Cushioning Performance of Hilbert Fractal Sandwich Packaging Structures under Quasi-Static Compressions

The sandwich structure of cushioning packaging has an important influence on the cushioning performance. Mathematical fractal theory is an important graphic expression. Based on Hilbert fractal theory, a new sandwich structure was designed. The generation mechanism and recurrence formula of the Hilbert fractal were expressed by Lin's language, and the second-order Hilbert sandwich structure was constructed from thermoplastic polyurethane. The constitutive model of the hyperelastic body was established by using the finite element method. With the unit mass energy absorption as the optimization goal, the fractal sandwich structure was optimized, and the best result was obtained when the order was 2.5 and the unit layer thickness was 0.75 mm. The Hilbert sandwich structure was compared with the rice-shaped sandwich structure commonly used in industry, and the Hilbert fractal structure had better energy absorption. This has practical significance for the development and application of new cushioning packaging structures.