Computational design of mechanical metamaterials through misaligned periodic microstructure

Abstract

Mechanical metamaterials, with their intricately designed microstructures, exhibit properties that are superior to those of natural materials. Computational optimization, which uses finite element analysis of periodic microstructures, enables the design of architected microstructures to achieve desired macroscopic properties. Traditionally, unit cells are defined within cuboidal domains; however, this study extends the design to parallelepiped domains, significantly expanding design possibilities. This study investigates the influence of geometric design domains on the topology optimization of negative Poisson's ratio (NPR) metamaterials. Using the mathematical homogenization method, unit cells within parallelogram or parallelepiped domains are represented within square or cubic domains under misaligned periodic boundary conditions. This approach enables the manipulation of macroscopic elastic stiffness components while maintaining the solid volume fraction. A comparative analysis was performed to examine the geometric characteristics of optimized microstructures and the resulting macroscopic anisotropy under both standard and misaligned periodic boundary conditions. 3D-printed NPR metamaterials were tested to validate the design. The results demonstrate the effectiveness of the computational design method in generating diverse microstructures with misalignment, opening new avenues for designing NPR metamaterials with enhanced properties.