Symmetry breaking induces polarized bandgaps and anomalous elastic wave behavior in gyroid lattices

We investigate the elastic wave dispersion of surface-based gyroid lattices and analyze how introducing material and geometric asymmetry affects their behavior. First, we show that unmodified (high-symmetry) gyroid lattices exhibit multiple degeneracies in their dispersion relations, preventing bandgap formation. To lift these degeneracies, we implement two asymmetry strategies: (1) Material asymmetry, by assigning different stiffness or density to distinct regions of the unit cell; and (2) Geometric asymmetry, by scaling the lattice unequally along coordinate axes to create anisotropic “gyroid-derived” shapes. Bloch–Floquet analysis of the infinite periodic lattices reveals that both approaches open new bandgaps. Material-asymmetric gyroids develop polarized-directional bandgaps that block one shear polarization in specific directions, and for moderate stiffness or density contrast, produce a “fluid-like” regime in which both shear polarizations ($S$ ${}_1$ and $S$ ${}_2$) are strongly attenuated, allowing only longitudinal ($P$) waves. Geometrically asymmetric gyroids likewise exhibit directional bandgaps and, at low frequencies, display anomalous propagation: shear wave phase velocities exceed longitudinal wave velocities—a reversal of the usual hierarchy. Computational homogenization confirms that these anomalies arise from anisotropic effective stiffness coefficients $C_{44}^{\ast }$ and $C_{66}^{\ast }$ surpassing $C_{11}^{\ast }$ along certain axes. Overall, our results demonstrate that deliberate material or geometric asymmetry in gyroid lattices enables precise tailoring of bandgaps and wave-speed hierarchies, offering an effective approach for the design of architected metamaterials for vibration isolation and wave control.