Fabricating Three-Dimensional Metamaterials Using Additive Manufacturing: An Overview

Abstract

Metamaterials are artificial materials composed of special microstructures that have properties with unusual and useful features and can be applied to many fields. With their unique properties and sensitivity to external stimuli, metamaterials offer design flexibility to users. Traditional manufacturing is often not up to the task of creating metamaterials, which are now more accurately and more effectively analyzed than they were in the past. Recent advances in additive manufacturing (AM) have achieved remarkable success, with ensemble machine learning models demonstrating R² values exceeding 0.97 and accuracy improvements of 9.6% over individual approaches. State-of-the-art multiphoton polymerization (MPP) techniques now reach submicron resolution (<1 μm), while selective laser melting (SLM) processes provide 20–100 μm precision for metallic metamaterials. This work offers a comprehensive review of additively manufactured 3D metamaterials, focusing on three categories of their fabrication: electromagnetic (achieving bandgaps up to 470 GHz), acoustic (providing 90% sound suppression at targeted frequencies), and mechanical (demonstrating Poisson’s ratios from −0.8 to +0.8). The relationship between different types of AM processes used in creating 3D objects and the properties of the resulting materials has been systematically reviewed. This research aims to address gaps and develop new applications to meet the modern demand for the broader use of metamaterials in advanced devices and systems that require high efficiency for sophisticated, high-performance applications.

1. Introduction

Artificially created metamaterials exist as engineered materials that demonstrate natural properties occurring only under specific conditions. The idea began with Victor Veselago in 1967 and then was revived by Sir John Pendry in 2000 [1,2]. The scientific community ignored Veselago‘s first proposal until it resurfaced after three decades, triggering widespread research and innovation. Metamaterials with their unique properties can transform multiple fields including medical applications, architectural development, military operations, sports equipment, automotive systems, and space exploration [3,4,5]. The original field of metamaterials emerged from electromagnetic metamaterials (EMMs) before expanding to include mechanical metamaterials (MMMs) and acoustic metamaterials (AMMs). The specific applications of AMMs require vibrating surface patterns to modify acoustic properties and superlenses, which enable super-resolution imaging. The internal geometries of metamaterials determine their unique behaviors because they influence permittivity, permeability, the refractive index, and the modulus of elasticity [6,7].

The production of metamaterials faces major obstacles because of their intricate internal structure, strict precision needs, and specific structural requirements. The production of traditional materials has required extensive manual assembly work and dielectric cube machining through subtractive operations. Traditional methods have proven to be both time-consuming and inconsistent while also limiting their practical use and scalability. Additive manufacturing (AM), or three-dimensional (3D) printing, has completely transformed this field for researchers, offering them a versatile means of realizing dimensions and intricate metamaterial structures. It burst onto the scene in the late 1990s and is still thriving. Unlike the old subtractive methods, AM makes an object one layer at a time. With cartoon images in multiple layers of digital files, a model is printed out using a computer and computer-aided design (CAD) software, one layer on top of the other. This method offers a high degree of control of material design, allowing the creation of structures with given geometrical and functional properties.

Recent developments in additive manufacturing, such as multiphoton polymerization (MPP), continuous liquid interface production, and advanced powder-based systems, have driven the limits of what is possible in the 3D-printing application to metamaterials. These mechanisms facilitate the supply of light components having special shapes and complex internal structures without the cost [8]. Furthermore, AM allows for the customization of internal designs of metamaterials to adjust their surface properties, such as how they interact with different wavelengths, how forces are distributed, how they collapse, and how they respond to heat. As a result, there have been significant advancements in areas like biomedicine, aerospace, automotive, and industry, where metamaterials are used to create components that are lighter in weight, are more energy-absorbing, and have unique qualities like a negative Poisson’s ratio (NPR) [9,10,11,12,13]. There is a growing belief that improvements in AM will continue to boost the application of metamaterials, making them part of our daily lives. With more design freedom comes the optimization of shapes, sizes, and orientations of unit cells to improve metamaterial performance. While several reviews have been conducted on individual metamaterial types or specific AM processes, none are as comprehensive as this current article, which thoroughly surveys combined electromagnetic, mechanical, and acoustic metamaterials with detailed AM process analysis. Previous studies by [14,15,16,17] focused on specific applications or single metamaterials categories, whereas our work offers unified coverage across all major metamaterial types and their AM fabrication methods. This review critically summarizes the current state of using AM for producing metamaterials. Following this introduction is an extensive discussion of the main types and characteristics of metamaterials, the exploration of different AM methods for making these materials, and finally the challenges faced and future possibilities ahead in this exciting field.

2. Metamaterial Classification

As mentioned previously, the concept of metamaterials to change how materials interact with electromagnetic waves was initially proposed by Victor Veselago and later expanded by Sir John Pendry. Since then, metamaterials have broadened significantly, finding uses in areas that require both mechanical and acoustic features. This section provides the main categories of metamaterials and what makes each one unique.

2.1. Electromagnetic Metamaterials

Electromagnetic metamaterials are artificial structures that are fabricated on scales much smaller than that of the light wavelength and possess electromagnetic properties that are unimaginable in natural materials [18]. Basically, they respond to electromagnetic waves according to two important material parameters—electric permittivity and magnetic permeability [19]. The intriguing unique nature of EMMs results from the design of their internal structure, rather than the materials of which they are made. This engineering of structure allows electromagnetic wave propagation to be steered in novel ways, some of which result in phenomena such as negative refraction, superlensing, and cloaking [20]. Pendry and co-workers proposed the concept of artificial magnetism based on the split ring resonator (SRR). An artificial structure can create negative permeability and is composed of two non-magnetized loops winding a conductive coil that produces magnetic mutual inductance and together act on the applied magnetic field [21]. This augments the incoming field, so the SRR can exhibit effects such as negative permeability, which would not be shown by natural materials [22].

Furthermore, SRRs have the potential to improve nonlinear effects, which are important for things like generating harmonics and optical switching. One downside, though, is that SRR structures tend to work best over narrow bandwidths, which can limit their use in microwave antenna systems [23]. Additionally, EMMs are crucial in modern technology areas, like 5G, photonics, and terahertz (THz) applications.

EMMs can be categorized into all–dielectric and metal–dielectric metamaterials. All-dielectric metamaterials are made up of one or more dielectric components that have very different dielectric constants. These materials have an advantage because they incur low losses due to their minimal interaction with electromagnetic waves, making them important for optical applications that need to be highly efficient [24]. On the other hand, metal–dielectric metamaterials, like SRRs, mix metal and dielectric elements to obtain interesting electromagnetic properties. Even though they are versatile, the interaction between the electromagnetic waves and the metal parts can cause higher losses, reducing their efficiency in some applications. The early days of EMMs saw significant strides forward, especially after Smith and colleagues introduced a structural model that could achieve a negative refractive index [25]. This was a game changer and led to various strategies for adaptation, including microfluidic, semiconductor, liquid crystal, and graphene-based metamaterials. For instance, Zhou et al. reported on a graphene-based absorber that increases absorption bandwidth and demonstrates the potential of advanced materials for the enhancement of EMM applications [26]. This opens up a new potential in the tailoring of EMMs for specific applications through alterations of their structure, tailored for a specific frequency response [27].

Another fascinating method in EMM design is the transmission line matrix (TLM) technique. This has enabled the realization of a leaky wave antenna that can scan electromagnetic waves in a large scanning angle and has a precise scanning property on the wave scattering. The TLM method has significantly contributed to the better performance of antennas and the widening range of applications for EMMs [28]. Ziółkowski and colleagues have contributed to the development of transmissible EMMs, thus stimulating an advance in optical metamaterials [29]. Moreover, the concepts of hyperlenses and superlenses have emerged, paving the way for super-resolution imaging and other advanced photonic applications [30,31]. Optical metamaterials use a negative-index response to realize imaging resolution, which is better than the usual diffraction limit.

2.2. Mechanical Metamaterials

Mechanical metamaterials are artificial materials engineered to exhibit extraordinary mechanical properties derived from the structural design of their unit cells rather than the properties of their constituent materials [32]. These unique characteristics arise from the geometry and arrangement of the internal structure, enabling properties that are not typically observed in conventional materials. The most prominent mechanical properties of MMMs include zero or negative Poisson’s ratio (commonly associated with auxetic metamaterials (AXMs)), vanishing shear modulus (as in pentamode metamaterials [PMMs]), negative stiffness, and negative compressibility [33,34]. Among the various types of MMMs, AXMs have garnered the most attention due to their numerous advantages over other categories. AXMs exhibit an NPR, meaning they expand laterally when stretched and contract when compressed. This unique behavior is often achieved through specific unit cell designs, such as re-entrant honeycomb structures. Upon application of force horizontally to these structures, the diagonal ribs of the cells spread out because of their shape. This leads to a phenomenon called NPR [35]. Because of this, AXMs are useful for objects that need to resist damage, handle indentations well, absorb vibrations, and take in considerable energy. These materials exhibit unique properties used in suitable applications like protective gear, biomedical devices, and flexible electronics [36], and also fine-tuning of their mechanical response by designing the unit cells to fit specific Poisson’s ratios [37].

The behavior of MMMs at rest or zero frequency does not depend on the size of the unit cells. But for dynamic uses at higher frequencies, those unit cells need to be much smaller than the wavelength in order to work properly. As a result, smaller cells are often needed for dynamic MMMs. Another origami-inspired MMM uses folding patterns to add flexibility. These materials mix their structural traits with clever folding designs, allowing them to have several stable shapes from one structure [38]. This flexibility is extremely helpful for creating deployable structures and soft robotics. Using origami concepts in these designs means they can be stored compactly and set up quickly, which is especially advantageous for aerospace and space exploration [39].

Pentamode metamaterials are a group of MMMs and have distinct mechanical behavior such as a large bulk modulus and a nearly zero shear modulus. This arrangement permits the material to deform with only a small change in volume, resulting in a Poisson’s ratio near 0.5. An example of PMM designs is rockers with conical beams forming diamond-lattice structures. These are useful in applications requiring light weight, vibration-damping, and even mechanical uniformity under compression [40]. Because they can separate the responses in compression and shear, they aid in designing materials that direct stress waves efficiently or absorb shock. In recent years, there has been a trend in research toward the development of multifunctional MMMs that provide additional functionalities such as sensing, actuation, and energy harvesting [41].

2.3. Acoustic Metamaterials

Acoustic metamaterials are engineered to control sound waves in a manner that is not possible with typical materials. They deploy carefully engineered structures to demonstrate some rather special acoustic properties, such as a negative bulk modulus and a negative refractive index, making them valuable for experimenting with sound, reducing noise, and controlling vibrations. The concept of AMMs made its first appearance in 2000 when Sheng et al. designed the first-ever man-made AMM using localized resonance structures [42]. They designed a formation of conical crystals composed of spheres coated in rubber that responded to focused acoustic waves. These rather disordered arrangements showcased some remarkable abilities, including negative elastic constants and functioning as total wave reflectors. Recent years have shown a surge in advancements in AMMs that have opened up exciting new ways to manage acoustic waves in air and other environments. Plus, these metamaterials are being considered for many industrial uses, like acoustic cloaking, imaging, and regulating sound fields. Acoustic cloaking, which enables objects to virtually disappear from sound waves by steering the waves around them, and imaging are also enhanced by the sharpness promoted by AMMs. In addition, AMMs are excellent for increasing sound absorption, which can contribute to the reduction in noise and vibration [43,44,45].

