Polymer foams are commonly used in the protective packaging of fragile products. Cushion curves are commonly used within the packaging industry to characterize a foam's impact performance. These curves are two‐dimensional representations of the deceleration of an impacting mass versus static stress. Cushion curves are currently generated from exhaustive experimental test data. This study represents the first time that the physics of the mass‐cushion impact have been analysed by modelling the foam as nonlinear, continuous rod. Using a single mode of vibration and excluding the effects of damping, the maximum displacement during the impact can be obtained from a polynomial describing the maximum elastic energy in the foam. The displacements can be used to recover the amplitude of the deceleration shock pulse. Numerical and analytical analysis of the model with damping is considered in its ability to predict the shock pulse shape, duration, and amplitude at various static stresses, foam thickness, and drop heights as compared with experimental data. Furthermore, both the analytical and numerical results agree and are primarily within the expected lab‐to‐lab variability of 18% documented in ASTM D1596 ‐ Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material.

中文翻译：

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使用非线性分布参数模型预测聚合物泡沫的缓冲曲线

聚合物泡沫通常用于易碎产品的保护性包装。缓冲曲线通常用于包装行业，以表征泡沫的冲击性能。这些曲线是冲击质量与静态应力的减速度的二维表示。缓冲曲线目前是根据详尽的实验测试数据生成的。这项研究代表了首次通过将泡沫建模为非线性连续棒来分析质量缓冲撞击的物理原理。使用单一模式的振动并排除阻尼的影响，可以从描述泡沫中最大弹性能的多项式获得冲击过程中的最大位移。位移可用于恢复减速冲击脉冲的幅度。与实验数据相比，考虑了具有阻尼的模型的数值和分析分析，可以预测各种静态应力，泡沫厚度和下落高度下的冲击脉冲形状，持续时间和振幅。此外，分析结果和数值结果均一致，并且主要在ASTM D1596 －包装材料动态冲击缓冲特性的标准测试方法中记录的18％的预期实验室间差异内。