Spectral variational multiscale model for transient dynamics of phononic crystals and acoustic metamaterials

Abstract

In this manuscript, a spectral multiscale model is developed for transient elastic wave propagation in periodic composites. The basis of the multiscale approach is the variational multiscale enrichment method that permits analysis of wave propagation in the scale-inseparable condition, i.e., short wave propagation. A spectral coarse-scale representation is proposed to capture the salient transient wave phenomena, such as wave dispersion and band gaps that occur in the short wavelength regime. A material-phase-based model basis reduction strategy is devised at the fine scale to achieve computational efficiency. An important feature of the proposed method is that it does not rely on the classical assumption of separation of scales, which permits its application to a broad range of architectured composites including phononic crystals and acoustic metamaterials. Transient elastic wave propagation in two-dimensional periodic structures is investigated. The proposed multiscale approach is verified against direct numerical simulations. The accuracy and computational efficiency of the approach are demonstrated for both phononic crystals and acoustic metamaterials.