Study On Cushioning Performance Of Tree-like Fractal Structure

Based on the growth law of trees in nature,tree-like structures have the ability to carry large loads with relatively small weight due to their self-similarity.Combining bionics and fractal theory,this paper presents a bionic fractal sandwich structure of tree-like with high energy absorption value is proposed in the field of packaging.In this study,a bionic fractal sandwich structure was designed and a 3D model is established.The 1^st-order tree-like bionic fractal structure experimental sample is prepared by using polyurethane elastomer material for vacuum injection.The quasi-static compression test and dynamic impact test are completed.The finite element model is established by Ansys Workbench and simulation analysis is carried out to verify the reliability of the model.Through finite element simulation,the effects of three structural parameters of different order（n）,branch thickness（t）and panel thickness（T）on its static cushioning performance are analyzed,and the size optimization of bionic fractal structure of tree-like is completed.The influence of different order（n）of simulation on its dynamic cushioning performance is analyzed,and the dynamic simulation cushioning performance of the optimized fractal structure is studied.Finally,the cushioning performance of 1^st-order tree-like bionic fractal sandwich structure,hollow sandwich structure and triangular sandwich structure under static compression and dynamic impact tests is analyzed and compared.The model verification of static compression and dynamic impact is carried out for the1^st-order fractal structure.The experimental results are consistent with the finite element results,which meets the reliability requirements of numerical simulation.Under the same mass condition,the energy absorption performance of 2^nd-order fractal structure is better.In static compression,the specific energy absorption（SEA）of 2^nd-order fractal structure is increased by 105.67%and 53.01%compared with that of 0^th-order fractal structure and1^st-order fractal structure.The average crushing force（F_S）increased by 105.67%and53.02%compared with that of 0^th-order fractal structure and 1^st-order fractal structure.In the dynamic analysis,when the mass of the rigid impact plate is 4.1kg,the SEA of the2^nd-order fractal structure is increased by 21.21%and 5.03%compared with that of0^th-order fractal structure and 1^st-order fractal structure.F_Sis increased by 32.62%and16.58%compared with that of 0^th-order fractal structure and 1^st-order fractal structure.Through the optimization of the 2^nd-order fractal structure,it is concluded that when T_nis1.45mm,T₀is 3.47mm,T₁is 2.22mm and T₂is 1.20mm,the SEA is the largest in static analysis,which is about 27.71%higher than the original structure size.In dynamic analysis,the size of SEA and F_Sincreased 56.77%and 65.31%respectively compared with that of the original structure.In addition,SEA of 1^st-order fractal sandwich panel is 509.78m J/g in static compression test,which is about 351 m J/g higher than hollow sandwich panel and445 m J/g higher than triangle sandwich panel,respectively.During the dynamic impact test,the opening radian of the maximum acceleration-static stress curve of the 1^st-order fractal sandwich plate is the largest,and the impact mass it can withstand is the largest.The lowest point of the maximum acceleration is about 130g.Therefore,this structure is more advantageous for cushioning products with large static stress values.