Topologically interlocking material systems: A review of geometry-driven design and mechanics

Topologically interlocking (TI) has emerged as a promising design paradigm for next-generation construction materials and structures, offering unique combinations of energy absorption, damage tolerance, and functional adaptability. This review provides a comprehensive synthesis of recent advances in the design and mechanical behaviour of TI systems. A classification of TI elements is first established based on their geometric characteristics and interlocking mechanisms. The review then examines the fundamental deformation and failure mechanisms governing TI assemblies under various loading conditions. Particular attention is given to the relationships between key design parameters and structural performance, highlighting how element topology, interface morphology, scale, and assembly configuration influence load transfer, energy dissipation, and failure modes. Quantitative metrics for evaluating interlocking efficacy are summarised, and a geometry-driven framework for performance tuning is discussed. Finally, future research directions are outlined, emphasising the potential of TI systems for developing sustainable, resilient, and adaptive engineering materials and structures.