A design method for hierarchical bionic venation Voronoi structures with integrated load bearing and sound absorption

Hierarchical venation in plant leaves and insect wings provides an efficient biological model for integrating load-bearing and auxiliary functions. Inspired by the hierarchical features of biological venation, this study proposes a design method for hierarchical bionic venation Voronoi (HBVV) structures with integrated load bearing and sound absorption. The primary-level skeleton is generated through layout optimization of principal stress line components to carry the main mechanical loads. The secondary structure consists of stress field-driven deformed Voronoi units, which provides auxiliary stiffness while forming parallel Helmholtz resonators for acoustic absorption. To tailor the absorption band, a fixed-point iteration based multi-network strategy is developed to coordinate single parameter neural networks for inverse design of resonator parameters. Numerical comparisons, supported by mechanical and acoustic experiments, show that the stiffness of the designed structures achieves improvements of 132.91%, 140.63%, 56.08%, and 18.10% relative to the conventional non‑hierarchical structures of angle grid, honeycomb, uniform Voronoi, and deformed Voronoi, respectively. The designed secondary-level structure achieves a 19.25% stiffness enhancement against the honeycomb secondary-level structures. Efficient and accurate multi‑parameter inverse design is implemented on 122 acoustic parameters consisting of the aperture radius and aperture depth of Helmholtz resonators, with the deviations of effective sound absorption bands limited to only 2 Hz-6 Hz in all discussed cases. These results demonstrate that the proposed HBVV framework provides an effective route for designing multifunctional porous structures with coupled load-bearing and sound-absorbing requirements.