Mechanical metamaterial

Mechanical metamaterials are metamaterials 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 optical metamaterials and electromagnetic metamaterials. Mechanical metamaterials are the broad umbrella term, 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. Three main types of mechanical metamaterials 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.

Classical mechanical metamaterials 3D printing, or additive manufacturing, has revolutionized the field in the past decade by enabling the fabrication of intricate mechanical metamaterial structures. Some of the unprecedented and unusual properties of classical mechanical metamaterials include:

Negative Poisson's ratio (auxetics) Poisson's ratio defines how a material expands (or contracts) transversely when being compressed longitudinally. While most natural materials have a positive Poisson's ratio (coinciding with our intuitive idea that by compressing a material, it must expand in the orthogonal direction), a family of extreme materials known as auxetic materials can exhibit Poisson's ratios below zero. Examples of these can be found in nature, or fabricated, and often consist of a low-volume microstructure that grants the extreme properties. Simple designs of composites possessing negative Poisson's ratio (inverted hexagonal periodicity cell) were published in 1985. In addition, certain origami folds such as the Miura fold and, in general, zigzag-based folds are also known to exhibit negative Poisson's ratio.

Negative stiffness Negative stiffness (NS) mechanical metamaterials are engineered structures that exhibit a counterintuitive property: as an external force is applied, the material deforms in a way that reduces the applied force rather than increasing it. This is in contrast to conventional materials that resist deformation. NS metamaterials are typically constructed from periodically arranged elements that undergo elastic instability under load. This instability leads to a negative stiffness behavior within a specific deformation range. The overall effect is a material that can absorb energy more efficiently and exhibit unique mechanical properties compared to traditional materials.

Negative thermal expansion These mechanical metamaterials can exhibit coefficients of thermal expansion larger than that of either constituent. The expansion can be arbitrarily large positive or arbitrarily large negative, or zero. These materials substantially exceed the bounds for thermal expansion of a two-phase composite. They contain considerable void space.

High strength to density ratio A high strength-to-density ratio mechanical metamaterial is a synthetic material engineered to possess exceptional mechanical properties relative to its weight. This is achieved through carefully designed internal microstructures, often periodic or hierarchical, which contribute to the material's overall performance.

Negative compressibility In a closed thermodynamic system in equilibrium, both the longitudinal and volumetric compressibility are necessarily non-negative because of stability constraints. For this reason, when tensioned, ordinary materials expand along the direction of the applied force. It has been shown, however, that metamaterials can be designed to exhibit negative compressibility transitions, during which the material undergoes contraction when tensioned (or expansion when pressured). When subjected to isotropic stresses, these metamaterials also exhibit negative volumetric compressibility transitions. In this class of metamaterials, the negative response is along the direction of the applied force, which distinguishes these materials from those that exhibit negative transversal response (such as in the study of negative Poisson's ratio).

Negative bulk modulus Mechanical metamaterials with negative effective bulk modulus exhibit intriguing and counterintuitive properties. Unlike conventional materials that compress under pressure, these materials expand. This anomalous behavior stems from their carefully engineered microstructure, which allows for internal deformation mechanisms that counteract the applied stress. Potential applications for these materials are vast. They could be employed to design acoustic or phononic metamaterials, advanced shock absorbers, and energy dissipation systems. Furthermore, their unique elastic properties may find utility in creating novel structural components with enhanced resilience and adaptability to dynamic loads.

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