Computational design of 3D printed flexible Voronoi lattices

Abstract This study introduces a novel computational framework for designing and analyzing highly flexible, stochastic lattice structures using 3D Voronoi tessellations. This design replicates the stochastic cellular morphology of porous foams while allowing precise control over structural parameters, which offers great versatility for engineering applications such as lightweight construction, energy dissipation, and acoustic insulation. A computational design methodology is developed, including additive manufacturing, mechanical testing, and numerical modeling. First, the mechanical behavior of 3D-printed materials is examined under cyclic tension using a visco-hyperelastic constitutive model, which is then integrated into nonlinear finite element simulations incorporating large deformations and contact interactions. Numerical simulations are validated against experimental compression tests under cyclic loading, showing strong agreement, particularly for relative densities ranging from 6 to 18%. Strain responses at 20% and 60% compression were analyzed at 2 to 50 mm/min deformation rates. Furthermore, the stress distribution exhibited heterogeneity during initial buckling and the plateau phase due to randomly oriented struts. However, as the load increased and strain reached 0.6, stress distribution became more uniform, marking the onset of densification, and suggesting that stochastic lattices may offer mechanical advantages such as smoother energy absorption compared to regular cellular structures. By bridging computational modeling with experimental validation, this work enhances the understanding of highly deformable lattice structures, enabling optimized engineering designs. Graphical abstract