Pentamode Metamaterials Research Articles

Theoretical and experimental study of a two-dimensional circular stealth acoustic lens

The detection of underwater acoustic signals is a key focus in ocean development, and acoustic metamaterials play a crucial role in achieving this goal. Pentamode metamaterials exhibit fluid-like properties, allowing for the propagation of compressional waves without shear waves. In this study, a two-dimensional circular stealth acoustic lens based on pentamode metamaterials was proposed. By applying the transformation acoustics theory, the theoretical properties of circular stealth acoustic lenses were calculated, and they were verified with Finite Element Method (FEM). A practical model was designed with pentamode metamaterials and silicone oil, and its performance was verified with FEM software. A half-model was fabricated, and underwater experiments demonstrate that it does not effectively affect the propagation state of acoustic waves. The consistency between theoretical results and experimental findings highlights practical significance and broad application prospects for the circular stealth acoustic lens in the field of acoustic detection.

Additive Manufacturing, Numerical and Experimental Analyses for Pentamode Metamaterials

Pentamodes are lattice structures composed of beams. Their main property is the low ratio of the shear to bulk modulus, making them suitable for aerospace, antiseismic, and bioengineering applications. At first, in our study, pentamode structures were fabricated using three-dimensional printing and were tested in a laboratory. Then, computational analyses of bulk strength have been performed. In addition, several preliminary computational analyses have been considered, comparing different pentamodes’ dimensions and topologies in order to understand their behaviour under different loading conditions. Experimental results have been compared with the numerical results in order to validate the forces applied to the lattice structures. Our new contribution is that for the first time, the experimental and numerical results are investigated up to the failure of the specimens, the effective Young’s modulus has been calculated for different pentamode lattice structures, and our results are also compared with analytical equations.

Closed-form analytical relationships for pentamode metamaterials

Pentamode metamaterials are a class of extremal materials exhibiting fluid-like mechanical behavior. The mechanical properties of pentamode metamaterials arise from their unique micro-architecture, rather than their constituent material. In this research, we present closed-form analytical relationships for the elastic modulus and Poisson’s ratio of pentamode lattice structures with double-cone struts based on cubic diamond morphology. To validate our analytical solutions, we performed numerical simulations and experimental tests, which confirmed the accuracy of the derived relationships. Our findings indicate that increasing the smaller diameter (d) and the larger-to-smaller diameter ratio (α) of the double-cones increases the elastic modulus of pentamode metamaterials. However, within the considered range of d and α, the Poisson’s ratio is nearly constant and lies within the range of approximately 0.5. These analytical relationships provide valuable insight into the mechanical behavior of pentamode metamaterials, which can aid in the design and optimization of new materials with unique properties.

Two-Dimensional Pentamode Metamaterials: Properties, Manufacturing, and Applications

Two-Dimensional Pentamode Metamaterials: Properties, Manufacturing, and Applications

An automated design framework for composite mechanical metamaterials and its application to 2D pentamode materials

Until relatively recently most mechanical metamaterial classes being studied have been composed of a single solid constituent phase and design has focused almost exclusively on structural geometry. Additional design dimensions can be introduced by accepting heterogeneity and varying materiality, i.e., allowing mechanical properties to vary across the metamaterial's unit cells or even from cell to cell in the metamaterial domain, creating composite metamaterials. This higher dimensionality significantly expands the effective property envelope, but the additional complexity also presents a significant hurdle. To overcome the design challenge, an automated design framework is proposed that leverages modern evolutionary computation techniques, combined with finite element analysis for fitness evaluation, to a discretized or voxelated design domain. However, this approach introduces stochastic and statistical aspects to the design process, which requires additional processing to successfully extract useful solutions. A case study is presented in which the proposed automated design framework is used to generate 2D structures that exhibit pentamode-like behavior. Pentamode metamaterials, which are best known for extreme bulk-to-shear modulus ratios (B/G), offer unique control over effective elastic properties and make for a particularly interesting test case. The evolutionary objective was defined as maximizing B/G over a voxelated square 2D domain. It was found that the evolutionary process converges to a solution relatively rapidly, generally in less that a hundred generations. B/G ratio values of 10,000 and more were obtained, largely exceeding those commonly found in the literature for experimental pentamode metamaterials. These generated designs feature reduced stress concentrations due to the elimination of point-like connections between lattice struts, which addresses a key practical limitation of diamond lattice pentamodes. It was observed that whatever the initial variety of elastic moduli values across the voxels of the design domain, as evolution progressed this variety collapsed to a much smaller number, most often a binary composite of very stiff voxels with a limited number of much softer voxels at key locations that acted as hinges.

