Evaluation of phenomenological model parameters using density dependent laws for prediction of mechanical response of cellular materials

Cellular materials have found wide-spread attention in structural applications involving impact energy absorption. The choice of the most suitable density of a cellular material, for a particular impact application, is based on its mechanical response, which may be obtained through experimental tests and/or models. A current study is focused on prediction of a mechanical response of a wide range of densities of a cellular material using available experimental data of very few densities. Best fitting-parameters of four selected phenomenological models, to fit the available experimental response of three distinct aluminum foam densities, are evaluated. The relationship between the best-fitting parameters and density of the foam is established by using two types of functions. The first function is based on a power law relationship between each parameter and foam density ρ, while the second function assumes each parameter as a linear combination of ρn and ρ, where n is any real number. The former function is found reasonable in the cases of both parameter interpolation and extrapolation while the latter is found reasonable for a parameter interpolation only. The findings of a current study emphasize for a conscious approach during selection of density dependent laws for phenomenological model parameters to avoid any erroneous or misleading design decision.