Trans-scale dynamic shear-lag model for wave attenuation in staggered composites

In this study, we develop the trans-scale dynamic shear-lag model based on the strain gradient theory to investigate the wave propagation in staggered composites with architectures down to micro- and nano-scale. The model yields an analytical expression of the wave attenuation factor for nacre-like staggered composites with building blocks at the submicron scale for the first time. We show that when the matrix thickness reduces, the size effect on the wave attenuation performance becomes significant - the first bandgap of the composites shifts to higher frequencies, and the materials lose the efficiency to filter lower-frequency waves. Furthermore, parametric studies demonstrate that the first bandgap width and location are influenced greatly by many factors, such as the length scale parameter, the tablet volume fraction, and the overlap length. Particularly, the first bandgap width varies non-monotonically with the above parameters. Our study sheds light on the understanding of the wave attenuation mechanisms of biological and bio-inspired composites with microscopic architectures when the size effect is non-negligible. The findings here provide valuable guidance for designing advanced composites with sophisticated micro- and nano-structures to achieve exceptional dynamic properties.