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

Xingye Xu1, Haiyan Song1,2,*, Lijun Wang1,2

1 College of Light Industry Science and Engineering, Tianjin University of Science & Technology, Tianjin, 300457, China
2 Key Laboratory of Food Packaging Materials and Technology of China Light Industry, Tianjin, 300457, China

* Corresponding Author: Haiyan Song. Email: email

(This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)

Computer Modeling in Engineering & Sciences 2023, 135(1), 275-292.


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.


Cite This Article

Xu, X., Song, H., Wang, L. (2023). Cushioning Performance of Hilbert Fractal Sandwich Packaging Structures under Quasi-Static Compressions. CMES-Computer Modeling in Engineering & Sciences, 135(1), 275–292.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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