The distinguishing feature of AMMs stems from their exotic inside designs. These structures are frequently created with properties of negative refraction and the coefficient of elasticity. Furthermore, the materials can have a negative bulk modulus, which responds to compression in the opposite way of “normal” materials, allowing incredible control over how sound waves are allowed to propagate [46]. This provides an overall negative acoustic refractive index, whereby even greater control over sound waves, such as bending or focusing sound energy, can be achieved. Researchers and scientists are also interested in integrating AMMs with other functional materials to enhance their performance. For example, a combination of AMMs and piezoelectric or thermosensitive materials may enable adaptive acoustics with external drive dependence [47]. These are finally opening the door to potentially multiuse AMMs that can perform multiple acoustic tasks at the same time. The precision control of sound waves has been in high demand for applications such as noise-canceling tech, vibration isolators, advanced acoustic imaging, and cloaking devices [48].

2.4. Other Metamaterials

Other specialized categories that have emerged with unique characteristics and applications, each presenting specific manufacturing challenges and opportunities for additive manufacturing implementation.

2.4.1. Optical Metamaterials

Optical metamaterials are a specific type of electromagnetic metamaterials that operate within the visible and near-infrared spectrum (380–2500 nm wavelengths). These materials obtain remarkable optical properties through subwavelength structuring, allowing phenomena that are not possible with traditional optical materials [49,50]. Superlenses, which use negative refractive index properties, can achieve resolution beyond the diffraction limit (λ/2), enabling imaging with a spatial resolution close to 50 nm. Optical cloaking devices, first demonstrated in 2006, redirect electromagnetic waves around objects, making them effectively invisible at certain wavelengths. Manufacturing optical metamaterials requires high precision due to their nano-scale features. Current AM methods, especially multiphoton polymerization and direct laser writing, provide the resolution needed for optical uses [51,52]. Recent progress has shown complete photonic band gaps with gap-to-center frequency ratios exceeding 20% in the visible spectrum. These metamaterials are used in advanced imaging systems, optical computing, telecommunication devices, and solar energy harvesting systems with efficiency gains of up to 40% compared to traditional designs [53].

2.4.2. Thermal Metamaterials

Thermal metamaterials control heat flow through engineered microstructures, enabling properties such as thermal cloaking, focusing, and negative thermal expansion. These materials function according to Fourier’s law of heat conduction, with effective thermal conductivity tensors that can be customized through structural design [54,55]. Thermal cloaking devices create temperature-neutral zones, shielding sensitive components from thermal damage while maintaining surrounding temperature profiles with deviations less than 5%. Additive manufacturing of thermal metamaterials often involves multimaterial approaches, combining materials with contrasting thermal properties. Copper–polymer composites produced via selective laser melting exhibit thermal conductivity gradients from 0.2 to 400 W/m·K within single components. Thermal expansion coefficients can be engineered from −50 × 10⁻⁶/K to +200 × 10⁻⁶/K, enabling zero thermal expansion structures for precision instruments and space applications [56,57].

2.4.3. Biomedical Metamaterials

Biomedical metamaterials merge structural functionality with biological compatibility, targeting specific medical uses such as tissue engineering, drug delivery, and medical devices. These materials must meet biocompatibility standards while preserving their engineered properties in physiological conditions [58,59,60]. Bone scaffolds with auxetic characteristics show a 250% increase in cell proliferation compared to traditional designs, supporting faster healing and better integration. Additive manufacturing allows for patient-specific customization with intricate pore structures optimized for particular tissue types. Titanium alloy scaffolds with porosity gradients ranging from 40 to 80% and pore sizes between 100 and 800 μm have been successfully produced using electron beam melting. Shape memory polymer stents, created through stereolithography, show deployment forces 50% lower than traditional designs while maintaining the same radial strength [61,62].

2.4.4. Multifunctional Metamaterials

Multifunctional metamaterials integrate various physical responses within single structures, creating systems that simultaneously control electromagnetic, mechanical, thermal, and acoustic waves. These hybrid systems save space and weight while offering increased functionality [63,64]. Magneto-electro-elastic metamaterials show coupling coefficients between different physical fields, enabling cross-domain sensing and actuation capabilities. Recent developments include structures that simultaneously provide electromagnetic shielding (over 40 dB attenuation), mechanical protection (energy absorption exceeding 50 J/g), and thermal management (thermal conductivity greater than 100 W/m·K) [65,66]. Manufacturing these complex systems requires multimaterial additive manufacturing (AM) processes capable of precise material placement and interface control. Current achievements include components with more than six different material types integrated within single printed parts, maintaining sharp interfaces with transition zones less than 100 μm wide [67].

3. Manufacturing Methods of Metamaterials

Producing metamaterials has long been a significant area of study because they require complex structures to gain their distinctive properties. These structures typically are smaller than the wavelength of light, and their internal structures can be quite elaborate, requiring a high degree of precision and accuracy in their fabrication. The manufacture of metamaterials has changed significantly with their development, expanding into numerous fields. A primary obstacle is the move from two-dimensional (2D) to three-dimensional (3D) forms. However, this move requires having the resolution of these complex unit cell designs along with the ability to print larger features. The difficulty here is to be able to replicate those unit cell shapes at different scales with optimal geometric fidelity to preserve the essential functionalities of the metamaterial [68].

When it comes to creating 2D metamaterials, one of the most popular methods is lithography, which covers techniques like photolithography, soft lithography, electron beam lithography, and two-photon lithography. These processes work like a stamp printing system, where a negative design is transferred onto a substrate and then exposed to an energy source like ultraviolet light or an electron beam. Lithography methods can produce features at submicron resolutions, making them ideal for creating complicated planar structures [69,70]. However, extending these methods to manufacture 3D metamaterial involves stacking multiple layers, which introduces challenges related to alignment and layer uniformity. Moreover, lithographic methods are typically slow, expensive, and limited in scalability.

The evolution of 3D metamaterials ideally requires a manufacturing process that is both cost-effective and capable of high throughput. However, most existing methods fall into one of two categories: high-resolution 3D fabrication or large-scale manufacturing, with only a few methods beginning to bridge the gap [71]. One of the earliest methods for manufacturing 3D metamaterials was direct laser writing (DLW) [72]. Despite its high resolution allowing us to build complex geometries, this technique faces limitations with material compatibility and the throughput of printing [73].

There have also been efforts toward converting conventional manufacturing methods for fabricating 3D metamaterials. Processes like ceramic casting and injection molding have been studied to explore potential in this regard [74]. These approaches include fabricating molds of metamaterial geometries followed by sintering to produce the final parts. Yet, the issues concerning the fabrication, resolution, and sintering process have prevented their use in generating 3D metamaterials with high precision. Additive manufacturing as a novel technique has great potential for narrowing the gap of resolution and scalability [9,10,11,12,13]. Processes such as stereolithography (SLA), selective laser sintering (SLS), and digital light processing (DLP) have enabled the direct production of intricate 3D shapes from digital CAD files. Moreover, AM enables the production of 3D metamaterial structures of complicated geometry, tailored unit cell designs, and multimaterial integration, and thus is considered a powerful competitor for the mass fabrication of metamaterials [75,76,77]. The following section explains the use of AM for fabricating 3D metamaterials, highlighting its advantages as well as the most recent achievements.

Table 1. Comparison of Metamaterial Manufacturing Methods [35,78,79,80,81,82,83,84,85,86,87,88].

Manufacturing Method	Resolution Range	Material Compatibility	Processing Speed	Cost Level	Scalability	Typical Applications	Key Advantages	Primary Limitations
Traditional Lithography	10 nm–1 μm	Photoresists, limited metals	Very Slow (hours/cm2)	Very High	Very Poor	Research prototypes, 2D structures	Ultra-high precision, established process	2D limitation, expensive equipment
Material Extrusion (FDM/FFF)	100–300 μm	Thermoplastics, composites, metals	Fast (10–100 cm3/h)	Low	Excellent	Large components, rapid prototyping	Cost-effective, wide materials, scalable	Lower resolution, layer adhesion
Vat Photopolymerization (SLA/DLP)	25–100 μm	Photopolymers, ceramics (limited)	Medium (5–50 cm3/h)	Medium	Good	Complex geometries, detailed parts	High accuracy, smooth surfaces	Material limitations, post-processing
Powder Bed Fusion (SLM/DMLS)	20–100 μm	Metals, alloys, ceramics	Medium (2–30 cm3/h)	High	Good	Aerospace, medical implants	Strong materials, design freedom	High cost, support structures
Multiphoton Polymerization (MPP)	50–200 μm	Specialized photoresists	Very Slow (μm3/h)	Very High	Very Poor	Nano-applications, research	Ultra-high resolution, 3D capability	Very slow, expensive, limited materials
Inkjet 3D Printing	50–200 μm	Polymers, metals, ceramics	Fast (20–200 cm3/h)	Medium	Excellent	Multimaterial parts, electronics	Multimaterial capability, speed	Material viscosity limits, resolution
Aerosol Jet Printing	10–300 μm	Conductive inks, polymers	Fast (7 cm2/min)	Medium	Good	Electronics, sensors, THz devices	Conformal printing, fine features	Material compatibility, equipment
Electron Beam Melting (EBM)	50–200 μm	Reactive metals, alloys	Medium (5–40 cm3/h)	Very High	Good	Biomedical, aerospace	Vacuum processing, reactive materials	Very high cost, limited materials
Binder Jetting	100–400 μm	Metals, ceramics, sand	Fast (50–500 cm3/h)	Medium	Excellent	Large parts, casting patterns	High speed, large builds	Post-processing required, limited strength
Direct Energy Deposition (DED)	200–2000 μm	Metals, alloys	Medium (10–100 cm3/h)	High	Good	Repair, large components	Material flexibility, repair capability	Lower resolution, rough surfaces

illustrates a comparative overview of various methods employed for the manufacturing of metamaterials. This clearly identifies the suitability of each technique based on its cost, scalability, merits, and demerits.

• Performance Metrics Summary:
• Among various manufacturing techniques, multiphoton polymerization (MPP) offers the highest resolution (<1 μm), followed by traditional lithography (10 nm) and stereolithography (SLA) at around 25 μm. In terms of processing speed, binder jetting is the fastest (500 cm³/h), ahead of inkjet printing (200 cm³/h) and fused deposition modeling (FDM) (100 cm³/h). When considering cost-effectiveness, FDM stands out as the most economical method, followed by binder jetting, inkjet, and SLA. For surface quality, MPP provides the best finish, followed by traditional lithography, SLA, and inkjet printing. Lastly, in scalability, FDM ranks highest, followed by binder jetting, inkjet, and SLA.

