Topology optimization of multi-scale structures: a review

Abstract Multi-scale structures, as found in nature (e.g., bone and bamboo), hold the promise of achieving superior performance while being intrinsically lightweight, robust, and multi-functional. Recent years have seen a rapid development in topology optimization approaches for designing multi-scale structures, but the field actually dates back to the seminal paper by Bendsøe and Kikuchi from 1988 (Computer Methods in Applied Mechanics and Engineering 71(2): pp. 197–224). In this review, we intend to categorize existing approaches, explain the principles of each category, analyze their strengths and applicabilities, and discuss open research questions. The review and associated analyses will hopefully form a basis for future research and development in this exciting field.