Composite curved hourglass cellular structures: Design optimization for stiffness response and crashworthiness performance

Auxetic lattice structures are known for their superior stiffness-to-density and strength-to-density ratios. Re-entrant hourglass exhibits an acceptable equivalent elastic modulus and remarkable energy absorption capacity among various auxetic configurations due to their flexibility and hinge deflecting during crushing loads. This study introduces a curved hourglass honeycomb which can be produced using 3D printing with pure or reinforced filaments incorporating continuous fibers. New closed-form formulations are analytically derived using an energy method by considering an extracted unit cell to predict the equivalent in-plane mechanical properties for the first time. The plateau stress of the proposed honeycomb is evaluated at the densification state of a unit cell using the energy conservation theory, equating external work with plastic energy dissipation. The accuracy of these extended relations is validated against experimental outcomes, demonstrating good agreement between analytical and experimental results. Additionally, robust linear and nonlinear finite element analyses are conducted to assess the accuracy of the obtained relations, including the equivalent stiffness and plateau stress for structures produced with reinforced filaments. The nonlinear finite element code employs appropriate subroutines to model plasticity/damage events. Based on the established analytical relations for stiffness and plateau stress, multi-objective optimization using Genetic Algorithm is applied to define optimum values for the Pareto front chart's objective functions of stiffness and plateau stress. The optimization process involves exploring the design space and defining the values of geometrical parameters to achieve the desired objectives. In conclusion, this study presents a novel approach to developing curved re-entrant honeycomb structures, with analytical formulations validated against experimental and numerical results. Optimization helps to identify optimal configurations concerning stiffness and plateau stress, offering potential applications in lightweight and high-strength materials design. According to the obtained results, for selection of the best value for curved strut angle which results in the optimum value of stiffness and plateau stress, a range between 10°-34° can be considered depending on the volume fraction of fibers.