4. Manufacturing Metamaterials Using Additive Manufacturing

Additive manufacturing has revolutionized the production of 3D parts with its layer-based process. It offers a high degree of design and material flexibility where the fabrication of complex structures is desired [89]. AM has many positive advantages, such as design freedom, mass customization, waste minimization, and producing complex shapes where traditional manufacturing fails. Given that AM allows for such fine-grained control makes it valuable when dealing with metamaterials that require micro-scale unit cells and macro-scale overall designs [90]. Recently, there have been significant strides in using AM for producing 3D metamaterials, tapping into popular techniques like material extrusion, vat polymerization, powder bed fusion (PBF), material jetting, and directed energy deposition (DED) [91].

One of the first examples of 3D metamaterials used direct laser writing, which is a type of vat polymerization [92]. While this technique was very precise, it faced challenges like slow production speeds and limited material options. Despite these challenges, AM remains necessary for achieving many properties of metamaterials. In theory, 3D metamaterials could be manufactured using conventional manufacturing methods. However, in practice, AM enables the creation of complex designs and structures that otherwise would be impossible [93]. The computer-controlled approach of AM ensures the reproducibility and accuracy required to fabricate the complex internal structures of 3D metamaterials, advancing the state of the art in this field [94].

The initial breakthrough in manufacturing 3D metamaterials using AM was achieved by Shelby et al. [95], who produced a metamaterial exhibiting a negative refractive index, initially limited to medium wave (MW) frequencies. Subsequent research extended the operational range of these metamaterials to terahertz and optical frequencies, expanding their applicability [20,96]. Early 3D metamaterial designs were typically single-layered structures. However, Valentine et al. [97] demonstrated the feasibility of 3D electromagnetic metamaterial structures by stacking multiple functional layers in precise arrangements. These advancements in electromagnetic and optical metamaterials led to applications designed to operate at much larger wavelengths and length scales, such as those in acoustics, thermodynamics, and mechanics [98].

Vat photopolymerization (VP) is one of the most widely used AM processes for manufacturing 3D metamaterials. While primarily suitable for photopolymers, VP has also been adapted for ceramics and metals in limited applications [99,100]. High-precision VP methods include stereolithography, multiphoton polymerization, and direct ink writing (DIW) [101]. SLA has been successfully applied to produce mechanical octet lattices for energy absorption and optical metamaterials [36]. MPP employs femtosecond pulsed lasers to initiate VP, offering exceptional precision; however, it is limited to a narrow range of materials and therefore is unsuitable for large-scale production [102].

On the other hand, DIW uses colloidal inks that solidify under pressure, providing a versatile alternative for specific applications. Material extrusion (ME) has been widely used to fabricate 3D polymeric metamaterials [103]. PBF methods, including SLS, direct metal laser sintering (DMLS), selective laser melting (SLM), and electron beam melting (EBM), have shown promise for manufacturing 3D metallic metamaterials. These processes are beneficial for MMMs, where strength and durability are critical [104,105,106]. DED techniques are starting to be considered for creating 3D metamaterials, although they are less commonly used [107]. However, additive manufacturing plays a significant role in making 3D metamaterials for many different applications. The following sections review the latest advancements in manufacturing 3D metamaterials using AM, categorizing them into electromagnetic, mechanical, and acoustic metamaterials, each with its respective subcategories.

4.1. Electromagnetic Metamaterials Using Additive Manufacturing

Additive manufacturing processes have been pivotal in advancing 3D EMMs by enabling the precise fabrication of complex structures. Three-dimensional EMMs produced through AM utilize materials such as acrylonitrile butadiene styrene (ABS), copper–graphene composites, and titanium dioxide (TiO₂)-doped polymers for functionalities including electromagnetic shielding, waveguiding, and refractive index tuning. High-resolution techniques, such as SLA and PBF, provide the spatial precision necessary for controlling electromagnetic behavior, enabling applications in antennas, sensors, and stealth technologies [108]. Commonly used AM processes for 3D EMMs include ME, VP, and PBF, each offering unique benefits depending on the design and functional requirements. ME, particularly fused deposition modeling (FDM), is one of the most widely adopted techniques. It constructs 3D structures by depositing layers of molten thermoplastic polymers, often blended with high-dielectric particles to create photonic crystal (PC) structures [109]. FDM’s compatibility with CAD-based design makes it highly efficient for producing intricate geometries. However, its inherent surface roughness can hinder the propagation of visible, ultraviolet, and infrared light. Despite this, FDM remains well-suited for fabricating 3D metamaterials operating in the THz and MW frequency ranges due to its resolution, speed, and material versatility [110,111].

Another ME-based process, inkjet printing (IJP), is used to manufacture flexible and intricate structured 3D EMMs by precisely depositing ink droplets [112]. Challenges with IJP include selecting suitable inks and curing processes, because conductive inks typically require heat treatment to evaporate the solvent and sinter metallic particles. In contrast, dielectric inks are often cured using ultraviolet radiation, which cannot withstand the high temperatures needed for conductive ink sintering [113]. In addition, split ring resonators are metal–composite metamaterials that exhibit strong interactions with electromagnetic radiation, which have been successfully manufactured using the IJP method. SRRs are more effective than all–dielectric metamaterial structures in interacting with electromagnetic waves [114].

Vat photopolymerization is another AM process often employed for manufacturing 3D EMMs. Processes such as SLA and MPP fall under this category. SLA operates based on the spatially controlled solidification of a photosensitive material, known as a photoresist, using a focused light source, such as a light-emitting diode (LED) light reflected by a light modulator. This process cures the photoresist layer by layer, creating detailed 3D structures [101]. SLA has been effectively utilized to fabricate core–shell metamaterials and graded-index photonic crystals, which enable control over electromagnetic wave absorption and transmission. For instance, Yin et al. [115] fabricated dome-shaped PCs using SLA with a dielectric core to emulate an electromagnetic “black hole” across 12–15 GHz. Additionally, embedding ceramic particles such as silica or titania into the SLA resin has enabled the production of high-dielectric PCs with tunable bandgaps, extending into the THz range. A full silicon dioxide (SiO₂) PC fabricated via SLA demonstrated a bandgap near 470 GHz, showcasing SLA’s capability in high-frequency applications [116].

Multiphoton polymerization is another VP-based process that uses the simultaneous absorption of multiple photons to initiate photopolymerization. This process allows the creation of extremely detailed 3D shapes with tiny features that resemble crystal lattice structures [117]. MPP has the best resolution among additive manufacturing techniques, so it is ideal for crafting complex metamaterial designs like woodpile or chiral photonic crystals. For instance, spiral and bi-chiral photonic crystals that have specific directional traits using MPP have been produced [118]. In addition, MPP-compatible photoresists photonic crystals with full band gaps in visible and near-infrared light regions can be fabricated by adding high-refractive-index nanoparticles such as TiO₂. MPP has also been indispensable in the fabrication of hybrid metal–dielectric metamaterials [79,119]. A combination of photopolymerization with methods such as photoreduction or post-deposition has been used to fabricate structures such as metallic helices and U-shaped resonators exhibiting optical properties, which are crucial for advanced sensing and communication [120].

As for the powder bed fusion techniques, they also contribute significantly in the preparation of 3D electromagnetic metamaterials [121]. Such methods entail melting and fusing layers of metal powder using a laser or an electron beam to form solid parts. Due to its precise nature, PBF processes work well in the fabrication of complex 3D EMM structures with exceptional electromagnetic properties. AM also permits mixing more materials in one 3D EMM design, hence enabling new functionalities. The integration of conductive, dielectric, and magnetic materials will provide multifunctional 3D EMMs that can be used for different purposes, for instance, gradient-index 3D EMM systems promoting electromagnetic wave manipulation in distinct frequency bands [122]. This unprecedented freedom in design that AM affords has ushered in the development of new 3D EMM shapes such as metasurfaces and volumetric metamaterials, thereby greatly extending the frontiers of our ability to manipulate electromagnetic waves. Having the possibility to fabricate ultra-small features and to align unit cells very accurately, AM has become an indispensable element in the modern field of EMM, which is bringing advances in the field of communication technologies, imaging systems, and secure applications [13].

Table 2. Electromagnetic metamaterials are produced through additive manufacturing with corresponding materials, functions, and targeted applications.

Material	Functionality	AM Processes/Production Method	Performance	Targeted Application	Ref.
Acrylonitrile butadiene styrene (ABS)	Multimeter-wave waveguide	Fused deposition modeling (FDM)	Impressive antenna aperture efficiency	Satellite communication	[123]
Copper–graphene composite	Electromagnetic shielding	Stereolithography (SLA)	Improved electrical conductivity	Aerospace, automotive	[124]
Silicon carbide (SiC)	Dielectric properties	Powder bed fusion (PBF)	High dielectric constant	Antennas, radar systems	[125]
Aluminum-doped zinc oxide	Transparent conductive coating	Atomic layer deposition (ALD)	High optical transmittance and conductivity	Optical sensors	[126]
Ferrite-based composites	Magnetic wave absorption	Selective laser melting (SLM)	Strong magnetic/electromagnetic response	Waveguides, stealth technology	[127]
TiO2-doped polymers	High refractive index	3D printing	Improve light manipulation	Lens fabrication	[126]
Graphene	Plasmonic waveguides	Chemical Vapor deposition (CVD)	Enhanced plasmonic resonance	Optical communication	[128]
Silver nanowires	Flexible electronics	Inkjet printing	Excellent conductivity and flexibility	Wearable device	[129]
Iron oxide nanoparticles	Magnetic resonance imaging (MRI)	3D printing	Enhanced imaging quality	Biomedical Imagine	[130]

presents electromagnetic metamaterials fabricated through additive manufacturing, highlighting their tailored materials, functions, and applications.

4.1.1. Microwave and Radiofrequency Metamaterials

Metamaterials for microwaves (MWs) and radiofrequency (RF) have caught the attention of the scientific community lately because they can work in frequency ranges where there is no molecular resonance, thereby offering considerable control over how electromagnetic waves behave. Three-dimensional MW and RF metamaterials are now often created using additive manufacturing processes, which makes it easier to create complex 3D structures for advanced uses [131]. For example, Garcia and his team showed how they could use fused deposition modeling to produce anisotropic 3D shapes that have strong resonant effects at high frequencies. These metamaterials were designed specifically for the MW range and showed impressive resonant performance [132]. Similarly, they produced 3D dielectric invisible cloaks that work in the MW X-band (8.6–12 GHz) using FDM, highlighting how AM can make detailed and functional MW metamaterials [133]. Moreover, Lu and colleagues created woodpile-like 3D metamaterials with a bandgap frequency of 95 GHz using FDM [134]. These structures, made from rods 0.4 mm in diameter with a periodic spacing of 1.6 mm, used high-purity alumina powder to make a dielectric paste for extrusion. The researchers found that the sintering and drying processes were crucial for the quality of the final 3D structures, achieving the best results with a slow heating rate of 2 °C/min [13].

In addition, Kronberger and his team also used FDM to create planar, periodic frequency-selective surfaces (FSSs) aimed at 10 GHz [135]. These were made from conductive filaments with consistent magnetic properties, ensuring they absorbed well and performed effectively in MW frequencies. Similarly, Isakov and his group also showed how FDM could be utilized with polymeric composites to produce 3D resonator structures [136]. They made 3D metamaterials with defined anisotropy, effective permittivity, and Mie-type resonance by layering thermoplastic filaments with high-permittivity inorganic microparticles and pure polymer. These metamaterials reached high absorption frequencies close to 15.75 GHz and even exhibited negative refractive indices, making them suitable for a variety of broadband MW applications.