Dual-functional pentamode metamaterial with water-like and topological transmission properties

In this paper, a water-like pentamode metamaterial (PM) with a single metallic material is designed and the topological edge-state transmission properties of elastic waves in the PM are thoroughly investigated. Numerical results indicate that by introducing structural perturbation into PM, the Dirac point degeneracy at K-point can be opened and topological band inversion can be generated. Topological edge states are also obtained by organizing PM structural units, which are robust to defects such as bending and cavities. In addition, it also has the mimics water in acoustic properties over a wide frequency range, i.e. it exhibits transparency when surrounded by water. Therefore, it will have both good transmission efficiency and acoustic stealth performance when used as an underwater waveguide. The dual-functional PM proposed in this study provides theoretical guidance for designing underwater stealth acoustic waveguides.

Low-frequency broadband acoustic modulation mechanism of composite pentamode metamaterials

In this paper, an acoustic bandgap (ABG) manipulation method for pentamode metamaterials is proposed, by which a composite pentamode metamaterial with the low-frequency broadband can be obtained. Combined with the spring-mass model, the generation and regulation mechanism of the low-frequency ABG is analyzed, and the approximate relationship between the ABG and the structural parameters is obtained. The effects of the narrow diameter ratio (n) and the soft material height ratio (r, s) on the first ABG are calculated by using the finite element method. The simulation results are in good agreement with the theoretical predictions. Through the ABG modulation method, a low-frequency ultra-wideband PM structure in the range of 43.91∼299.26 Hz can be obtained without changing the structural parameters. The proposed mechanism provides theoretical guidance for PMs to widen the low-frequency bandgap and modulate the ABG frequency range.

A transformable anisotropic 3D penta-mode metamaterial

Penta-mode metamaterials, composed by solids but behaving as liquid, have great potential in manipulating acoustic wave in fluids. Most work concentrates on 2D penta-mode metamaterial consisting of classic honeycomb lattice and their acoustic applications. However, the 3D penta-mode exploration is still limited to traditional diamond lattice. Here, we propose a novel 3D penta-mode metamaterial design whose geometry is based on truncated octahedron. The configurations of regular truncated octahedron (RTO) and transformed truncated octahedron (TTO) exhibit isotropic and anisotropic penta-mode property, respectively. By introducing the modular origami and boundary constrains, a transformable penta-mode design metamaterial between RTO and TTO configurations is proposed. The tunable anisotropy of the penta-mode is experimentally demonstrated, based on which we analyze the effective acoustic impedance and wave velocity, and illustrate their ability to manipulate the amplitude and wavefront of acoustic waves. Our findings offer a wider 3D transformable penta-mode metamaterial flatform to achieve the tunable control of acoustic wave in fluids.

Ultrahigh compression-shear ratio of sandwich pentamode metamaterials

Pentamode metamaterials (PMs) are a novel class of mechanical metamaterials showing the unusual decoupling relationship between compression and shear moduli. This study originates from the contradictory question of how to improve the compression-shear ratio without sacrificing the crucial size as much as possible. Here, novel sandwich PMs with ultrahigh compression-shear ratios are proposed. For example, under the same crucial size like d/a = 1 % (ratio of diameter of intersections d to lattice constant a, which dominates the mechanical properties of PMs and the smallest size limiting the fabrication), the compression-shear ratio of new PMs can be up to 1877, whereas the classical diamond-like lattice is 4.7, corresponding to a 391-fold increase. The finite element results by COMSOL Multiphysics and experimental results match well, mutually verifying the validity. The influence of single-layer and multi-layer sandwich lattices is further investigated, which shows that stiffening plates tip the scales. This study escapes the current limitations of limited compression-shear ratio, extreme crucial size, and high-cost fabrication, which promotes the concept of PMs towards practical applications.

3D Printed Biomimetic Metamaterials with Graded Porosity and Tapering Topology for Improved Cell Seeding and Bone Regeneration.

