Design of mechanical metamaterials using a level-set based topology optimization method

Metamaterials are a family of artificially engineered materials consisting of an array of periodically arranged microstructures, offering unusual material properties that may not be easily found in nature. This paper will propose a new topological shape optimization method for the design of mechanical metamaterials with negative Poisson’s ratios, by integrating the numerical homogenization method with a powerful level set method. The homogenization method is used to calculate the effective properties of the microstructure, and the level set method is utilized to implement shape and topology optimization of the microstructure until the desired material properties are obtained. The proposed method can retain the unique features of the level set methods, while avoid unfavourable numerical issues occurred in the conventional level set methods. Several typical numerical examples are used to showcase the effectiveness of the proposed design method