Vat photopolymerization has also been employed to manufacture 3D MW and RF metamaterial. Cai et al. [137] produced water-embedded 3D metamaterial structures coated with metal using micro-stereolithography, achieving negative permeability and permittivity at RF frequencies with negative refraction properties. Yin et al. [138] developed radar absorption-based 3D metamaterials with gradient refractive indices using SLA. These structures, composed of a gradient-index refractor, absorber, and reflector, exhibited enhanced an absorption performance of –10 dB across the 12–18 GHz broadband. The manufactured 3D structures were among the first radar absorption-based 3D metamaterials designed for stealth aircraft, demonstrating controlled wave propagation and efficient attenuation of radar signals. Selective laser melting, a subset of powder bed fusion, has been used to manufacture MW-based slow-wave 3D metamaterials. These metamaterials convert electric beam energy into radiation by associating the alternating current (AC) beam with an interaction circuit. Innovative MW sources have been discovered by replacing conventional interaction circuits with 3D metamaterial structures. However, strong interactions between electromagnetic waves and metallic components in these 3D metamaterials result in high losses, limiting their efficiency in optical applications [139]. Recent applications of 3D MW and RF metamaterials include advanced antennas, electromagnetic isolation devices, nano-scale metamaterial absorbers, and imaging systems [140,141]. Furthermore, various materials have been utilized in AM to enhance the properties of 3D MW and RF metamaterials [142,143,144].

4.1.2. Terahertz Metamaterials

Terahertz metamaterials, operating in the frequency range of 0.1–10 THz, have become a critical area of research due to their potential applications in security, imaging, communication, and sensing [145]. These metamaterials are designed with specific unit cell shapes to control THz waves, resulting in some very interesting electromagnetic features—like a negative refractive index, better wave absorption, and customized transmission traits. But making 3D THz metamaterials is not easy. The unit cell size must be smaller than a few tens of micrometers to obtain the right properties [146]. Many traditional manufacturing techniques are not satisfactory when it comes to precision and scaling up, which is why additive manufacturing is such a great fit for developing these materials. Techniques like laser decal transfer, electrohydrodynamic jet (e-jet) printing, and digital aerosol jet printing (AJP) have been successfully used to create 3D THz metamaterials [147,148]. For instance, Tenggara et al. [149] employed e-jet printing to make a 3D THz metamaterial sensor from electrically tuned SRR unit cells, as shown in Figure 1. This sensor had patterns as tiny as 5 µm and was printed on a flexible polyimide substrate, which allowed it to be six times more sensitive than those made on silicon wafers, thereby showing how flexible substrates can boost the performance of 3D THz metamaterial sensors.

Moreover, micro-fused deposition modeling (micro-FDM) processes with resolutions close to 100 µm have been employed to manufacture 3D THz metamaterials. This AM process enables the manufacturing of complex 3D metamaterials for THz wave manipulation. In addition, inkjet printing has been utilized to manufacture 3D THz metamaterial absorptive surfaces, achieving absorption rates of 93.5% at 0.102 THz and 99% at 9.21 GHz [150]. Murata et al. [151] specified an IJP system that facilitated the manufacturing of 3D metallic strands of a few microns on an unprocessed substrate for THz application. Kashiwagi et al. [152] utilized a micro-IJP that included silver ink to manufacture 3D THz metamaterials with resonant frequencies of 0.305 THz and 0.137 THz for X- and Y-polarized waves, respectively.

Aerosol jet printing has bridged the gap between high-resolution and low-cost AM processes by using low-viscosity inks (1–25,000 cP) to fabricate micron-sized features. AJP has been employed to manufacture 3D THz metamaterial-based filters operating at 230 GHz, 245 GHz, and 510 GHz. These advancements demonstrate its capability to produce high-performance filters, mixers, and reservoirs for THz applications [153]. Additionally, multiphoton polymerization has demonstrated exceptional promise in manufacturing 3D THz metamaterials with submicron-scale features. MPP was also used in a double-molding process to manufacture highly refractive silicon photonic bandgap 3D metamaterials [154]. Steinberg et al. [155] manufactured wooden pile 3D metamaterials using SU-8, a negative photoresist epoxy. These 3D structures were subsequently treated with helium, immersed in a titanium isopropoxide and ethanol mixture, and air-dried to form a solid TiO₂ layer. The 3D polymeric structure was then subjected to heat treatment at 600 °C for four hours, resulting in high-quality 3D TiO₂-based THz metamaterials.

High-resolution techniques like MPP are impressive for making complex features, but for practical, large-scale 3D THz metamaterials, lower-resolution methods like IJP and FDM really excel. Plus, with the rise in multimaterial and multihead printing systems, additive manufacturing has become more flexible in creating 3D metamaterials for THz applications. This means that different materials can be mixed in one structure, even if those materials need different curing processes. From sensors and absorptive surfaces to filters and photonic bandgap devices, AM keeps broadening the horizons for creating 3D THz metamaterials, tackling challenges head-on and expanding how electromagnetic waves are managed.

4.1.3. Photonic Crystals

Photonic crystals are a special kind of metamaterial, and their unique properties come from their structures, setting them apart from other metamaterials. In the case of PCs, the size of each unit cell is often similar to the wavelength of the light radiation, providing precise control over electromagnetic waves. A common configuration for such crystals is the woodpile, a 3D structure known to form a stop band and exhibit an optical bandgap [156]. Özbay and colleagues [157] showcased how effective this design can be in forming those optical bandgaps. To manipulate waves efficiently, the ideal unit cell length in PC structures is often the same as or shorter than the operational wavelength. Additive manufacturing methods have been applied to create these 3D PCs, which allows for considerable flexibility in both design and materials. For example, 3D PCs were made from TiO₂ using the fused deposition modeling process. These structures demonstrated functional stop bands around 38 GHz and 39 GHz, highlighting how adaptable FDM can be for creating millimeter-scale PCs [158]. The ability of FDM to deposit multiple materials further enhances its suitability for manufacturing 3D PCs. Vat photopolymerization processes, including stereolithography have also been employed for manufacturing 3D PCs.

Moreover, the use of ceramic particles in photoresist materials has allowed the manufacture of structures with higher dielectric properties, resulting in PCs with tailored bandgaps. For example, 3D PCs manufactured using SLA made with 40 vol% silica–epoxy resin demonstrated a bandgap between 3.2 GHz and 10.9 GHz, while those made with 10 vol% titania–epoxy resin had a bandgap between 0.7 GHz and 6.9 GHz. These differences between bandgaps highlight the role of dielectric constants in determining the operational frequency range of PC structures [159]. Kirihara and Ceram [160] utilized SLA and manufactured 3D PCs by diffusing 50 vol.% SiO₂ in a photoresist and sintering at high temperatures (600 °C–1400 °C). This process resulted in shrinkage of approximately 24.5% in the X-Y direction and 26% in the Z direction. SLA has also been employed to create inverse 3D PCs by casting ceramic slurries into epoxy molds. Yin et al. [161] designed inverse diamond-shaped 3D PCs composed of SiO₂-TiO₂ ceramics, achieving an attenuation of 30 dB around 17 GHz. Moreover, Liang et al. [162] employed SLA and manufactured 3D PCs with broader bandgaps by using two different ceramic concentrations (55 vol% and 60 vol%) and producing a gradient in the dielectric constant of the PC. The bandgap width increased by 117% using the higher ceramic concentration.

Furthermore, multiphoton polymerization is a promising AM process for manufacturing chiral 3D PCs with superior mechanical stability. These chiral PCs are exceptionally efficient in generating bandgaps and can be manufactured using low-refractive-index materials. The chiral 3D PCs manufactured using MPP exhibited a complete photonic bandgap with a 3.5% gap ratio and a high refractive index of chalcogenide glass (2.45–2.53), achieved by depositing a thin layer on the surface via thermal vapor deposition [163]. Moreover, Duan et al. [164] demonstrated the formation of TiO₂ nanoparticles on a 3D structure and the existence of photonic bandgaps from a TiO₂-doped resin. Further advancements in MPP have enabled the incorporation of advanced materials, such as quantum dots, into 3D PCs. Quantum dot-doped photoresists enable controlled impulsive emission, thereby enhancing applications in quantum optics and optical communication. A well-defined 3D array of dielectric particles can be created with enhanced optical properties by backfilling MPP-manufactured 3D PCs with high-refractive-index materials [165].

In addition, 3D metallic dielectric PCs have been fabricated using MPP to create composite structures that combine photoresists with metal salts. These metallic dielectric structures exhibit high spatial resolution, opening new paths for PC development. However, achieving high-resolution composite structures often requires the use of expensive two-photon absorption dyes, which pose limitations. Chaudhary et al. [166] addressed this challenge by manufacturing 3D composite structures composed of metal and polymer, achieving minimum feature sizes of 390 nm without relying on dyes. This demonstrates the potential for cost-effective fabrication of 3D PCs. In recent times, direct laser writing has been combined with self-assembly techniques to manufacture advanced 3D PCs, such as waveguides within colloidal crystals. These waveguides enable light propagation along radial paths with radii only several times the wavelength of the propagating light. Figure 2 presents a 3D bi-chiral PC created using MPP and metal-enhancement. The structure was detached and repositioned onto a secondary substrate for improved optical function, illustrating a pathway for hybrid AM-integrated photonic devices [167]. The development of 3D PCs using the additive manufacturing process has significantly advanced their application potential. Titanium-doped acrylate monomers, oligomers, and other high-refractive-index materials integrated into 3D PCs have enabled the manufacture of 3D structures with photonic bandgaps, demonstrating the feasibility of AM in producing optically active devices for various applications, including waveguides, optical filters, and quantum communication systems.

4.1.4. Other Electromagnetic Metamaterials

Three-dimensional electromagnetic metamaterials with unique functionalities continue to evolve through additive manufacturing processes, enabling the manipulation of material properties such as permittivity and permeability. For instance, 3D-printed blocks of polymer–ferrite composites demonstrated nearly constant permittivity and permeability over the tested frequency range, overcoming the conventional dependency of material properties on operational frequencies. Kim et al. [168] manufactured cylindrical 3D-shaped flexible structures using AM processes, achieving over 96% absorption across all polarization angles. These 3D structures demonstrate the versatility of AM in manufacturing flexible and efficient electromagnetic absorbers. IJP has been utilized to produce resonant surfaces for biological sensors, highlighting its capability for integration into microfluidic systems. For example, Ling et al. [169] demonstrated the use of IJP to manufacture absorbent conductive adhesives within polymethyl methacrylate (PMMA) microfluidic channels. Their results showed a reduction in resonant frequency from 4.4 GHz to 3.97 GHz, achieving absorption rates below 90% in both empty and water-filled channels. Combining the AM technique with microfluidic channels enables the creation of small 3D structures with particular electromagnetic properties.

