Mechanical models of cellular solids: Parameters identification from experimental tests

Cellular materials have large use in many components acting as impact energy absorbers. These components have to be designed on the basis of the kind of impact, of the involved energy amount and of the maximum admissible load. The choice of the most suitable density for the selected type of foam is based on stress-strain behaviour, obtained by means of experimental tests and/or models. Only a few micro-mechanical models, as the Gibson model, take into account the density effects. These models could result quite complex to manage because of the need of, at least, a rough analysis of the actual foam structure. Conversely, most of the models used for numerical simulations are phenomenological models and have simple parameter identification based on fitting of experimental data, but they do not account for density effect. Experimental uniaxial compression tests performed for several types of foams, namely EPP, PUR (Bayfill EA), EPS and PPO/PS (Noryl GTX), at different density levels are used in order to identify, with an optimisation procedure devoted to the minimisation of the fitting residual evaluated by the least square method, the parameters of four cellular solid models. The considered models are four: the Gibson model [Gibson LJ, Ashby MF. Cellular solids. Structure and properties. Cambridge: Cambridge University Press; 1997], the Rusch model [Rusch KC. Load-compression behavior of flexible foams. J Appl Polym Sci 1969;13:2297-311; Rusch KC. Energy-absorbing characteristics of foamed polymers. J Appl Polym Sci 1969;14:1133-47; Rusch KC. Load-compression behavior of brittle foams. J Appl Polym Sci 1970;14:1263-73], a modified version of the Gibson model and a new empirical model. The third and fourth models have been developed in order to better fit the experimental stress-strain curve. The obtained improvements in terms of weighted sum of the squared errors are shown. The experimental data are a good representation of the typical behaviour of these kinds of foams and can be useful for the validation of models and the comparison of their performance. Moreover the large basis of experimental data for different types of foams at different densities could be used for the analysis of the influence of the density on the model parameters. Explicit empirical formulations are proposed to express the dependency of the phenomenological model parameters on the foam density. These relationships permit the identification of whatever density foam derived from the same solid material and with the same micro-structure by means of a minimum set of experimental tests. At the same time the availability of a large quantity of experimental data is helpful to reach a higher level of confidence in the model parameter values. Finally the identified parameters vs. density laws for the considered types of foam could be used in order to assist the design of a given absorber and to find the optimum density for the specific application. Closed form expression for the specific energy W and the efficiency E can be obtained, based on the resulting identified phenomenological models. © 2006 Elsevier Ltd. All rights reserved.