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

Abstract

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 theHilbert fractal were expressed by Lin's language, and the second-orderHilbert sandwich structure was constructed fromthermoplastic 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. TheHilbert 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 newcushioning packaging structures.