Mechanical metamaterial

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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 properties, including elasticity, viscoelasticity, and thermoelasticity, are central to the design of mechanical metamaterials. They are often also referred to as elastic metamaterials or elastodynamic metamaterials. Their mechanical properties can be designed to have values that cannot be found in nature, such as negative stiffness, negative Poisson’s ratio, negative compressibility, and vanishing shear modulus. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

Contents

Classical mechanical metamaterials

A significant portion of current research in mechanical metamaterials focuses on exploring novel geometric designs of micro/nano-architectures to achieve or discover exceptional mechanical properties. 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, [14] [15] 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. [16] [17] 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. [18] [19] [20] [21]

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. [22] [23] [24] [25] 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. [26] [27] [28] 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. [29] [4]

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). [30] When subjected to isotropic stresses, these metamaterials also exhibit negative volumetric compressibility transitions. [31] 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 [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] . Furthermore, their unique elastic properties may find utility in creating novel structural components with enhanced resilience and adaptability to dynamic loads.

Vanishing shear modulus

SEM image of a pentamode metamaterial (with a size of roughly 300mm) Pentamode.png
SEM image of a pentamode metamaterial (with a size of roughly 300μm)

A pentamode metamaterial is an artificial three-dimensional structure which, despite being a solid, ideally behaves like a fluid. Thus, it has a finite bulk but vanishing shear modulus, or in other words it is hard to compress yet easy to deform. Speaking in a more mathematical way, pentamode metamaterials have an elasticity tensor with only one non-zero eigenvalue and five (penta) vanishing eigenvalues. Pentamode structures have been proposed theoretically by Graeme Milton and Andrej Cherkaev in 1995 [42] but have not been fabricated until early 2012. [43] According to theory, pentamode metamaterials can be used as the building blocks for materials with completely arbitrary elastic properties. [42] Anisotropic versions of pentamode structures are a candidate for transformation elastodynamics and elastodynamic cloaking.

Chiral micropolar elasticity

Very often Cauchy elasticity is sufficient to describe the effective behavior of mechanical metamaterials. When the unit cells of typical metamaterials are not centrosymmetric it has been shown that an effective description using chiral micropolar elasticity (or Cosserat [44] ) was required. [45] Micropolar elasticity combines the coupling of translational and rotational degrees of freedom in the static case and shows an equivalent behavior to the optical activity.

Infinite mechanical tunability

In addition to the well-known unprecedented mechanical properties of mechanical metamaterials, "infinite mechanical tunability" is another crucial aspect of mechanical metamaterials. This is particularly important for structural materials as their microstructure and stiffness can be tuned to effectively achieve theoretical upper bounds for specific stiffness and strength. [46] [47] [48] While theoretical composites that achieve the same upper bound have existed for some time, [49] they have been impractical to fabricate as they require features on multiple length scales. [50] Single length scale designs are amenable to additive manufacturing, where they can enable engineered systems that maximize lightweight stiffness, strength and energy absorption.

Active Mechanical Metamaterials

To date, most mainstream studies on mechanical metamaterials have focused on passive structures with fixed properties, lacking active sensing or feedback capabilities. [51] [13] Deep integration of advanced functionalities is a critical challenge in exploring the next generation of metamaterials. [52] Composite mechanical metamaterials could be the key to achieving this goal. However, the entire concept of composite mechanical metamaterials is still in its infancy. Obtaining programmable behavior through the interplay between material and structure in composite mechanical metamaterials enables integrating advanced functionalities into their texture beyond their mechanical properties. The “mechanical metamaterial tree of knowledge” [13] implies that chiral, lattice and negative metamaterials (e.g., negative bulk modulus or negative elastic modulus) are ripe followed by origami and cellular metamaterials.

