Spectral variational multiscale enrichment method—A new computational approach to transient dynamics of phononic crystals and acoustic metamaterials

Abstract

Phononic crystals and acoustic metamaterials hold tremendous potential in controlling mechanical and acoustic waves, thereby enabling remarkable and novel engineering applications such as seismic wave mitigation, impact wave mitigation, elastic cloaking, and acoustic superlens. Given the potential complexity associated with the microstructure of these materials, direct numerical simulation of irregularly shaped and/or large engineering components could be computationally very costly and in many cases prohibitive. Multiscale computational modeling, coupled with model order reduction methodologies present a feasible strategy to simulate the dynamic response of phononic crystals and acoustic metamaterials. In this study, we present the spectral variational multiscale enrichment approach that allows the analysis of a broad range of material microstructures for phononic crystals and acoustic metamaterials. The 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 order reduction strategy is devised at the fine-scale. By using the reduced basis for the fine-scale problem, significant numerical efficiency is achieved. Transient elastic wave propagation in two-dimensional phononic crystals and acoustic metamaterials are investigated and the proposed multiscale approach is verified against direct numerical simulations.