Pyramid-Shaped Metamaterials with Tunable Mechanical Properties and Broad Frequency Bandgaps

We propose a novel elastic metamaterial offering a number of tunable macroscopic mechanical properties, including effective elastic moduli, overall anisotropy, mass density, and frequency band structures. The unit cell of the periodic metastructures is composed of three-dimensional pyramid-shaped inclusions, similar to the geometry of a traditional Chinese food, Zongzi. A unique feature of this configuration is that the geometry can be described by a simple algebraic equation, enabling transformation of the geometric configuration into a few variant forms upon simple coordinate scalings. We demonstrate that a number of macroscopic properties can be adjusted by geometric parameter scaling without altering the internal structure or the constituent materials. Numerical simulations are conducted to estimate the effective elastic properties. Specifically, the effective elastic moduli can be reduced by two to three orders of magnitude compared to those of the original constituent material. In addition, the tunable mechanical properties offer flexibilities to control the frequency bandgap with adjustable bandwidths. We find that the periodic array of Zongzi matastructure could generate very wide frequency bandgaps, which can be utilized to control wave propagation characteristics. A number of specimens fabricated with three-dimensional printing have been tested for validation of the numerically estimated effective mechanical properties of Zongzi microstructures. The present study provides insightful information toward a new three-dimensional metastructure with tunable mechanical properties and frequency band structures.