Penta-mode metamaterials, composed by solids but behaving as liquid, have great potential in manipulating acoustic wave in fluids. Most work concentrates on 2D penta-mode metamaterial consisting of classic honeycomb lattice and their acoustic applications. However, the 3D penta-mode exploration is still limited to traditional diamond lattice. Due to the multiple mobilities and irregular boundaries, the traditional diamond lattice also owns natural disadvantages in transformability.

        Recently, the team of Professor Yan Chen from the school of mechanical engineering of Tianjin University, in cooperation with the team of Professor Rui Zhu of the school of aerospace engineering of Beijing Institute of Technology, propose a novel 3D penta-mode metamaterial design whose geometry is based on truncated octahedron. The configurations of regular truncated octahedron and transformed truncated octahedron exhibit isotropic and anisotropic penta-mode property, respectively.

        In order to design the unit cell for 3D penta-mode metamaterial, the researchers explore regular polyhedrons that could be densely tessellated in three dimensions. The regular truncated octahedron is verified to be a 3D penta-mode metamaterial with tailorable anisotropic factors, by deformation under uniaxial tension or compression，as shown in Fig. 1 and Fig. 2. Q is defined as the anisotropic factor and Q=1 indicates that it is an isotropic penta-mode metamaterial.

Fig. 1 The lattice structure of regular truncated octahedron.

Fig. 2 The anisotropic factor of modulus Q as a function of β

        The above proposed pin-jointed unit cell has 30 degrees of freedom (DOFs) according to Maxwell’s Rule. To make the transformation controllable, we have to decrease its DOFs. We investigated the motion of each bar during the transformation process to develop an alternative linkage system and then the modular origami form is obtained, as shown in Fig. 3. Its mobility is reduced to 12, which allows us to realize the transformation among different configurations.

Fig. 3 The mechanism design and its modular origami form.

        The steps for configuration conversion are shown in Fig. 4. First, install the fixture, fix the model as the target configuration, and then perform heat treatment to eliminate internal stress. Due to the use of thermoplastic material TPU, the model remains at the target configuration with fixtures removed after cooling. Researchers calculated the DOF of n×n×n array and found that this method can be used for structures containing any numbers of cell to reconstruct the initial configuration to the target configuration.

Fig. 4 The transformation process between the configurations.

        A 2×2×2 array is fabricated using 3D printing method, Fused Deposition Modeling, as shown in Fig. 5. Except for the regular truncated octahedron configuration, four typical configurations of transformed truncated octahedron were selected to conduct the compress, shear, and Poisson’s ratio tests. All configurations indicate one maximum eigenvalue while the other five is two orders smaller at least, which confirms the penta-mode. The anisotropy factor Q calculated from experiment results fits well with the FEM results. The tendency is that, with parameter β changing from 15° to 75°, the anisotropy character varies from low z-direction pressure to high z-direction pressure, and there are three or more orders of magnitude of broad tunable range.

Fig. 5 Typical configurations with different anisotropy

        With the proposed transformable anisotropic penta-mode metamaterial, we demonstrate the adjustable wave velocity and impedance, which can be further harnessed for the novel 3D waveguide design, as shown in Fig. 6.

Fig. 6 Tunable anisotropic pressure wave transmission

        This work was published online 9th Sept, 2023 in the Journal of Materials & Design. The proposed novel design offers a wider 3D transformable penta-mode metamaterial flatform to achieve the tunable control of acoustic wave in fluids.

Wei Z#, Hu Z#, Zhu R*, Chen Y*, Hu G. A transformable anisotropic 3D penta-mode metamaterial. Materials & Design, 2023, 234, 112306.
(https://doi.org/10.1016/j.matdes.2023.112306)