Unstructured growth of irregular architectures for optimized metastructures

Mechanical metastructures have been prevailing recently owing to their unusual mechanical responses. Despite notable progress in designing periodic metastructures, creating irregular and stochastic metastructures with optimized performance remains challenging because of the enlarged design space. In this study, we introduce a novel approach to realize the unstructured growth of irregular architectures for optimized metastructures. A “growth”-like design scheme is proposed to facilitate random yet controllable growth of predefined building blocks on an unstructured graph toward desired bulk properties. We also formulate a topology optimization framework that simultaneously optimizes building block selection and transformation (scaling, skew, and rotation) to generate metastructures with various optimized mechanical functionalities. These functionalities are achieved by harnessing the diverse homogenized material properties spanned by various frequency combinations of building blocks and the microstructure's transformations. We discover metastructures that ensure geometric integrity and exhibit explicitly controllable and globally uniform feature sizes beneficial for fabrication. Moreover, the transformation-based topology optimization ensures these metastructures naturally conform to the boundaries of the design domain and can serve as mechanical infills. The proposed approach holds promise for uncovering optimized metastructures applicable across a wide array of engineering applications.