Multi-objective crashworthiness optimization for a newly developed 3D re-entrant auxetic structure using response surface method and MOPSO algorithm

With the quick advancement of the vehicle industry, attention to automobile safety has increased. Crash boxes, which are placed in front of the side rails, play an essential role in preventing much damage to the front part of the car and also protecting passengers. Improving and optimizing these crash boxes’ energy absorption properties is necessary. In this study, a new structure of three-dimensional re-entrant auxetic has been presented for use as a crash box. Quasi-static uniaxial loading has been investigated experimentally and numerically. With the validation of the numerical simulation, the response surface method was implemented to investigate the value and type of different parameters’ effect on peak load and specific absorbed energy. Variables of the base and re-entrant strut thicknesses ( t1) and ( t2), the length of the base to re-entrant strut ( L/H), and the re-entrant angle ( θ) were considered in three levels. Through ANOVA analysis in Design-Expert software, it was found that the parameters t2 and θ had the highest effect on the peak load, energy absorption, specific energy absorption, and mean crashing force responses. With the increasing of t2 and θ, all responses increase and decrease, respectively. Also, multi-objective optimization based on minimum peak load and maximum specific energy absorption was performed by the desirability function method in Design-Expert software and the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm. The proposed optimized structure exhibits enhanced energy absorption when compared to the optimized cylindrical auxetic structure and the thin-walled circular structure within the peak load range below 80 kN. Therefore, the proposed structure due to low peak load, uniformity collapse in the force-displacement diagrams, and stability of the structure during compression loading, can be used as the crash box.