Abstract
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.
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