Biomimetic metallic biomaterials prepared for bone scaffolds have drawn more and more attention in recent years. However, the topological design of scaffolds is critical to cater to multi-physical requirements for efficient cell seeding and bone regeneration, yet remains a big scientific challenge owing to the coupling of mechanical and mass-transport properties in conventional scaffolds that lead to poor control towards favorable modulus and permeability combinations. Herein, inspired by the microstructure of natural sea urchin spines, biomimetic scaffolds constructed by pentamode metamaterials (PMs) with hierarchical structural tunability were additively manufactured via selective laser melting. The mechanical and mass-transport properties of scaffolds could be simultaneously tuned by the graded porosity (B/T ratio) and the tapering level (D/d ratio). Compared with traditional metallic biomaterials, our biomimetic PM scaffolds possess graded pore distribution, suitable strength, and significant improvements to cell seeding efficiency, permeability, and impact-tolerant capacity, and they also promote in vivo osteogenesis, indicating promising application for cell proliferation and bone regeneration using a structural innovation.

Topological transmission of elastic waves on a macroscopic pentamode metamaterial plate

In this paper, we devise a pentamode metamaterial plate exhibiting topological characteristics. By organizing pentamode metamaterial structural elements, topological boundary states are attained, effectively safeguarding propagation of elastic waves. Moreover, based on the numerical simulation model, we employ a polymer to fabricate a macro-scale specimen via additive manufacturing. Through assessing the vibrational response of the sample, we corroborate its topological attributes in governing elastic wave transmission. This discovery paves the way for a novel approach to manipulating acoustic/elastic waves employing pentamode metamaterials.

An efficient underwater absorber using pentamode metamaterials for broadband frequency

To further design and develop broadband and efficient underwater sound absorption structure, we propose a hybrid acoustic structure composed of a rubber matrix layer, cylindrical cavity, pentamode metamaterial (PM) layer, impedance matching layer, and steel backing plate. Thanks to the special properties of the PMs, the hybrid acoustic structure obtains excellent broadband sound absorption performance (SAP) in the frequency range of 500–10000 Hz than that of the traditional cavity acoustic structure. To this end, we study the design principle of PM structure and its metal–water characteristics and analyze the sound absorption mechanism at the working frequency. In addition, the research shows that the material and geometric parameters of the structure have a significant impact on the SAP. By the optimization of structural material parameters, the average absorption coefficient at 500–10000 Hz can further increase to above 0.781. Finally, we also demonstrate that the structure still has good SAP under a wide range of oblique incidence angles. The research in this paper opens up bright perspectives for the design of underwater anechoic coatings for multifunctional applications.

Tetramode Metamaterials as Phonon Polarizers.

In classical Cauchy elasticity, 3D materials exhibit six eigenmodes of deformation. Following the 1995 work of Milton and Cherkaev, extremal elastic materials can be classified by the number of eigenmodes, N, out of these six that are "easy". Using Greek number words, this leads to hexamode (N= 6), pentamode (N= 5), tetramode (N= 4), trimode (N= 3), dimode (N= 2), and monomode (N= 1) materials. While hexamode materials are unstable in all regards, the possibility of pentamode metamaterials ("meta-fluids") has attracted considerable attention throughout the last decade. Here, inspired by the 2021 theoretical work of Wei, Liu, and Hu, microstructured 3D polymer-based tetramode metamaterials are designed and characterized by numerical band-structure calculations, fabricated by laser printing, characterized by ultrasound experiments, and compared to the theoretical ideal. An application in terms of a compact and broadband polarizer for acoustical phonons at ultrasound frequencies is demonstrated.

Bandgap properties and multi-objective optimization of double-cone pentamode metamaterials with curved side

