Topology optimization design of microstructures with zero Poisson's ratio

Mechanical metamaterials are materials that possess unconventional mechanical properties that are not found in homogeneous materials, achieved through specific artificial microstructures. Topology optimization is an effective design method for such materials. In this paper, a topology optimization-based method for designing zero Poisson's ratio mechanical metamaterials is proposed. Firstly, a zero Poisson's ratio topology optimization objective function is constructed based on the energy homogenization method, and the optimal microstructure topology configuration and elastic coefficient matrix under different initial topologies and volume fractions are obtained through the boundary density evolution topology optimization method. To improve the saw tooth effect of the boundaries, the node density level set method is used to smooth the boundaries of the microstructure. Then, in finite element simulation analysis, it is demonstrated that the proposed method can effectively design microstructures with zero Poisson's ratio properties. It is also shown that microstructures with expected stiffness and zero Poisson's ratio properties can be obtained by changing the volume fraction and selecting materials with different stiffnesses. Finally, the unit cell is periodically arranged to form a multi-lattice metamaterial, and its zero Poisson's ratio mechanical performance in both X and Y directions is verified.