To address the lack of a quantitative method for determining the bottoming boundary of the maximum acceleration-static stress curve in cushioning packaging design, the work aims to propose a successive approximation method for accurately determining the bottoming critical point, and establish a high-precision prediction model to provide a theoretical basis for refined cushioning packaging design. Expanded polyethylene with a density of 25 kg/m3 was selected as the research object, and drop impact tests were conducted via ANSYS LS-DYNA finite element simulations. Tests were carried out on nine groups of specimens with thicknesses ranging from 0.02 to 0.06 m. A successive approximation method based on iterative contraction of the static stress interval was proposed, with the convergence criterion defined as the relative error of the maximum acceleration between two consecutive non-bottoming tests prior to bottoming being less than 0.5%, to accurately determine the bottoming critical point. Data from five thicknesses (0.06, 0.05, 0.04, 0.03, 0.02 m) were selected as the training set. A fully interactive cubic polynomial model was then constructed, with drop height and material thickness as the independent variables and the critical maximum acceleration as the dependent variable. Data from four thicknesses (0.055, 0.045, 0.035, 0.025 m) were used as the test set to validate the model accuracy. The critical maximum acceleration decreased nonlinearly with the increasing thickness and increased with the increasing drop height. The coefficient of determination for the fitting accuracy of the model is 0.9948, and the coefficient for the prediction accuracy of the test set was 0.991 4 with a mean absolute percentage error of 3.99%, indicating that the model had outstanding fitting performance. The proposed successive approximation method enables accurate determination of the bottoming critical point, and the established model effectively characterizes its variation law of the critical point, providing a reliable basis for refined cushioning packaging design. However, this work is limited to a single density of EPE material and employs the ANSYS LS-DYNA finite element simulation method, and future research should conduct comparative studies on different materials and different working conditions to further verify the generalizability of the model.
Key words
cushioning packaging /
maximum acceleration-static stress curve /
bottoming critical point /
successive approximation method /
expanded polyethylene /
multivariate nonlinear regression
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
References
[1] 金强维, 孙德强, 李国志, 等. 密度对聚丙烯泡沫材料动态冲击性能的影响[J]. 包装工程, 2018, 39(23): 88-92.
JIN Q W, SUN D Q, LI G Z, et al.Influence of Density Upon Dynamic Crushing Behaviour of Polypropylene Materials[J]. Packaging Engineering, 2018, 39(23): 88-92.
[2] 余天丹, 李志强, 袁亮, 等. EPE的缓冲性能试验研究及缓冲包装设计[J]. 轻工科技, 2021, 37(2): 94-96.
YU T D, LI Z Q, YUAN L, et al.Experimental Study on Cushioning Performance and Cushioning Packaging Design of EPE[J]. Light Industry Science and Technology, 2021, 37(2): 94-96.
[3] 邢紫玉. 聚丙烯夹芯板缓冲性能研究[D]. 天津: 天津科技大学, 2020: 54-55.
XING Z Y.Research on Cushioning Properties of Polypropylene Sandwich Board[D]. Tianjin: Tianjin University of Science & Technology, 2020: 54-55.
[4] 尹兴, 陈志强, 崔久刚, 等. 快递包装EPE/瓦楞纸板动态缓冲性能[J]. 包装工程, 2022, 43(1): 52-57.
YIN X, CHEN Z Q, CUI J G, et al.Dynamic Buffering Performance of EPE/Corrugated Board Used in Express Packaging[J]. Packaging Engineering, 2022, 43(1): 52-57.
[5] 陈家璇, 周卫中, 张美, 等. 高弹EPE泡沫两自由度连续冲击包装动力学响应研究[J]. 包装工程, 2024, 45(19): 318-324.
CHEN J X, ZHOU W Z, ZHANG M, et al.Dynamic Response of Two-Degree-of-Freedom Continuous Impact Packaging for High Elasticity EPE Foam[J]. Packaging Engineering, 2024, 45(19): 318-324.
[6] 许聪怡. 变密度Gyroid结构力学性能研究及其缓冲包装应用[D]. 无锡: 江南大学, 2025: 63-64.
XU C Y.Research on the Mechanical Property of Gyroid Structure and Its Application in Cushioning Packaging[D]. Wuxi: Jiangnan University, 2025: 63-64.
[7] TOMIN M, LENGYEL M Á, PÁRIZS R D, et al. Measuring and Mathematical Modeling of Cushion Curves for Polymeric Foams[J]. Polymer Testing, 2023, 117: 107837.
[8] CASTIGLIONI A, CASTELLANI L, CUDER G, et al.Relevant Materials Parameters in Cushioning for EPS Foams[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2017, 534: 71-77.
[9] BURGESS G.Consolidation of Cushion Curves[J]. Packaging Technology and Science, 1990, 3(4): 189-194.
[10] 李光, 要志雯. 基于能量密度确定缓冲材料性能曲线的研究[J]. 包装工程, 2020, 41(23): 103-108.
LI G, YAO Z W.Determining Performance Curves of Cushioning Material Based on Energy Density[J]. Packaging Engineering, 2020, 41(23): 103-108.
[11] 宋卫生, 薛阳. 发泡聚乙烯最大加速度-静应力曲线快速获取方法研究[J]. 包装工程, 2024, 45(5): 309-314.
SONG W S, XUE Y.Rapid Acquisition Method of Maximum Acceleration-Static Stress Curve for Foamed Polyethylene[J]. Packaging Engineering, 2024, 45(5): 309-314.
[12] 王思宇, 孙德强, 赵文, 等. 由材料的一条已知缓冲曲线构建其任一缓冲曲线[J]. 包装工程, 2025, 46(21): 271-278.
WANG S Y, SUN D Q, ZHAO W, et al.Construction of any Cushion Curve of a Material from a Single Known Instance[J]. Packaging Engineering, 2025, 46(21): 271-278.
[13] 李志强, 牛文倩, 马淑芳. 基于发泡聚苯乙烯的缓冲曲线快速获取方法研究[J]. 包装工程, 2025, 46(5): 228-234.
LI Z Q, NIU W Q, MA S F.Method for Fast Acquiring of Buffer Curve Based on Expanded Polystyrene[J]. Packaging Engineering, 2025, 46(5): 228-234.
[14] 滑广军, 金澳威, 刘奇龙, 等. 缓冲包装信息融合设计方法及应用[J]. 包装工程, 2025, 46(5): 216-220.
HUA G J, JIN A W, LIU Q L, et al.Design Method and Application of Cushioning Packaging Based on Information Fusion[J]. Packaging Engineering, 2025, 46(5): 216-220.
[15] 周卫中, 周笃波, 周文德, 等. 连续冲击载荷下EPS缓冲系统的动力学行为分析[J]. 包装工程, 2025, 46(19): 41-47.
ZHOU W Z, ZHOU D B, ZHOU W D, et al.Dynamic Response Prediction of Expanded Polystyrene under Successive Impact Conditions[J]. Packaging Engineering, 2025, 46(19): 41-47.
[16] PIATKOWSKI T, OSOWSKI P.Modified Method for Dynamic Stress-Strain Curve Determination of Closed-Cell Foams[J]. Packaging Technology and Science, 2016, 29(6): 337-349.
PDF(728 KB)
