Acoustic properties of porous microlattices from effective medium to scattering dominated regimes

Microlattices are architected materials that allow for an unprecedented control of mechanical properties (e.g., stiffness, density, and Poisson's coefficient). In contrast to their quasi-static mechanical properties, the acoustic properties of microlattices remain largely unexplored. This paper analyzes the acoustic response of periodic millimeter-sized microlattices immersed in water using experiments and numerical simulations. Microlattices are fabricated using high-precision stereolithographic three-dimensional printing in a large variety of porosities and lattice topologies. This paper shows that the acoustic propagation undergoes a frequency dependent transition from a classic poroelastic behaviour that can be described by Biot's theory to a regime that is dominated by scattering effects. Biot's acoustic parameters are derived from direct simulations of the microstructure using coupled fluid and solid finite elements. The wave speeds predicted with Biot's theory agree well with the experimental measures. Within the scattering regime, the signals show a strong attenuation and dispersion, which is characterized by a cut-off frequency. The strong dispersion results in a frequency dependent group velocity. A simplified model of an elastic cylindrical scatterer allows predicting the signal attenuation and dispersion observed experimentally. The results in this paper pave the way for the creation of microlattice materials for the control of ultrasonic waves across a wide range of frequencies.