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On asymptotic elastodynamic homogenization approaches for periodic media

Abstract : A fairly large family of asymptotic elastodynamic homogenization methods is shown to be derivable from Willis exact elastodynamic homogenization theory for periodic media under appropriate approximation assumptions about, for example, frequencies, wavelengths and phase contrast. In light of this result, two long-wavelength and lowfrequency asymptotic elastodynamic approaches are carefully analyzed and compared in connection with higher-order strain-gradient media. In particular, these approaches are proved to be unable to capture, at least in the one-dimensional setting, the optical branches of the dispersion curve. As an example, a two-phase string is thoroughly studied so as to illustrate the main results of the present work.
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Hussein Nassar, Qi-Chang He, Nicolas Auffray. On asymptotic elastodynamic homogenization approaches for periodic media. Journal of the Mechanics and Physics of Solids, Elsevier, 2016, 88, pp.274-290. ⟨hal-01249157⟩

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