In addition, incorporating stereolithography with other AM methods dramatically enriches the options for fabricating 3D EMMs. For instance, Rudolph and Grbic [170] successfully fabricated 3D cubes with SLA they metalized with copper and added capacitors. This configuration, however, turned out to yield a negative value for the refractive index at 1.5 GHz. Meanwhile, Fernandez et al. [171] constructed a multiphoton polymerization system with high-speed laser scanning arrangement in a combination with a piezoelectric stepper, and demonstrated the fabrication of better-precision millimeter-sized 3D shapes. Takeyasu et al. [172] demonstrated that the development of new materials would allow them to incorporate metal sensitive functionalities in MPP photoresists, in order to enable selective metal deposition onto polymers. These applications enabled the fabrication of hybrid overcast 3D structures with enhanced electromagnetic performance. All of this highlights how capable the AM process can be in overcoming the manufacturing challenges of 3D EMMs. The researchers and academics are anxious to provide innovative 3D designs and manufactured structures that possess tailored electromagnetic performance through the use of AM methods such IJP, SLA and MPP, which have the potential to open up applications ranging from sensors, absorbers, and waveguides to antennas. As AM continues to be combined with material optimization and sophisticated surface treatments, the possibilities for 3D EMMs remain expansive.

4.2. Mechanical Metamaterials Using Additive Manufacturing

Mechanical metamaterials show remarkable mechanical properties that come from their special microarchitectures, not just the materials from which they are made. Features like a negative Poisson’s ratio, their ability to absorb energy, and adjustable stiffness make MMMs very useful for a range of engineering applications [173]. In the world of 3D metamaterials, MMMs have gained considerable attention because of their intricate shapes and multi-scale characteristics that can be created with great precision in additive manufacturing. Additive manufacturing has been crucial in pushing forward the design and creation of 3D MMMs, making it possible to produce lattice structures that would be difficult or even impossible to make with traditional methods. Two of the most common AM techniques for making 3D MMMs are vat photopolymerization and selective laser melting, which help in developing auxetic metamaterials and pentamode metamaterials—two key subtypes, each with their own unique structures and functions [174,175].

Table 3. Mechanical metamaterials fabricated using additive manufacturing processes, showing materials, functionalities, processes, and applications.

Material	Functionality	AM Process/Production Method	Performance	Targeted Application	Ref.
Epoxy resin	Energy absorption	Stereolithography (SLA)	Lightweight, excellent recovery after 70% strain	Airplanes, trucks, battery electrodes	[176]
Low-melting-point alloy (LMPA)	Tunable energy absorption	3D-printed with PVA	Dynamic performance	Reusable energy absorption	[177]
Epoxy resin	Negative Poisson’s ratio	Multimaterial 3D printing	Enhanced mechanical properties	Flexible armor, actuators	[178]
Ti-6Al-4V	Vanishing shear modulus	Selective laser melting (SLM)	Improved load bearing	Elastic absorbers, cloaking	[179]
Polyamide 6 (PA6)	Property tuning	Multijet fusion (MJF)	Improved mechanical properties	Energy conservation	[180]
Polyurethane (PU)	Enhanced mechanics	Fused filament fabrication (FFF)	Higher stiffness, energy dissipation	Protective equipment	[181]
PEGDA	Twistable compression	3D laser micro printer	>2% twist per axial strain	Cloaking Structure	[182]
Polylactide (PLA)	Enhanced strength	Selective laser melting (SLM)	Better mechanical properties	Biomedical	[183]
Carbon nanotube (CNT) composites	Energy absorption	Selective laser sintering (SLS)	Superior mechanical properties	Aerospace, military	[184]
Nickle–titanium (Ni-Ti) alloy	Shape memory	Selective laser melting (SLM)	Reversible deformation	Smart devices	[185]
Titanium grade 5 allow (Ti-6Al-4V)	Dynamic behavior	Selective laser melting (SLM)	Higher failure strain and toughness	Energy production, aerospace	[186]
Thermoplastic polyurethane (TPU)	Tunable sensing	Fused deposition modeling (FDM)	Wide sensing range and higher sensitivity	Wearable applications	[187]

presents a selection of 3D MMMs fabricated using different AM processes, demonstrating properties such as energy absorption, NPR, and twistable deformation with materials like epoxy resin, titanium grade 5 alloy (Ti-6Al-4V), and poly (ethylene glycol) diacrylate (PEGDA). The wide range of mechanical functionalities and performance from enhanced stiffness to shape memory effects, highlights the design versatility that AM brings to structural and protective applications.

Auxetic metamaterials characterized by a negative Poisson’s ratio, expand laterally when stretched, offering superior energy absorption, damage resistance, and vibration damping. Vat photopolymerization, including stereolithography and multiphoton polymerization, are often used to manufacture 3D AXMs with high precision [188]. The layer-by-layer curing process in VP enables the creation of re-entrant and chiral 3D geometries, which are essential for auxetic behavior. For instance, SLA has been utilized to manufacture lightweight 3D auxetic lattice structures for protective applications, resulting in controlled deformation and enhanced mechanical stability. MPP has further enabled the manufacturing of 3D AXMs at micro- and nano-scale resolutions, expanding their potential applications in the biomedical and aerospace industries.

On the other hand, 3D pentamode metamaterials exhibit extreme mechanical anisotropy, resembling a fluid-like solid with a near-zero shear modulus and a high bulk modulus. These properties make PMMs ideal for vibration isolation, acoustic wave manipulation, and shock absorption [189,190]. Selective laser melting has been extensively used to manufacture 3D PMMs from metallic powders, achieving the high strength and stiffness required for load-bearing applications. The layer-by-layer fusion process in SLM allows for the precise construction of conical beam lattices and diamond-shaped 3D geometries, both of which are integral to pentamode behavior [191,192]. SLM has also been employed to manufacture 3D metallic MMMs for biomedical applications, particularly in manufacturing 3D lattice structures for implants and prosthetics. MMMs with functionalities beyond extremal behavior have also been fabricated using VP. Figure 3 shows a structure designed by Frenzel et al. [180], which undergoes a controlled twist under axial compression. Fabricated using 3D laser microprinting, these metamaterials achieve twist rates exceeding 2° per percent axial strain.

Several studies have compared the mechanical properties of different lattice 3D geometries, including diamond, truncated cuboctahedron, and cubic designs that were manufactured using SLM, highlighting their suitability for load-bearing and biomedical applications [193]. Its ability to control mechanical properties by changing the unit cell geometry and material composition has made SLM an invaluable tool for the production of the patient-specific biomedical devices. The coupling of AM with computational design platforms has also increased the scope of 3D MMM manufacture. Topology optimization and generative design algorithms help design large, efficient structures that have the right strength-to-weight ratio. These methodologies are especially suitable for fabricating 3D AXMs and PMMs in which performance is very sensitive to the geometric structures [194]. Additionally, AM allows for the incorporation of multimaterial printing, enabling the combination of stiff and flexible materials within a single 3D structure, further enhancing the functionality of 3D MMMs. The following sections discuss the several applications of AM processes for manufacturing 3D AXMs and PMMs.

4.2.1. Auxetic Metamaterials

Auxetic metamaterials are recognized by their zero or negative Poisson’s ratio, which sets them apart from conventional materials that typically have a positive Poisson’s ratio. The unique property of AXMs, which expand laterally when stretched, results in enhanced mechanical characteristics, including increased indentation resistance, improved fracture toughness, a higher transverse shear modulus, exceptional impact energy absorption, and better wave damping. These properties make AXMs suitable for a wide range of applications. Despite their unconventional behavior, auxetic properties have been observed in various material categories, including metals, ceramics, polymers, composites, and biological tissues [195,196]. Elipe and Lantada [197] developed a comprehensive CAD library of 3D auxetic geometries, exploring how cell shape, beam alignment, and hinge angles influence Poisson’s ratio and other mechanical properties. These systematic studies have guided the optimization of 3D AXMs for various applications.

Selective electron beam melting (SEBM) has been instrumental in manufacturing 3D metallic AXMs, particularly those made from the Ti-6Al-4V alloy. In a research work presented by Schwerdtfeger and co-workers [198], SEBM was employed to fabricate accurate 3D auxetic lattices by electron-beam fusing 100 µm thick metal powder layers. Their compression tests of these 3D materials indicated that the Young’s modulus depends on the relative density following a power-law with an exponent of approximately 2.5. On another note, Yang et al. [199] utilized SEBM to fabricate 3D auxetic lattices using the Ti-6Al-4V alloy and subjected them to compressive characterization. Their findings demonstrated how crucial accurate numerical models are for achieving optimal designs, revealing significant improvements in the precision of metallic cellular structures. SEBM was also recently employed to examine the mechanical behavior of 3D auxetic lattices in various orientations, in order to gain insight into how to tune their structural parameters for specific applications [200].

Selective laser melting is now taking this process even further, opening the door to even more methods of creating 3D AXMs. Li et al. [201] fabricated SLM-processed NPR Ni-Ti-based 3D shape memory alloys (SMAs), performing subsequent heat treatment to lower stress-cracked and residual porosity and to improve ductility. This consists of a multidisciplinary approach that is critically necessary for establishing 3D AXMs that are appropriate for advanced usages. Moreover, Ingrole et al. [202], fabricated re-entrant 3D AXMs using fused deposition modeling. Their designs showed a 65% increase in compressive strength and a 30% enhancement in energy absorption compared to conventional re-entrant 3D structures, showcasing how AM can improve auxetic performance.

Multiphoton polymerization has allowed fabricating 3D AXMs with submicron resolution. Bückmann et al. [203] manufactured 3D AXMs with submicronic unit cells, to an extent where a Poisson’s ratio of −0.13 was possible. MPP has also been utilized to develop advanced 3D auxetic structures, including chiral and hybrid types, which merge re-entrant geometries with other features for better mechanical stability and flexibility. For instance, Xiong et al. [204] refined re-entrant 3D auxetic structures using MPP by substituting overhanging struts with inclined ones, which lessened the need for support structures and reduced stress concentrations. Finite element modeling (FEM) revealed that these modifications reduced the Poisson’s ratio and improved mechanical stability. Similarly, multi jet fusion (MJF) processes were employed to manufacture the 3D auxetic structure of both macroscopic and microscopic polymers, exhibiting a Poisson’s ratio of –0.8 [205]. Figure 4 shows a 3D AXM fabricated using MJF, designed for applications in energy absorption, vibration mitigation, and stretchable electronics. The structure measures 100 mm × 100 mm, with beam ligaments approximately 1 mm thick [206].

Three-dimensional AXMs have demonstrated significant potential in biomedical applications. For instance, 3D auxetic stents fabricated using SEBM molds and polymeric materials provide enhanced stability and performance due to their unique deformation mechanisms. Auxetic foam and honeycomb filters help clean fouled filters, adjust pore size and shape, and compensate for pressure build-up due to fouling, more effectively than non-auxetic filters. Stretching the auxetic filters enhances performance by allowing pores to open in both directions [174]. Geng et al. [207] manufactured 3D cylindrical stents with chiral microstructures using SLS, observing that the NPR varied based on circumferential strut numbers and ligament angles. Orthopedic devices such as auxetic bone screws and bone plates have also benefited from AM processes. Yao et al. [208] manufactured auxetic bone screws using SLM, highlighting their excellent fixation capabilities and mechanical strength. Vijayavenkataraman et al. [209] manufactured re-entrant 3D honeycomb and rib structures for orthopedic bone plates using direct metal laser sintering, demonstrating improved mechanical performance in clinical applications.

