Mode-enriched dispersion models of periodic materials within a multiscale mixed finite element framework

A group of methods is presented for the high frequency dispersive modeling of elastic wave propagation in periodic media. The methods fall within the framework of the multiscale assumed strain projection methodology. In previous work, the solution field was projected onto a subspace spanned by a set of high-order characteristic functions generated by a hierarchical homogenization analysis scheme. In the present study, the projection space is replaced, or alternatively enhanced, with periodic eigenvectors obtained from direct solution of the eigenvalue problem governing the dispersion relation. In a novel manner, these Floquet–Bloch eigenvectors are selected in both the spatial and temporal frequency domains. The new mode enrichment techniques are shown to provide excellent accuracy for dispersion curves calculations across wide frequency ranges. Substantial savings in computational costs are documented for large problems compared to the direct solution approach.