Prediction of cushion curves of polymer foams using a nonlinear distributed parameter model

Abstract

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.