A composite package cushioning system consists of multiple layers of cushioning materials in series. Such composite cushioning systems will enhance the protection capability to the packaged products. However, the dynamic analysis of the composite cushioning system becomes more difficult because of the strong nonlinear characteristics of cushioning materials. To overcome the difficulty in calculation, the method of virtual mass is proposed to form the system equations of motion as a set of multidimensional ordinary differential equations so that the Runge-Kutta method can be applied to obtain the numerical solution of the system response. The rationale of the method is shown both analytically and numerically by assessing the reliability of the virtual mass method. For a specific composite cushioning system consisting of two layers of expanded polystyrene (EPS) and expanded polyethylene (EPE) materials, experiments were carried out first for each material to obtain the stress-strain behaviours under both static and dynamic loadings. On the basis of these data, the stress-strain constitutive models were developed for EPS and EPE. Then, experiments were conducted for the composite cushioning system under different system parameters, and the measured data are compared with the analytical results using the method of virtual mass. The agreement between the analytical and the experimental results substantiates the accuracy of the proposed virtual mass method. Copyright © 2012 John Wiley & Sons, Ltd. One of the important functions of transport package is to shield products from damage using cushion elements. To measure the product fragility and determine protection capability of the package, the method of damage boundary curve, proposed originally by Newton 1 for linear packaging systems, has been applied to various nonlinear packaging systems. Because the cushioning materials exhibit stronger and complex nonlinear mechanical characteristics, simplified mathematical models were proposed for the nonlinearity in order to predict damage boundary curves of packaging systems. Wang 2 obtained displacement damage boundary curves for a bilinear packaging system. Hyperbolic tangent type of nonlinear packaging systems were considered 3,4 for investigating the drop damage boundary curve. On the basis of the rotation effect occurring in asymmetric packaging systems, Gao 5,6 studied shock response of nonlinear tangent packaging system from the damage boundary curve point of view.In addition to theoretical analyses, experiments have been conducted to investigate the dynamic performance of typical cushioning materials. Polymeric foam or structural cushioning materials have

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Fig. 1 (a) A schematic diagram of noncoplanar mesh design with islands chemicaily bonded to the compliant substrate and the interconnects ioosely bonded; (b) SHM image of noncoplanar mesh design under shearJournal of Applied Mechanics