Recent research trends have been entering a space beyond merely exploring unprecedented mechanical properties. Emerging directions envisioned are sensing, energy harvesting, and actuating mechanical metamaterials.The tree of knowledge reveals that digital computing, digital data storage, and micro/nano-electromechanical systems (MEMS/NEMS) applications are one of the pillars of the mechanical metamaterials future research. Along this direction of evolution, the final target can be active mechanical metamaterials with a level of cognition. Cognitive abilities are crucial elements in a truly "intelligent mechanical metamaterials". Similar to complex living organisms, intelligent mechanical metamaterials can potentially deploy their cognitive abilities for sensing, self-powering, and information processing to interact with the surrounding environments, optimizing their response, and creating a sense–decide–respond loop.

Mechanical metamaterial tree of knowledge Mechanical metamaterial tree of knowledge.jpg
Mechanical metamaterial tree of knowledge

Programmable mechanical metamaterials

Programmable response is an emerging direction for mechanical metamaterials beyond mechanical properties. [53] [54] [55] [56] [57] [58] [59] Electrical responsiveness is an important functionality for designing adaptive, actuating, and autonomous mechanical metamaterials. [60] [61] For example, research ideas have been opened by active and adaptive mechanical metamaterials that design electrical materials into the microstructural units of metamaterials to autonomously convert mechanical-strain input into electrical-signal output. [51] [62]

Responsive mechanical metamaterials

Integrating functional materials and mechanical design is an emerging research area to explore responsive mechanical metamaterials [51] . Recent studies explore new classes of mechanical metamaterials that can response to different excitation types such acoustic [63] , thermophotovoltaic [64] and magnetic [65] .

Sensing and energy harvesting mechanical metamaterials

Recent studies have explored the integration of sensing and energy harvesting functionalities into the fabric of mechanical metamaterials. Meta-tribomaterials [66] [67] proposed in 2021 are a new class of multifunctional composite mechanical metamaterials with intrinsic sensing and energy harvesting functionalities. These material systems are composed of finely tailored and topologically different triboelectric microstructures. Meta-tribomaterials can serve as nanogenerators and sensing media to directly collect information about its operating environment. They naturally inherit the enhanced mechanical properties offered by classical mechanical metamaterials. Under mechanical excitations, meta-tribomaterials generate electrical signals which can be used for active sensing and empowering sensors and embedded electronics. [66]

Electronic mechanical metamaterials

Electronic mechanical metamaterials [68] are active mechanical metamaterials with digital computing and information storage capabilities. They have built the foundation for a new scientific field of meta-mechanotronics (mechanical metamaterial electronics) proposed in 2023. [68] These material systems are created via integrating mechanical metamaterials, digital electronics and nano energy harvesting (e.g. triboelectric, piezoelectric, pyroelectric) technologies. Electronic mechanical metamaterials hold the potential to function as digital logic gates, paving the way for the development of mechanical metamaterial computers (MMCs) that could complement traditional electronic systems. [68] Such computing metamaterial systems can be particularly useful under extreme loads and harsh environments (e.g. high pressure, high/low temperature and radiation exposure) where traditional semiconductor electronics cannot maintain their designed logical functions.

Related Research Articles

A nanowire is a nanostructure in the form of a wire with the diameter of the order of a nanometre. More generally, nanowires can be defined as structures that have a thickness or diameter constrained to tens of nanometers or less and an unconstrained length. At these scales, quantum mechanical effects are important—which coined the term "quantum wires".

<span class="mw-page-title-main">Young's modulus</span> Mechanical property that measures stiffness of a solid material

Young's modulus is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Young's modulus is defined as the ratio of the stress applied to the object and the resulting axial strain in the linear elastic region of the material.

<span class="mw-page-title-main">Poisson's ratio</span> Measure of material deformation perpendicular to loading

In materials science and solid mechanics, Poisson's ratioν (nu) is a measure of the Poisson effect, the deformation of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, ν is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. For soft materials, such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer foams, Poisson's ratio is near zero, since the cells tend to collapse in compression. Many typical solids have Poisson's ratios in the range of 0.2 to 0.3. The ratio is named after the French mathematician and physicist Siméon Poisson.