Emerging applications of 3D AXMs include stretchable electronics, vibration isolation, and advanced energy absorbers. For example, Jiang and Li [210] introduced re-entrant 3D core cells into primary chiral cells, creating hybrid 3D auxetic designs that combine multiple deformation mechanisms. These 3D structures exhibited auxetic behavior across a wide range of strains and offered tunable mechanical properties through geometric modifications. Moreover, Wang et al. [211] manufactured 3D AXMs using the PolyJet™ additive manufacturing process with elastic joints and stiff beams, a dual-material 3D auxetic structure that enables the metamaterials to deform without the inevitable issue of beam buckling. The influence of design parameters on auxeticity and the equivalent of Young’s modulus was investigated using FEM. Meanwhile, the equivalent Young’s modulus can be tuned independently by varying the elastic region’s material stiffness. The NPR at the stable stage and the equivalent Young’s modulus will increase with an increase in the fraction of the stiff region.

In the past, some AXMs were unable to resist large deformations due to volatility and loss of auxetic properties resulting from cracking in the symmetric level of the material. Although recently additively manufactured 3D AXMs can withstand large deformation, their mechanical properties change substantially. An example includes Poisson’s ratio, which cannot be less than –1. Studies have attempted to overcome this drawback by modifying the structure, because the mechanical properties of various auxetic structures are highly dependent on the internal structures of the unit cells [212,213]. AM processes continue to drive innovation in 3D AXMs, offering precise control over geometric and material properties. Processes such as SEBM, SLM, FDM, and MPP have enabled the creation of 3D auxetic structures with outstanding mechanical performance. Multimaterial AM processes have further enhanced the performance of 3D AXMs, allowing for mechanically tunable Poisson’s ratios and optimizing Young’s modulus through these processes. These advancements have expanded the scope of AXMs, enabling their functionality and applicability in stretchable electronics, vibration control, and wearable devices.

4.2.2. Pentamode Metamaterials

Pentamode metamaterials, often referred to as mechanical fluids, are a distinctive class of artificial structures characterized by their near-zero shear modulus and finite bulk modulus. This property enables PMMs to deform more easily in shape, providing them with fluid-like mechanical behavior while retaining a solid form. Their distinct mechanical properties make them ideal for applications in vibration isolation, seismic protection, and elastomechanical cloaking. The theoretical foundation of PMMs was first proposed by Milton and Cherkaev in 1995 [214]. Figure 5 shows the completion of this concept, experimentally fabricated using polymer-based 3D printing and followed by metallic versions produced via SLM. In 2014, Kadic et al. [215] successfully fabricated a pentamode structure using laser lithography, marking the first experimental completion of this type of metamaterials. Bückmann et al. [216] expanded this work by designing and manufacturing an unfeelability cloak, a mechanical equivalent of an optical invisibility cloak. They fabricated 3D polymeric PMMs with elastomechanical core–shell configurations using DLW. The displacement fields of these 3D metamaterials were analyzed using autocorrelation-based techniques, revealing exceptional cloaking performance. These findings demonstrated that PMMs could elastically hide objects from detection, a transformative capability for mechanical systems.

Additive manufacturing processes such as electron beam melting and selective laser melting have played a crucial role in advancing the development of 3D PMMs. Amendola et al. [217] experimentally investigated the mechanical responses of 3D PMMs manufactured using EBM from Ti-6Al-4V alloy. The manufactured specimens confined between stiffening plates were subjected to lateral and vertical force–displacement tests. The results revealed that the ratio between the effective compression modulus and shear modulus was significantly influenced by the stiffening plates, highlighting the importance of structural boundary conditions. This study also encouraged interest in using 3D PMMs for seismic isolation devices and shear-wave band gap systems. Moreover, Hedayati et al. [218] used SLM to fabricate 3D metal PMMs of Ti-6Al-4V alloy. These 3D forms presented an elastic modulus between 506.9 and 942.5 kPa when exposed to a low-energy laser and between 3.642 and 7.603 MPa when exposed to a high-energy laser. The improved values of elastic modulus are important for load-bearing and biomedical applications. This high degree of tunability of the mechanical response achieved by 3D PMMs further emphasizes the versatility and promise of AM in designing 3D PMMs tailored to specific applications.

4.2.3. Other Mechanical Metamaterials

As high-resolution AM methods, MPP [2] and projection micro-stereolithography (PμSL) have been commonly used for the 3D MMM fabrication. These methods have made it possible to fabricate 3D MMMs with outstanding properties like strength, ductility, energy absorption, and recoverability. By modulating the wall thickness, the 3D hollow-tube octahedral gold nanolattices that were prepared by two-photon lithography and columnar-grained gold sputtering displayed an increased yield strength [219]. Material size effects influence this behavior, deviating from standard mechanical predictions. Similarly, Meza [220] manufactured 3D hollow-tube alumina nanolattices using two-photon lithography, atomic layer deposition, and oxygen plasma etching, exhibiting ultralight, strong, and energy-absorbing properties. These 3D structures maintained their original shape even after compressive strains exceeding 50%. Zhu et al. [221] utilized DIW to manufacture periodic 3D graphene aerogel microlattices with exceptional compressive properties. These 3D structures were lightweight, highly conductive, and capable of withstanding compressive strains of up to 90%. Figure 6 displays high-resolution 3D structures for mechanical and biological use cases. MPP enabled the fabrication of alumina nanolattices and three-dimensional micropatterned cell-adhesive ligand-functionalized scaffolds that effectively guided cells for directional migration, demonstrating AM’s relevance for multifunctional MMMs [222].

Furthermore, Zheng et al. [223] employed a scalable, high-resolution, large-area AM process to manufacture hierarchical 3D MMMs with distributed architectures. The combination of hybrid designs across successive hierarchies resulted in high tensile strength. At a relative density below 0.1%, the hierarchical 3D MMMs exhibited a specific tensile strength of 40.8 MPa, outperforming non-hierarchical stretch-dominated 3D lattices and low-density metal alloys. Advanced AM processes have been used to manufacture 3D MMMs, which are glassy carbon nanolattices with near-theoretical strength and enhanced stiffness-to-density ratios. Jacobsen et al. [224] manufactured 3D glassy carbon nanolattices using a self-propagating photopolymer waveguide technique and pyrolysis. The resulting 3D nanolattices demonstrated exceptional mechanical strength, approaching theoretical values while significantly improving the stiffness-to-density ratio. Additionally, metal-polymeric 3D microlattices were manufactured by electroless plating of nickel-boron (NiB) on polymer scaffolds printed using DLW. The mechanical properties of these 3D MMMs were found to be highly dependent on the NiB layer thickness, highlighting the importance of controlled deposition processes in tailoring material behavior [225].

Frenzel et al. [180] designed and manufactured twisting 3D MMMs capable of delivering axial twists exceeding 2% per strain. These MMMs were manufactured using 3D laser microprinting and illustrated innovative deformation mechanisms suitable for advanced applications in soft robotics and mechanical systems. On a macroscopic scale, octet-truss 3D lattice-structured MMMs manufactured through SLA demonstrated excellent recoverability and energy absorption. The energy absorption efficiency was approximately 11% higher than that of Duocel aluminum foam, with recoverability sustained up to a strain of 70%. Elastomeric 3D MMMs have enabled ultra-high reversible stretchability [98]. Jiang and Wang [226] manufactured 3D hollow microlattice-structured scaffolds using PμSL, which were filled with cured elastomers and subsequently chemically etched. The resulting elastomeric 3D MMMs exhibited stretchability four times higher than existing counterparts, with linear scaling of moduli to density under large strain tension. These 3D MMMs also demonstrated tunable negative stiffness under large strain compression, leading to high energy absorption. By combining these properties with precise design and manufacturing, elastomeric 3D MMMs offer advanced solutions for applications in energy damping and stretchable electronics.

Three-dimensional MMMs have been extensively applied in robotics, where their flexibility and adaptability provide significant advantages. Clausen et al. [227] used numerical simulations to design 3D MMMs with tunable Poisson’s ratios ranging from −0.8 to 0.8. These 3D MMMs were fabricated using silicon-based elastomeric inks and were applied to soft robotic systems capable of navigating pipes with a single actuator. Furthermore, rhombohedral and hexagonal unit cells of 3D MMMs made from soft polylactide (PLA) using fused deposition modeling were also assessed under tension and compression, revealing distinct metamaterial responses based on unit cell geometry and size [228]. Three-dimensional MMMs manufactured from brittle materials, such as ceramics, have also shown potential for ultralight and recoverable designs. VP-based processes have been utilized to manufacture 3D ceramic nanolattices with exceptional recoverability and energy absorption.

4.3. Acoustic Metamaterials Using Additive Manufacturing

Acoustic metamaterials are engineered to manipulate sound waves in ways that surpass the capabilities of conventional materials. Their distinctive properties arise primarily from micro-structured geometries rather than intrinsic material composition [229].

Table 4. Acoustic metamaterials enabled by additive manufacturing highlight key materials, AM methods, and performance attributes.

Material	Functionality	AM Processes/Production Method	Performance	Targeted Application	Ref.
Magnetorheological fluid (MRF)	Modulated acoustic super scatterer	Numerical representation in COMSOL	Superscatterer performs tunability at low frequency	Autonomous underwater vehicles (AUVs), submersible vehicles	[232]
Silicon-based gel	Customized acoustic impedance	Multimaterials 3D printing	Tunable sound reflection and absorption	Biomedical ultrasound devices	[233]
Kevlar	Impact sound dampening	Resin infusion	High resistance to sound transmission	Ballistic shields	[234]
Nylon composite	Soundproofing panels	Fused deposition modeling (FDM)	Durable with effective noise cancelation	Industrial equipment	[235]
Thermoplastic polyurethane (TPU)	Acoustic energy absorption	Selective laser sintering (SLS)	Excellent sound absorption	Protective headgear	[236]
Polypropylene	Broadband noise attenuation	Fused deposition modeling (FDM)	High noise suppression	HVAC systems	[237]
Titanium alloy	Sound wave scattering	Laser Powder bed fusion (LPBF)	Improved acoustic cloaking	Military submarines	[238]
Silicon rubber	Tunable acoustic impedance	Multimaterials 3D printing	Adjustable sound reflection	Architectural acoustic	[239]

summarizes representative AMMs fabricated using various AM techniques. Materials such as Kevlar, silicon rubber, and polypropylene are employed for functionalities like sound dampening, acoustic cloaking, and broadband attenuation. These structures demonstrate the versatility of AM in applications ranging from architectural acoustics and biomedical ultrasound to defense technologies enabled by processes such as FDM, SLS, and multimaterial printing. AM has significantly advanced the development of 3D AMMs by enabling the fabrication of complex geometries optimized for acoustic performance. These metamaterials exploit local resonances to achieve negative constitutive parameters, such as negative mass density or negative bulk modulus, key mechanisms underlying acoustic wave manipulation [230]. Periodic 3D structures incorporating resonators, including Helmholtz resonators, are commonly used to induce these effects. Acoustic metamaterials based on symmetric acoustic layers produced by AM are attractive because of how sound behaves with their use, their application for source cloaking, extraordinary refraction, superlensing, and active noise canceling [230,231].

