Multifunctional multiphysics metamaterials via decomposition-based multiobjective optimization design

Metamaterials offer unprecedented control over physical fields through their microstructure, but current design methods cannot meet the demands of scenarios involving active sources, multiphysics field coupling, and multifunctional requirements. Moreover, existing approaches are generally developed for specific functions, making it difficult to integrate different functionalities and select the functional priorities within a single structure. To overcome these limitations, this study presents a systematic inverse design framework for multifunctional multiphysics metamaterials via multiobjective optimization. To uniformly explore the Pareto front, which clearly exhibits trade-offs among functionalities and facilitates the selection of functional priorities, we employ dynamic normalization into the decomposition-based multiobjective evolutionary algorithm. A robust anisotropic unit-cell database is constructed and used for generating metamaterials with optimized microstructures for multifunctionality. Three complex cases are studied that can simultaneously achieve mechanical cloaking plus stress minimization, thermal cloaking plus stress minimization, and direct current cloaking plus thermal stress minimization. Furthermore, the proposed framework is employed in potential engineering problems, for example, to realize mechanical cloaking by embedding functional components in structural materials, while minimizing the surrounding stress on functional components for mechanical protection when the assembled structures are compressed, thereby decoupling the interaction between functional and structural components. This systematic framework expands the capabilities of metamaterials in complex multiphysics coupling, offering a robust blueprint for future intelligent, structurally and functionally integrated systems.