<span class="mw-page-title-main">Roton</span> Collective excitation in superfluid helium-4 (a quasiparticle)

In theoretical physics, a roton is an elementary excitation, or quasiparticle, seen in superfluid helium-4 and Bose–Einstein condensates with long-range dipolar interactions or spin-orbit coupling. The dispersion relation of elementary excitations in this superfluid shows a linear increase from the origin, but exhibits first a maximum and then a minimum in energy as the momentum increases. Excitations with momenta in the linear region are called phonons; those with momenta close to the minimum are called rotons. Excitations with momenta near the maximum are called maxons.

An elastic modulus is the unit of measurement of an object's or substance's resistance to being deformed elastically when a stress is applied to it.

<span class="mw-page-title-main">Metamaterial</span> Materials engineered to have properties that have not yet been found in nature

A metamaterial is a type of material engineered to have a property that is rarely observed in naturally occurring materials. They are made from assemblies of multiple elements fashioned from composite materials such as metals and plastics. These materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry, size, orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, or bending waves, to achieve benefits that go beyond what is possible with conventional materials.

<span class="mw-page-title-main">Auxetics</span> Materials that have a negative Poissons ratio

Auxetics are typical structures of the representative mechanical meta-materials. Mechanical meta-materials are structures whose mechanical properties are artificially derived from sophisticated structures and refer to unique structures that do not take place in nature. Herein, the basic concept of meta implies something that goes beyond naturally occurring substances. Generally, materials have a positive Poisson's ratio. Unlike general materials, Auxetics are structures or materials that have a negative Poisson's ratio. In terms of general materials, it is noted that while elongating along the x axis, the length in the y axis is decreased. Interestingly, in terms of the auxetic structure, while it expands along the x axis, y axis also expands simultaneously. In other words, elongation occurs in both directions, causing a rapid increase in volume.

<span class="mw-page-title-main">Acoustic metamaterial</span> Material designed to manipulate sound waves

An acoustic metamaterial, sonic crystal, or phononic crystal is a material designed to control, direct, and manipulate sound waves or phonons in gases, liquids, and solids. Sound wave control is accomplished through manipulating parameters such as the bulk modulus β, density ρ, and chirality. They can be engineered to either transmit, or trap and amplify sound waves at certain frequencies. In the latter case, the material is an acoustic resonator.

<span class="mw-page-title-main">Photonic metamaterial</span> Type of electromagnetic metamaterial

A photonic metamaterial (PM), also known as an optical metamaterial, is a type of electromagnetic metamaterial, that interacts with light, covering terahertz (THz), infrared (IR) or visible wavelengths. The materials employ a periodic, cellular structure.

A seismic metamaterial, is a metamaterial that is designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the Earth. Current designs of seismic metamaterials utilize configurations of boreholes, trees or proposed underground resonators to act as a large scale material. Experiments have observed both reflections and bandgap attenuation from artificially induced seismic waves. These are the first experiments to verify that seismic metamaterials can be measured for frequencies below 100 Hz, where damage from Rayleigh waves is the most harmful to artificial structures.

A metamaterial absorber is a type of metamaterial intended to efficiently absorb electromagnetic radiation such as light. Furthermore, metamaterials are an advance in materials science. Hence, those metamaterials that are designed to be absorbers offer benefits over conventional absorbers such as further miniaturization, wider adaptability, and increased effectiveness. Intended applications for the metamaterial absorber include emitters, photodetectors, sensors, spatial light modulators, infrared camouflage, wireless communication, and use in solar photovoltaics and thermophotovoltaics.

A plasmonic metamaterial is a metamaterial that uses surface plasmons to achieve optical properties not seen in nature. Plasmons are produced from the interaction of light with metal-dielectric materials. Under specific conditions, the incident light couples with the surface plasmons to create self-sustaining, propagating electromagnetic waves known as surface plasmon polaritons (SPPs). Once launched, the SPPs ripple along the metal-dielectric interface. Compared with the incident light, the SPPs can be much shorter in wavelength.

