Compression Response of Composite Cushioning Materials in Series by Virtual Parameter Methods

With the assumption that the constitutive relationship of every single cushioning layer is known in advance, this paper presents virtual parameter methods for predicting compressive responses of composite cushioning materials in series (i.e. multi‐layered cushioning materials). In the proposed methods, a derivative term is introduced to transform nonlinear algebraic equations for characterizing compressive behaviours of the composite cushioning materials into explicit differential equations under quasi‐static loadings. Introducing a first or second order derivate term is equivalent to introducing a virtual damping or virtual mass to the cushioning system. It is found that the solutions with the virtual parameter methods will diverge if the order of the introduced derivative term is higher than two, and the virtual parameter (i.e. the coefficient of the introduced derivative) must be larger than zero if first or second order derivative is used. The analytical results indicate that the terms associated with the virtual parameter in the predicted responses are a monotonically decreasing function of the virtual parameter if the latter is nonnegative. To trade off between prediction precision and computation convergence speed, an analytical process is developed for estimating the range of the virtual parameter. Then a scheme for jointly predicting the compressive response and optimizing the virtual parameter is proposed. For comparison, both simulations and quasi‐static compressive tests have been carried out on layered foam and corrugated paperboard structures, which correspond to materials without and with negative stiffness zone in the stress–strain curves, respectively. The results show that the predicted responses obtained using the proposed method match the experimental data very well. Moreover, unlike the Newton–Raphson iteration method, the proposed methods are able to capture the progressive buckling phenomenon for multi‐layered corrugated paperboard subjected to quasi‐static loading condition. Copyright © 2015 John Wiley & Sons, Ltd.