A simple model of effective elastic properties of materials with inclusions
نویسندگان
چکیده
The aim of this study is to develop a simple phenomenological model for the elastic moduli of a composite material formed by localized inclusions embedded in an elastic matrix. It is assumed that the material can be characterised by only two aggregated parameters, viz., volume fraction of inclusions and their resonance frequency within the elastic matrix. The values of these two parameters are assumed to be given (i.e. from experimental measurements) or deduced from other models (also presented in the paper). The shear wave velocity in the elastic matrix is assumed to be much smaller than the velocity of longitudinal waves. A simple analytical expression for the effective longitudinal wave velocity that is uniformly valid for the entire frequency domain is derived (including proximity to the resonance frequency of inclusions) and validated with some paradigmatic results of the mean-field theories.
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