Several modeling and printing technologies, like stereolithography and multiphoton polymerization, have been commonly used to generate high-precision 3D AMMs in the vertical direction. SLA is excellent for detailed, acoustic 3D structures in large numbers of volumes. This makes it useful for fabricating soundproof panels, vibration isolators, and acoustic waveguides. MPP, on the other hand, is employed for making micro-scale resonators and complex 3D shapes, improving the acoustic performance for higher frequencies. It has made possible 3D AMMs involving subwavelength resonators exhibiting negative bulk modulus and mass density, of the utmost importance for advanced noise-canceling, sound-cloaking. Fused deposition modeling, also used for the manufacture of 3D polymeric AMMs [240,241], is a cheap and effective approach for larger, lighter, 3D structures with suitable acoustic properties. Inkjet printing has emerged as another intriguing AM method for the production of 3D AMMs, which permits the fabrication of acoustic multilayers with different materials and acoustic impedances. This allows for the design of 3D gradient-index AMMs that are capable of focusing or steering sound waves with high precision. IJP has also been utilized in applications such as acoustic lenses and ultrasound devices, where it can demonstrate its promising medical and imaging ability.

Furthermore, powder bed fusion methods such as selective laser sintering and selective laser melting have been used for fabricating 3D metallic AMMs. These methods have been successful in obtaining strong resonant structures that enable the manipulation of acoustic waves. SLM, in particular, has been used to create 3D AMMs for more demanding applications that need to be tough and accurate, such as ultrasonic waveguides and sound-absorbing panels for challenging environments. A few studies have created 3D superlenses capable of focusing sound waves well below the diffraction limit—a game changer for medical ultrasound and non-destructive testing. Three-dimensional AMMs meant for noise cancelation have begun to be incorporated into duct systems and machinery to reduce industrial noise pollution. Acoustic cloaking devices, which redirect sound waves around an object to make it invisible to acoustic detection, have also been manufactured using AM processes [242,243,244]. As AM processes continue to evolve, their impact on AMMs is expected to grow, unlocking new applications in industries ranging from healthcare and aerospace to construction and consumer electronics. The following sections discuss the applications of AM processes for manufacturing 3D AMMs.

4.3.1. Phononic Crystals

Phononic crystals (PnCs) are engineered metamaterials with a periodic arrangement of acoustic scattering inclusions embedded within a matrix. These inclusions exhibit a significant difference in acoustic impedance compared to the surrounding medium, allowing for the effective scattering of acoustic waves and the formation of bandgaps. Bandgaps are frequency ranges where acoustic wave propagation is prohibited due to the interaction between multiple scattering effects and local resonances [245,246]. The ability to control bandgap characteristics makes PnCs highly suitable for applications such as vibration control, noise insulation, sound directionality, and high-resolution imaging [247]. The design of PnCs often requires careful attention to the interaction of acoustic signals with scattering structures to achieve desired bandgap properties. Conventional manufacturing techniques have imposed limitations on the complexity and scalability of these designs, which often rely on solid granules or rods embedded within a substrate [248]. However, additive manufacturing has significantly expanded the scope of 3D PnCs manufacturing, enabling the creation of complex and hierarchical structures with exceptional precision and flexibility.

Fused deposition modeling has been employed to manufacture 3D PnCs for low-frequency vibration control applications [249]. Selective laser sintering has also been used to manufacture 3D PnCs with desired acoustic properties [250]. D’Alessandro et al. [251] produced 3D PnCs from nylon-based unit cells using SLS, operating at frequencies up to 20 kHz, with bandgaps enhanced by significant differences in acoustic impedance between the solid material and air. Zhang [252] utilized SLA to manufacture 3D PnCs optimized for sound directionality, resulting in reproducible designs that performed effectively at frequencies up to 6.3 kHz. Zhang’s high-resolution 3D structures with features as small as 50 µm enabled applications at higher frequencies, extending to 2 MHz. PμSL has also been applied to manufacture 3D PnCs with embedded inclusions. Laureti et al. [253] developed 3D PnCs consisting of evenly spaced steel balls embedded in an acrylic matrix. The manufacturing process involved 3D printing acrylic layers using FDM with spherical recesses to hold the steel ball inclusions, followed by additional acrylic layers to complete the structure. The AM process enabled the precise alignment of inclusions, resulting in functional 3D PnCs that efficiently manipulate sound waves. Electron beam melting has enabled the manufacturing of durable 3D PnCs from Ti-6Al-4V alloy [254]. Wormser et al. [255] manufactured 3D PnCs with curved struts measuring less than 0.5 mm in diameter and spaced approximately 5 mm apart. These designs exhibited fractional bandgaps in the range of 75–110 kHz, validated through both simulations and experimental measurements. The ability of EBM to manufacture high-strength, complex geometries has expanded the potential applications of PnCs.

4.3.2. Helmholtz Resonant Acoustic Metamaterials

Helmholtz resonant acoustic metamaterials (HRAMs) are a class of metamaterials specifically developed to control the sound wave through localized resonance, enabling both separate manipulation of the acoustic wave transmission and dissipation [256,257]. Such metamaterials affect the resonators like the sonic hyperbolic surface (SHS) or harmonic resonators to obtain dispersive responses in the bulk modulus of a material at certain frequencies. Additive manufacturing has made it possible to manufacture these complex designs accurately, leading to new geometries and increasing the potential of applications [191,192]. The versatile nature of various AM processes, such as SLS, FDM, or SLA, provides a way to quickly prototype and customize 3D HRAMs at specific frequency bands. Three-dimensional HRAMs fabricated by AM have been proven their great potential for entrainment and attenuation in acoustics [258]. Reynolds et al. [259] demonstrated the manufacturing of 3D HRAMs using SLS. This design consisted of an array of SHS resonators suspended within an acoustic transparent mesh. The overall arrangement enabled the adjustment of the dispersive effective bulk modulus at the resonant frequencies of the components, effectively altering the acoustic properties.

Furthermore, Sanchis et al. [260] utilized FDM to manufacture a 3D acoustic cloak, demonstrating the ability of Helmholtz resonators to control sound fields. The 3D structure of this design consisted of 60 concentric, acoustic rigid tori encircling a cloaked object, a sphere with a radius of 4 cm, as represented in Figure 7.

By precisely positioning and sizing the tori, the device achieved nearly complete suppression of scattered sound waves, reducing the wave distribution by 90% at a frequency of 8.55 kHz. Casarini et al. [261] employed SLA to manufacture small-scale 3D HRAMs designed to break the mass law of sound transmission. These structures demonstrated the capability of creating bandgaps where sound transmission was significantly reduced, with resonators operating at approximately 7 kHz. The 3D HRAMs achieved sound suppression of up to 30 dB, highlighting the effectiveness of tuned harmonic resonators in expanding and deepening bandgaps [262]. Scientists and researchers have achieved enhanced sound attenuation across wider frequency ranges by precisely tuning the geometry and harmonic resonances of these 3D AMMs. As AM processes continue to evolve, the ability to produce more complex and highly tuned resonant 3D structures is expected to drive further innovation in 3D AMMs, unlocking new possibilities in sound management and wave manipulation.

4.3.3. Other Acoustic Metamaterials

Additive manufacturing has enabled the development of various types of 3D AMMs with unique properties desired for sound manipulation. Ba et al. [263] utilized FDM to manufacture 3D membrane-based AMMs, comprising flexible membranes and additional masses made from the same elastic material. The inclusion of ring-like structures allowed for enhanced control over absorption characteristics, particularly at low frequencies. By strategically adjusting the position of the flexible ring, high-frequency bandgaps with significant absorption could also be achieved, indicating the versatility of FDM in manufacturing such structures. Additionally, SLM has been utilized to manufacture 3D AMM structures from the Ti-6Al-4V alloy with acoustic metamaterial properties [264]. These 3D metallic structures were compared to 3D polymeric structures produced using DLW lithography. While the 3D metallic structures exhibited higher stiffness, the polymeric counterparts displayed lower elastic modulus values, making them suitable for specific applications requiring flexibility. However, the manufacturing of 3D polymeric structures remains complicated due to the stiffness of the struts and the precision required during the manufacturing process [265].

Active 3D locally resonant acoustic metamaterials (LRAMs) have been investigated as a technology for sound energy harvesting. This is an efficient and sustainable technology for generating energy from sound waves. Furthermore, high-resolution patterns have been employed to demonstrate noise reduction, acoustic cloaking, and waveguides, again demonstrating the versatility of the materials [266]. Matlack et al. [267] used FDM for 3D LRAMs by incorporating steel cubes coated with polycarbonate into a mesoscopic lattice. The polycarbonate lattice was printed inside of voids created such that the steel cubes could be added in, providing control over the size and frequency of bandgaps using local resonances. This was constructed to work up to 10 kHz. Cantilevered 3D LRAMs with heterogeneously customized acoustic properties have been produced by way of DIW process.

Qureshi et al. [268] manufactured cantilevered 3D LRAMs consisting of long square bars with thin elastic branches and resonator masses at their ends. These designs effectively suppressed stress waves at specific resonant frequencies. Raza et al. [269] developed a proprietary 3D printer capable of manufacturing advanced 3D LRAMs using multiple deposition methods.

Recent advancements in AM have introduced 3D magnetoactive AMMs manufactured using SLA. Yu et al. [270] developed a model that utilizes remote magnetic fields to reversibly modify acoustic parameters, including double-positive, single-negative, and double-negative properties. By applying magnetic fields, these 3D lattice structures could be deflected, resulting in additional negative modulus values and the creation of voids with negative density. This capability enables applications in the subwavelength regime, including rapid and reversible modulation of acoustic transport, imaging, refraction, and focusing. The use of 3D resonant rod-shaped AMMs has also been shown to create bandgaps for surface acoustic waves. FDM has proven suitable for manufacturing these structures at low frequencies, where it can further enhance performance by integrating additional features, such as holes and evenly distributed cylindrical masses, to generate trampoline effects and widen bandgaps [271].

Fu et al. [272] utilized PolyJet™ technology to manufacture 3D space-coiling spheres, which exhibited monopolar and dipolar resonances due to their spatially coiled structure. These 3D spheres blocked sound wave propagation in frequency ranges between the two resonances while also displaying negative mass density and effective volume moduli around the monopolar and dipolar resonances. Another notable approach was demonstrated by Xie et al. [273], who fabricated 3D cubic AMM structures using SLA. The integration of AM with advanced computational design tools has expanded the horizons of 3D AMMs, enabling the exploration of previously unexplored geometries and mechanisms. AM continues to drive innovation in the field of AMMs, from membrane-based absorbers and magnetically tunable structures to space-coiling spheres and resonant rods.

