## 2 Method
### Construction of Multitype Cells and Verification of Their Water-like Properties
In order to validate the water-like characteristics of ss1 and re1, we employ COMSOL Multiphysics software to construct a two-dimensional square water model measuring 1600 mm \(\times\) 1600 mm, as illustrated in Figure 5. Perfectly matched layers are implemented around the model to eliminate boundary reflections. The scatterer consists of an array of \(6\times 40\) cells in accordance with the cell cycle. The entire model utilizes the sound-solid coupling module in COMSOL Multiphysics, where the solid material within the scatterer represents the mechanical physical field, while the air domain and the water region represent the acoustic pressure physical field. The interface between these two physical fields is set as the sound-solid coupling boundary. Within this model, the water area without a cell array is set as the background sound pressure field, indicating the direction of the incident wave. To conduct a comparative analysis, steel block scatterers with identical dimensions are introduced in this study (as depicted in Figure 5). Except for significant scattering observed for steel blocks, shown in Figure 5a,e, all other scatterers allow for efficient transmission of plane waves with minimal scattering when vertically or obliquely incident. To quantitatively analyze this phenomenon, a measurement curve with a radius of 300 mm is added at the center of the water area; the scattering ability of each scatterer is assessed by calculating the ratio between scattered wave intensity and mean sound intensity within a background field along said curve (mean scattering intensity: MSI). The MSI curves of the three scatterers under vertical incidence and 45\({}^{\circ}\) angle incidence are depicted in Figure 6a and Figure 6b, respectively. In Figure 6a, the black dotted line represents the MSI of the steel block, while the red curve represents the MSI of ss1, and the blue curve represents the MSI of re1. The results demonstrate that when an acoustic wave is vertically incident, the MSI of the steel block is significantly larger than that of both cells. At 5000 Hz, the measured MSI values for the steel block, ss1, and re1 are 0.32, 0.3 \(\times\) 10\({}^{-3}\), indicating a three orders of magnitude difference between them. Within a frequency range of 5000 Hz to 35,000 Hz, it can be observed that ss1 exhibits a \"bump\" near 10,000 Hz, while re1 shows a \"bump\" around 13,000 Hz; moreover, at frequencies above 30,000 Hz, their scattering intensities become comparable to that produced by steel blocks. Figure 6b illustrates how these three scatterers behave under oblique sound wave incidence at an angle of 45\({}^{\circ}\); here, we observe similar \"bumps\" for both cells. The scattering properties exhibited by both cell arrays align well with their respective band diagrams shown in Figures 2a and 4b. As detailed in references [33,43], the presence of this \"bump\" is associated with local resonance within a unit cell. The occurrence of local resonance introduces minor discontinuities in what would otherwise be an approximately linear energy band curve, potentially leading to \"singular values\" in the equivalent parameters of the single cell within a narrow frequency range. This phenomenon may, to some extent, influence the broadband water-like properties of the single cell. So, within a frequency range of 5000 Hz-27,000 Hz, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **r/mm** & **h/mm** & **r1/mm** & **h1** & **Re-Entrant** & **Relative** & **Relative** & **Equivalent** \\  & & & & & **Factor: e** & **Density** & **Sound Velocity** \\ \hline ss1 & 5 & 0.5 & & & 0 & & \\ \hline re1 & 5 & 0.58 & 3 & 0 & 0.048 & & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometric parameters of two cells with similar properties to water. except near these \"bump\" frequencies, re1 and ss1 demonstrate excellent broadband water-like characteristics.