Inverse design and 3D printing of programmable functional metamaterials: thermomechanical performance, vibration isolation & durability

Three-dimensional (3D)-printed quasi-zero-stiffness (QZS) metamaterials offer great potential for low-frequency vibration isolation but remain constrained by limited programmability, poor load-bearing capability, and a lack of understanding of their durability and thermomechanical behaviour. This study employs an evolutionary optimisation-based inverse design framework that simultaneously optimises constant-force plateau bandwidth, load-bearing capability, and lightweight architecture through coupled structural and material design. A sustainable thermoplastic polyurethane (TPU) bio-composite reinforced with 2.5 wt.% eggshell powder is developed for material-extrusion 3D printing, increasing tensile stiffness by 38%, improving energy dissipation by 27%, and reducing printing shrinkage by 35% while preserving large-deformation recoverability. The framework enables programmable bio-inspired metamaterials with tailored QZS responses and enhanced structural performance. Comprehensive thermomechanical, fatigue, creep, and vibration investigations reveal excellent durability, with only a 5.5% reduction in force after 750 loading cycles and a stable creep strain of 3.6% after 15 h. The metamaterials provide effective vibration isolation over 0–100 Hz and retain reliable performance under elevated temperatures. Finally, the optimised cylindrical metamaterial is validated as a vibration isolator for cylindrical nickel-metal hydride and prismatic lithium-ion batteries. The proposed framework establishes a practical route towards durable, programmable, and sustainably manufactured functional metamaterials for advanced engineering applications.