5. Challenges for Additively Manufactured Metamaterials

Additive manufacturing creates some exciting avenues for creating metamaterials, enabling the production of complex 3D structures with unique properties that are sometimes impossible to replicate using common manufacturing methods. Yet as appealing as these prospects are, several hurdles must be overcome to properly exploit AM in the manufacture of high-quality 3D metamaterials for multiple applications. One of the issues of the latter configuration is precision and resolution through fabrication. Because the peculiar properties of metamaterials are so closely tied to their geometric design, nailing the details is crucial to their remaining useful. For some AM processes, if the resolution is inadequate, then shape complexity can mean that final parts deviate from the original design, harming performance or even losing the metamaterial’s unique capabilities altogether. For one, electromagnetic metamaterials depend on perfect periodicity for them to control light (or radio frequency [RF] waves) properly, and the smallest errors interfere with their operation. To address this issue, increasing the resolution in AM technologies such as multiphoton polymerization and projection micro-stereolithography is crucial to provide accurate production of these complex geometries [274].

The complexity of constraints in metamaterial structure is a source of difficulty. The complex 3D shapes of these materials can often stretch the limits of AM. For instance, delicate struts or the complicated internal structure in 3D lattice structures employed in mechanical metamaterials or acoustic metamaterials may be required but are difficult to realize by present techniques. High-precision AM techniques, such as direct laser writing and selective laser melting, are necessary to realize such fine details in complicated metamaterial structures.

In addition, the choice of appropriate (combinations of) material(s) as well as their compatibility remains a considerable challenge. Metamaterials frequently require materials with specific mechanical, thermal, or electromagnetic properties, which may not be compatible with traditional AM methods. For example, high-performance EMMs may require media that have a high dielectric constant or low loss, either of which might be a challenge to manufacture employing AM. Lack of materials that fulfill such expectations, either to be found, developed, or adapted, is a fact that remains a recurrent problem. More research is necessary to understand the synergy between materials and processes as well as the control of bulk properties that are vital for addressing this challenge.

Scalability, which is also crucial for fabricating 3D metamaterials using AM, is also a critical factor. Although AM can produce detailed structures, scaling up for mass production with economical fabrication time and cost-effective methods remains a challenge. For example, in making 3D EMMs for antennas or radar systems, enlarging them at scale makes precise control on a large scale difficult to achieve. Additionally, the slower speed of AM can limit their use in mass production. WE43, a magnesium allow, is used here because it is the most widely utilized laser AM powder for Mg alloys, and its properties reflect real-life cases, highlighting the main challenges. To address these issues, efforts are focused on developing new, faster, and more economical AM processes with higher resolution. Another complication is that after drawing, modifications are often needed. Surface finishing, heat treatment, or polishing may be required to achieve desired properties, but these processes are typically time-consuming, costly, and difficult to integrate into the AM workflow. For instance, SLM-manufactured metamaterials may require polishing to reduce surface roughness and improve performance. Increasing the process temperature can also remove residual stresses, but this might cause distortions that affect geometric accuracy. Therefore, developing efficient and integrated post-processing techniques is essential for maintaining material integrity and reducing fabrication time and costs associated with 3D metamaterials.

Multistructural and multimaterial designs are also integrated. Most of the 3D metamaterial concepts rely on assembling two or more materials with different properties, which must be distributed with high precision in the structure. For instance, EMMs may be composed of metal and polymer materials, and MMMs might comprise stiff and soft materials. This multimaterial integration in AM requires careful engineering of the materials interfaces to avoid cross-contamination. While considerable advances have been made in multimaterial AM, issues of compatibility, contamination, and process efficiency still exist. The capacity to mix different materials into a single metamaterial offers new potential but requires fine-tuning to keep the desired properties and avoid degradation due to material interaction. Nevertheless, continuous upgrading of AM technology and materials science provides realistic responses. Further studies in high-resolution 3D printing, multimaterial integration, and next-generation simulating tools could allow the design and realization of 3D metamaterials with unparalleled performance. Overcoming these challenges will not only expand the applications for 3D metamaterials but also reinforce AM’s role as a transformative process in advanced manufacturing.

6. Developments and Future Trends of Metamaterials Using Additive Manufacturing

The field of metamaterials has witnessed significant advancements through the integration of additive manufacturing, and future trends indicate continued growth and innovation across various applications. From the expansion of 3D electromagnetic metamaterials to the advent of smart structures and the exploration of four-dimensional (4D) printing, the development trajectory for metamaterials is both promising and transformative. Three-dimensional EMMs are anticipated to lead the next phase of development, driven by their applications in telecommunication systems, radar, and cloaking devices. Future innovations will focus on integrating these 3D metamaterials into smart structures and films that can dynamically adapt to environmental stimuli. For example, EMMs can optimize signal reception by detecting and enhancing the strongest signal across a broad frequency range in communication systems [130]. Such innovations are particularly relevant for bullet trains and recreational vehicles, which require uninterrupted media streaming and reliable connectivity. Smart EMMs will also play a pivotal role in the Internet of Things (IoT), wearable devices, and adaptive antennas, where real-time environmental adaptation is critical [275].

The adoption of multiphysics and multimodel design approaches in materials science is expected to expand. These methodologies integrate concepts from various fields, including electromagnetism, mechanics, thermodynamics, and optics, into unified systems for advanced metamaterial design and control. The focus will increasingly shift towards creating multifunctional systems that synergize structural and material properties to achieve exceptional performance. The introduction of 4D printing, which incorporates the time dimension into the fabrication process, represents another major trend in the development of metamaterials. Early research in 4D printing has demonstrated the feasibility of manufacturing tunable and switchable metamaterials that respond to environmental stimuli such as temperature, light, or magnetic fields [276]. This time-based adaptability enables metamaterials to dynamically alter their behavior, paving the way for applications in soft robotics, aerospace, and biomedical engineering. In addition, structures that morph or self-assemble in response to external stimuli could revolutionize deployable systems for space exploration or minimally invasive medical devices [277].

Material innovations such as flexible substrates with enhanced durability and new polymeric compounds with tailored mechanical properties will drive advancements in this field. AM processes, such as multijet fusion and inkjet printing, are promising for manufacturing intricate structures on flexible substrates, offering scalable solutions that significantly improve system efficiency. Transformational opportunities also arise from stimuli-responsive materials. Shape memory alloys and shape memory polymers (SMPs) have played a vital role in recent 4D printing research. Combining these materials into multimaterial systems unlocks new possibilities for metamaterials capable of reversible shape transformations. For example, AM can be used to fabricate origami-inspired metamaterials that combine SMAs and SMPs, resulting in foldable and lockable structures. These could find applications in deployable space structures, biomedical implants, and adaptive building materials. The integration of smart metallic materials with SMP-based designs offers additional flexibility and functionality. A potential innovation could involve embedding SMAs into SMP-based metamaterials to create structures that can fold, unfold, and maintain their shape under various stimuli. Such designs have implications for space-based systems that require compact loading during launch and expansion during deployment, as well as for medical devices that adapt to patient-specific anatomy [278].

Further exploration into hybrid materials and advanced additive manufacturing processes will enable the manufacture of metamaterials with multifunctional capabilities, such as energy harvesting, thermal management, and vibration damping. As AM processes evolve, the integration of artificial intelligence and machine learning into design processes can facilitate the optimization of metamaterial architectures, reducing the time to market for innovative solutions. Advanced generative design software will enable scientists and researchers to explore complex geometries and material combinations, pushing the boundaries of metamaterial performance. The development of 3D metamaterials using AM is poised to transform numerous industries by enabling the creation of highly functional, adaptive, and scalable materials. Future research and development will focus on overcoming existing limitations in precision, material compatibility, and scalability while exploring new boundaries such as 4D printing, multimaterial integration, and stimuli-responsive systems.

7. Conclusions

This review highlights the dynamic and productive interaction between the fields of metamaterials and additive manufacturing, which have experienced significant growth and integration in recent years. The synergy between these fields has facilitated the existence of successive innovations, enabled by a deeper understanding of material behavior, advanced modeling tools, and the ability to approximate mathematically ideal geometries through physical fabrication. As the field continues to mature, several key conclusions and future directions emerge:

• Synergy Between AM and Metamaterials as an Enabling Technology: The primary conclusion is that additive manufacturing has been a transformative force, not merely an alternative fabrication method. AM provides unprecedented design freedom, enabling the physical fabrication of complex, multi-scale geometries that were previously confined to theoretical models or were impossible to produce with conventional methods [52,56]. This has accelerated the exploration of new theoretical and practical dimensions in metamaterial science, bridging the gap between computational design and tangible, functional components.
• Significant Advancements Across All Metamaterial Categories: AM has propelled the state of the art across all major domains. In electromagnetic metamaterials, it has enabled the creation of structures with negative refractive indices, gradient-index lenses, and effective absorbers from microwave to terahertz frequencies [58,96,112]. For mechanical metamaterials, techniques like Powder Bed Fusion (PBF) and Vat Photopolymerization (VP) have been instrumental in producing auxetic and pentamode structures with tailored properties like negative Poisson’s ratios and extreme anisotropy [137,178]. In acoustic metamaterials, AM has facilitated the fabrication of complex resonant structures for applications in sound cloaking, superlensing, and broadband noise attenuation [193,223].
• Persistent Challenges Requiring Further Innovation: Despite the progress, significant challenges remain that hinder the widespread adoption of AM for metamaterial production. These include limitations in fabrication resolution and precision, which are critical for performance, especially at optical frequencies [237]. The limited palette of compatible materials with desired electromagnetic, mechanical, or thermal properties remains a bottleneck. Furthermore, issues of scalability for mass production and the need for complex, often time-consuming post-processing steps must be addressed to move from laboratory-scale prototypes to industrial applications.
• Future Trends Toward Multifunctional and Intelligent Systems: The future of this field is trending towards increasingly intelligent and multifunctional systems. The emergence of 4D printing is enabling the creation of stimuli-responsive metamaterials that can change their shape or function over time in response to heat, light, or magnetic fields [239]. Multimaterial additive manufacturing is another key frontier, allowing the integration of disparate materials (e.g., conductive and dielectric, or rigid and soft) to create highly functional, monolithic components [279]. Such work demonstrates a clear pathway toward creating active 4D-printed metamaterials that can be controlled electronically. Surface roughness, often considered an undesirable artifact in AM processes like Fused Filament Fabrication (FFF), can be strategically controlled and utilized as a design feature. For instance, recent advancements in slicing software allow for the creation of a “fuzzy skin,” which intentionally introduces random oscillations in the extruder path to produce a rough, textured surface [280,281,282,283]. Looking ahead, the integration of artificial intelligence and generative design will further accelerate innovation, enabling the autonomous discovery and optimization of novel metamaterial architectures with unprecedented performance. The ability to design, simulate, and manufacture 3D structures tailored to specific needs is paving the way for exciting new developments across science, technology, and industry.

As researchers gain a deeper understanding of the theory of metamaterials and improve the application of AM techniques, there will be changes in what can be created and innovations across a range of technologies, from quantum computing and telecommunications to sustainable infrastructure and biomedical devices. The ability to design, simulate, and manufacture 3D structures with tailored properties at multiple scales is opening new frontiers in materials science and engineering.