Concurrent topological optimization of multiple-phase materials with variable periodic patterns

Periodic structures have been widely utilized across various fields, such as thermodynamics, solid mechanics, electromagnetism, and acoustics, owing to their lightweight nature, high strength-to-weight ratio, and ease of manufacturing. However, traditional design approaches for periodic structures typically rely on a uniform periodic pattern across the entire design domain, without considering the potential for varying periodic modes in different subdomains or accounting for the comprehensive functional requirements of multiphase materials. The objective of this study is to develop a comprehensive topological optimization framework for designing multiphase materials with variable periodic patterns. By integrating predefined subdomain design spaces into the topological optimization process, along with a multiphase material interpolation model, the framework can effectively address diverse requirements for varying periodic patterns across multiple subdomains. To demonstrate the efficacy of the proposed algorithm, several numerical examples are presented, showcasing its ability to implement variable periodic patterns in different subdomain design spaces. The results reveal that the maximum disparity in global compliance values is 37.8%, 8.8%, and 28.2% across variations in periodic numbers, arrangement orders, and material volume fractions, respectively. Moreover, the numerical findings confirm that the algorithm ensures fully connected connectivity across multi-subdomain spaces, while the inclusion of multiphase materials provides flexible design strategies for optimal performance.