Aerographene or graphene aerogel is the least dense solid known to exist, at 160 g/m3. The material reportedly can be produced at the scale of cubic meters.

Rigidity theory, or topological constraint theory, is a tool for predicting properties of complex networks based on their composition. It was introduced by James Charles Phillips in 1979 and 1981, and refined by Michael Thorpe in 1983. Inspired by the study of the stability of mechanical trusses as pioneered by James Clerk Maxwell, and by the seminal work on glass structure done by William Houlder Zachariasen, this theory reduces complex molecular networks to nodes constrained by rods, thus filtering out microscopic details that ultimately don't affect macroscopic properties. An equivalent theory was developed by P. K. Gupta and A. R. Cooper in 1990, where rather than nodes representing atoms, they represented unit polytopes. An example of this would be the SiO tetrahedra in pure glassy silica. This style of analysis has applications in biology and chemistry, such as understanding adaptability in protein-protein interaction networks. Rigidity theory applied to the molecular networks arising from phenotypical expression of certain diseases may provide insights regarding their structure and function.

<span class="mw-page-title-main">Borophene</span> Allotrope of boron

Borophene is a crystalline atomic monolayer of boron, i.e., it is a two-dimensional allotrope of boron and also known as boron sheet. First predicted by theory in the mid-1990s, different borophene structures were experimentally confirmed in 2015.

In materials science, the term single-layer materials or 2D materials refers to crystalline solids consisting of a single layer of atoms. These materials are promising for some applications but remain the focus of research. Single-layer materials derived from single elements generally carry the -ene suffix in their names, e.g. graphene. Single-layer materials that are compounds of two or more elements have -ane or -ide suffixes. 2D materials can generally be categorized as either 2D allotropes of various elements or as compounds.

A two-dimensional semiconductor is a type of natural semiconductor with thicknesses on the atomic scale. Geim and Novoselov et al. initiated the field in 2004 when they reported a new semiconducting material graphene, a flat monolayer of carbon atoms arranged in a 2D honeycomb lattice. A 2D monolayer semiconductor is significant because it exhibits stronger piezoelectric coupling than traditionally employed bulk forms. This coupling could enable applications. One research focus is on designing nanoelectronic components by the use of graphene as electrical conductor, hexagonal boron nitride as electrical insulator, and a transition metal dichalcogenide as semiconductor.

<span class="mw-page-title-main">Nanolattice</span>

A nanolattice is a synthetic porous material consisting of nanometer-size members patterned into an ordered lattice structure, like a space frame. The nanolattice is a newly emerged material class that has been rapidly developed over the last decade. Nanolattices redefine the limits of the material property space. Despite being composed of 50-99% of air, nanolattices are very mechanically robust because they take advantage of size-dependent properties that we generally see in nanoparticles, nanowires, and thin films. The most typical mechanical properties of nanolattices include ultrahigh strength, damage tolerance, and high stiffness. Thus, nanolattices have a wide range of applications.

<span class="mw-page-title-main">Microstructures in 3D printing</span>

The use of microstructures in 3D printing, where the thickness of each strut scale of tens of microns ranges from 0.2mm to 0.5mm, has the capabilities necessary to change the physical properties of objects (metamaterials) such as: elasticity, resistance, and hardness. In other words, these capabilities allow physical objects to become lighter or more flexible. The pattern has to adhere to geometric constraints, and thickness constraints, or can be enforced using optimization methods. Innovations in this field are being discovered in addition to 3D printers being built and researched with the intent to specialize in building structures needing altered physical properties.

<span class="mw-page-title-main">Katia Bertoldi</span> Professor in Applied Mechanics

Katia Bertoldi is the William and Ami Kuan Danoff Professor of Applied Mechanics at Harvard University. Her research has been highlighted by many news sources including the BBC, and as of June 2020 had been cited over 11,000 times.

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