Table 3.

Potential application of HMMMs in engineering problems in terms of their unique features.

Feature	Static Property	Dynamic Property	Application
Vibration damping and isolation	Load-bearing capacity	Tunable band gap	1) Infrastructure design: mitigate vibrations caused by seismic activity or machinery [226]
			2) Automotive and aerospace: isolate sensitive components from engine vibrations or mechanical shocks [227]
			3) Machinery and equipment: in industrial settings for reducing vibrational impact on sensitive tools, enhancing precision [228]
Sound insulation and control	Structural integrity	Attenuation or redirection of sound waves	1) Noise barriers: In urban environments and around highways to reduce noise pollution [229]
			2) Underwater acoustics: reduction of noise emission during offshore foundation installation [230], while keeping resistance to high hydrostatic pressure
Wave manipulation and energy harvesting	High durability	Wave propagation control for guiding, trapping or focusing energy	1) Energy harvesting from vibrations: In bridges, railways, buildings, or vehicles where the metamaterial converts mechanical vibrations into electrical energy [231]
Impact and shock absorption	High strength, flexibility or lightweight structure to absorb static loads	High energy absorption capacity under dynamic impacts or shocks	1) Personal protective equipment (PPE): helmets, body armor, and protective clothing that absorb impacts while remaining lightweight and flexible [232]
			2) Crash-resistant structures: in automotive and aerospace industries to absorb energy during collisions, protecting passengers and sensitive components [233]
			3) Sports equipment: helmets, pads, and shoes to enhance performance and safety by absorbing impact forces [158]
Biomedicine	Structural support and stiffness for implants or prosthetics	Tunable mechanical responses and absorb dynamic loads	1) Bone implants: hybrid metamaterials designed to mimic the mechanical properties of natural bone, combining strength with dynamic load absorption [234]
			2) Wearable medical devices: flexible, adaptive materials for devices that monitor and respond to the body's mechanical movements [235]