Mechanical analyses of Félix Candela’s N-edged hyperbolic paraboloid umbrellas as tubular structures under uniaxial compression

This research investigates the nonlinear mechanical properties and post-yield deformation mechanisms of hyperbolic paraboloid (hypar) shells inspired by the architecture of Félix Candela for the first time. 3D-printed tubular structures derived from non-Euclidean hypar umbrellas with 3, 4, and 6 edges (capable of forming regular tessellations) across three rise-to-area ratios were benchmarked against Euclidean thin-walled prismatic and pyramidal geometries under uniaxial quasi-static compression. For the same relative density, hypar structures exhibited markedly improved stiffness, strength, and energy absorption over their Euclidean counterparts. 6-edged hexagonal umbrellas were also observed to be more efficient than 3- and 4-edged hypars for a constant shell thickness, with their mechanical performance being positively correlated with the extent of hypar warping. Moreover, the relative stiffness and strength exhibited by tubular structures based on hexagonal hypar umbrellas compared favorably with alternative lattice and honeycomb metamaterials across the relative densities considered within this study. These findings highlight the attractiveness of hypars as novel (micro)architectures and provides further impetus towards the utilization of non-Euclidean geometries for ultra-light and ultra-stiff applications.