Two-Phase Topology Optimization for Metamaterials with Negative Poisson's Ratio

Abstract: Although recent developments in 3D printing technology have made it possible to fabricate metamaterials with characteristic mechanical properties, it is not easy to fabricate complex shapes containing cavities. In this study, a composite structure comprising two types of materials without a cavity was optimized. Moreover, a mechanical metamaterial with a negative Poisson's ratio that can be fabricated using an additive manufacturing method was developed. First, a homogenization method that characterizes the properties of composite structures was briefly described. Then, an optimization problem to realize a negative Poisson's ratio was formulated, and a level set-based topology optimization method was proposed to solve the abovementioned problem. Next, three-dimensional numerical examples are presented to confirm the effectiveness of the proposed method, and the deformation behaviors of the optimized designs are numerically examined. Furthermore, a sample containing the optimized design with negative Poisson's ratio for the tensile test was fabricated using a 3D printer. We conducted some experiments to evaluate its mechanical performance.