Gyroid, Schwarz P, Schwarz D) and aperiodic spinodal shells. Each architecture is represented as the zero level set of a scalar field defined on a periodic domain, and hybridization is performed directly in Fourier space, enabling a clean separation between wavelength content and topology. A spectral-entropy metric is introduced to quantify the degree of Fourier-space disorder, while the midsurface geometry is characterized through principal (κ1,κ2), mean (Μ) and Gaussian curvature (Κ) statistics. Small-strain finite-element homogenization of Reissner-Mindlin shell models is then used to compute bulk, shear and directional Young’s moduli for ensembles of realizations along the interpolation parameter α. Across all topologies and seeds we find that the effective bulk and Young’s moduli collapse when plotted against a single geometric quantity: the area fraction of the midsurface with negative Gaussian curvature. As hybridization progresses, this fraction decreases from almost unity in the TPMS limit to 0.85 in the spinodal limit, and all normalized moduli follow the same trend. Displacement‑controlled hydrostatic loading simulations further show that saddle-like regions (Κ<0) systematically carry higher von Mises stresses than positively curved caps, identifying negative Gaussian curvature as the primary load-bearing “resource’’ of these shell networks. The area fraction of K<0 thus emerges as a simple, topology-independent predictor of stiffness in hybrid shell metamaterials and provides a curvature-based guideline for the structural design of shell lattices.