Topology optimization in flexible electrical heaters: status and perspective

• Review advances in flexible electrical heaters and composite architectures. • Overview topology optimization methods (density, level set, ESO, BESO) for FEHs. • Application analysis examines defrosting, de-icing, and wearable heaters. • Provide future prospects of optimized FEHs. Flexible electrical heaters (FEHs) have found extensive applications in emerging technological domains including wearable electronics, new-energy vehicles, and biomedical devices, owing to their properties such as lightweight, high flexibility, and rapid thermal response. However, traditional FEHs still face significant challenges in electrical-thermal conversion efficiency, temperature uniformity, and structural stability. Recently, rational design of composite heating structures in FEHs through advanced topological optimization strategies has demonstrated its potential of achieving highly efficient and uniform Joule heating, on the basis of flexible materials and systems. This paper reviews the progress of material and structural design of flexible heating structures, with an emphasis on the topological optimization techniques including density method, level set method, evolutionary structural optimization (ESO), and bidirectional evolutionary structural optimization (BESO). By optimizing conductive network distribution through multi-physics coupling models, significant improvements in heating uniformity and energy efficiency were achieved. Then, case studies of topological optimization of flexible heating structures in defrosting systems, de-icing applications, and wearable medical devices were discussed. Future directions on further boosting the performance and applications of FEHs were also highlighted.