Elastic wave propagation in structures with triply periodic minimal surfaces

Abstract

We study the elastic wave propagation behavior of triply periodic minimal surface structures. Triply periodic minimal surfaces (TPMS) are surfaces with periodicity in three independent directions and a mean surface curvature of zero. Here, we apply the finite element method to obtain the dispersion curves of six different TPMS structures: Schwarz' P, Schwarz' D, Gyroid, Fischer-Koch's S, Schoen's I-WP, and Schoen's F-RD. The dispersion curves are obtained by modeling their respective unit cells, appropriately applying the Floquet-Bloch periodic boundary condition, and then performing an eigenfrequency analysis while sweeping over the boundaries of their respective irreducible Brillouin zones. We then classify each band according to their respective propagation modes (P- or S-waves) and study the effect of surface topology on each mode. Finally, we discuss the generation of directional and polarized bandgaps in these structures.