Design 3D improved star-shaped honeycomb with different tip angles from 2D analytical star-shaped model

Two-dimensional star-shaped honeycombs (2D SSHs) exhibit an effective negative Poisson's ratio due to the abundant internal space and re-entrant angle, while the strength and the deformation of the three-dimensional (3D) SSHs are still limited owing to the finite tuneability of the tip angle. By adding different tip re-entrant angles into the SSH, multiple improved star-shaped honeycombs (ISSHs) with tunable Poisson's ratio are proposed. The in-plane elastic properties, including the effective Young's moduli and effective Poisson's ratio, are both derived by 2D analytical model using the energy method. The finite element simulation and compression experiment are used to verify the correctness of theoretical results. Based on the work, the deformation mechanism of the 3D ISSHs is discussed by quasi-static compression experiment and numerical simulation. The simulation results and experimental results show a great agreement with theoretical results. Different tip angles heighten the normalized Young's modulus and make the Poisson's ratio more tunable, respectively. In addition, the 3D ISSHs show an enhanced effect among higher strength and stability while bearing the compression load. This work provides a good reference for constructing 3D symmetrical multicellular structures, especially honeycombs.