Abstract:To systematically summarize the theoretical foundations, design methodologies, fabrication strategies, and engineering translation of multiphysical coupled programmable metamaterials, and to elucidate the key scientific questions and emerging trends in current research, this review proposes an integrated research framework that connects “theory-design-manufacturing-characterization-application-engineering”. The framework aims to provide a solid theoretical insights and engineering guidance for the on-demand functional design and intelligent responsiveness of metamaterials. Based on effective-medium and homogenization theories, we elucidate the modeling principles of Bloch-wave analysis and topological phases, and discuss the integration of nonlinear multistability with physics-constrained machine learning to achieve hybrid data-physics-driven modeling. Furthermore, we compare advanced design paradigms, such as topology optimization, Bayesian optimization, reinforcement learning, and generative modeling, and highlight the importance of explicitly incorporating manufacturability constraints and tolerance robustness at the design stage. Subsequently, the development routes of additive manufacturing and 4D printing from micro/nano to macro scales are summarized, together with multi-material and time-varying programmable strategies. Finally, cross-domain characterization metrics and standardized protocols are consolidated, and a unified framework is proposed based on data assimilation and parameter inversion. The study reveals that metamaterials research is evolving from the discovery of isolated exotic properties toward integrated, reconfigurable, and programmable multifunctionality. By integrating intelligent optimization and additive manufacturing, metamaterials have achieved remarkable performance enhancements and prototype demonstrations in vibration isolation, energy absorption, electromagnetic absorption and cloaking, acoustic focusing and noise control, thermal management, flexible sensing, biomedical applications, and lightweight aerospace systems. The proposed framework provides a generalizable technical roadmap for functional design and engineering translation of programmable metamaterials. Future research should focus on understanding multiscale coupling mechanisms, improving fabrication precision, enhancing reliability evaluation, and promoting system-level integration to bridge the gap between laboratory demonstrations and real-world engineering applications.
