Tension/compression-torsion mechanical metamaterials: A review on cell design paradigms and multimodal applications

Traditional advanced structural materials are strictly bounded by their intrinsic physical properties, creating persistent design trade-offs between load-bearing capacity, weight, and directional deformation control. Tension/compression-torsion mechanical metamaterial (T/C-T MMs) break through these classic limitations by utilizing artificially engineered micro-architectures to smoothly convert standard one-dimensional axial stress waves into continuous, programmatic in-plane torsional rotations. This critical review provides a comprehensive synthesis of the recent milestones driving the rapid advancement of T/C-T MMs. We systematically map the core framework of microstructural synthesis into three dominant methodologies: parametric optimization based on predefined inclined-strut or ligament typologies, continuous and discrete topology optimization, and advanced data-driven machine learning schemes for rapid inverse structural discovery. Beyond basic geometric design, we comprehensively evaluate the translation of this cross-axis coupling mechanism into exceptional engineering application frontiers, specifically analyzing its role in low-frequency vibration damping, high-efficiency mass-specific energy absorption, compliance-guided soft robotics, and reconfigurable mechanical logic concealment arrays. Finally, we critique the underlying bottlenecks regarding scale-dependent boundary constraints, structural fatigue, and fabrication sensitivity, outlining future development trajectories that integrate multi-field stimuli-responsive materials and advanced additive manufacturing to pioneer next-generation intelligent structures.