Electromagnetic metamaterials in the context of Negative-index metamaterial

Mechanical metamaterials are rationally designed artificial materials/structures of precision geometrical arrangements leading to unusual physical and mechanical properties. These unprecedented properties are often derived from their unique internal structures rather than the materials from which they are made. Inspiration for mechanical metamaterials design often comes from biological materials (such as honeycombs and cells), from molecular and crystalline unit cell structures as well as the artistic fields of origami and kirigami. While early mechanical metamaterials had regular repeats of simple unit cell structures, increasingly complex units and architectures are now being explored. Mechanical metamaterials can be seen as a counterpart to the rather well-known family of optical metamaterials and electromagnetic metamaterials. Mechanical metamaterials are the broad umbrella, defined by architected structures at nano, micro, meso, and macro scales that produce properties unattainable in conventional materials. Mechanical properties, including elasticity, viscoelasticity, thermoelasticity, and thermal conductivity, are key design targets in mechanical metamaterials. Under the mechanical metamaterials umbrella, three main branches can be distinguished. The first involves static or quasi-static responses, such as auxeticity, tunable stiffness, multistability, or programmable deformation. The second involves dynamic wave phenomena in solids, often referred to as elastic or elastodynamic metamaterials, where resonant or periodic architectures control both longitudinal and shear wave propagation through effective properties such as negative mass density or modulus. Acoustic metamaterials fall within this dynamic branch and are designed to control longitudinal pressure waves in fluids as well as in solids where shear effects are negligible, through tailored effective density and bulk modulus. The third branch encompasses thermal metamaterials, which manipulate heat conduction and diffusion. These are considered mechanical metamaterials because their unusual thermal responses arise from engineered architecture rather than composition, enabling anisotropic conduction, thermal cloaking, and directional heat management using structures such as aligned fibers or carbon nanotube arrays. Mainstream research on mechanical metamaterials has focused on static and quasi-static properties that can be designed to take values not found in nature, such as negative stiffness, negative Poisson's ratio, negative compressibility, and vanishing shear modulus.