Pentamode metamaterials (PM) have a promising application in noise reduction fields. In this paper, in order to improve the acoustic modulation capability of PMs, several novel curve PMs are proposed by replacing the straight sides of conventional PMs with curves. At first, the elliptic PMs (EPMs) with various unit cell arrangements (i.e., triangular, square, and hexagonal) are designed, respectively, and their bandgap properties are studied numerically in detail. The EPM with hexagonal unit cell arrangement (EPMH) presents better comprehensive bandgap properties in the EPMs. Subsequently, sinusoidal and power curves are introduced into the EPMH respectively to explore the influences of curve types on bandgap properties. The results show that the bandgap properties improvement of EPMH is higher in comparison with introducing other curves, and the reasons behind these improvements are carefully disclosed in combination with the spring-mass system. Finally, to further improve the bandgap properties of EPMH, a high accuracy Kriging model is constructed according to both the Latin hypercube design and double-point infilling. The Pareto optimal solution sets are determined using a non-dominated sorting genetic algorithm (NSGA-II), and the final compromise solution is gained by employing a fitness function. The bandwidths of phononic bandgap and single mode bandgap, and the total bandwidth of optimized EPMH are increased respectively by about 114.5, 4.3, and 7.7 times than those of the conventional straight side PMs. This investigation provides a fresh strategy for designing PMs with excellent bandgap properties.

Parametric Analysis and Multi-Objective Optimization of Pentamode Metamaterial

Pentamode metamaterial (PM) has enormous application potential in the design of lightweight bodies with superior vibration and noise-reduction performance. To offer systematic insights into the investigation of PMs, this paper studies the various effects (i.e., unit cell arrangement, material, and geometry) on bandgap properties through the finite element method (FEM). With regards to the influences of unit cell arrangements on bandgap properties, the results show that the PM with triangular cell arrangement (PMT) possesses better bandgap properties than the others. The effects of material and geometry on bandgap properties are then explored thoroughly. In light of the spring-mass system theory, the regulation mechanism of bandgap properties is discussed. Multi-objective optimization is conducted to further enhance the bandgap properties of PMT. Based on the Latin hypercube design and double-points infilling, a high-accuracy Kriging model, which represents the relationship between the phononic bandgap (PBG), single mode phononic bandgap (SPBG), double-cone width, and node radius, is established to seek the Pareto optimal solution sets, using the non-dominated sorting genetic algorithm (NSGA-II). A fitness function is then employed to obtain the final compromise solution. The PBG and total bandgap of PMT are widened approximately 2.2 and 0.27 times, respectively, while the SPBG is narrowed by about 0.51 times. The research offers important understanding for the investigation of PM with superior acoustic regulation capacity.

Research on the structural design and pentamodal property of three-dimensional multilayer cylindrical pentamode metamaterials for tuning acoustic waves

Pentamode metamaterial (PM) is an artificial solid form metamaterial with fluid characteristics. In this paper, a three-dimensional (3D) PMs based on multilayer cylindrical elements are proposed for increasing tunable structure parameters, obtaining great pentamodal property, reducing band gap frequency and decreasing connection overlap areas of elements. Compared with the PMs with double-cone elements, under the same parameters, the lower edge frequency of the single-mode band gaps can be reduced by 33.2%, the maximum value of figure of merit can be increased by 84.8% and the phononic band gaps can be reduced by 73.9%.

Electropolishing-enhanced, high-precision 3D printing of metallic pentamode metamaterials

Additive 3D printing has been one of the most powerful and effective techniques to realize 3D intricate structures. However, its limitations including a high threshold for high-precision preparation and poor surface roughness in metalworking impede further development, such as metallic pentamode metamaterials (PMs) due to the special structural regimes and extremely strict size requirement at the intersection nodes. Herein, a novel electropolishing-enhanced 3D printing method is proposed to fabricate high-precision metallic PMs with improved precision and surface smoothness. Experimental results evince that this hybrid additive-subtractive method can fabricate PMs with much smaller critical size and smoother surface, which cannot be achieved by the same-level 3D printing methods. The minimum processable size can reach ∼ 100 μm that greatly breaks through the limitation of initial additive manufacturing (EOS M280 SLM, ∼ 200 ± 50 μm). A ∼ 100 μm intersection can support 107 times its own weight. Moreover, the D/d of elementary biconical rods can be refined from an initial 6 to an astounding 52, which is beyond the scope of conventional 3D printing. This proposed hybrid additive-subtractive method, namely electropolishing-enhanced 3D printing, breaks the limits of conventional 3D printing by significantly improving the precision and shows great potential in low-cost but high-precision manufacturing.

Elastic Metamaterials of Hexagonal Unit Cells with Double-Cone Arms from Pentamode to Band Gap at Low Frequencies

Metamaterials are artificial materials with properties that can be designed by man-made structures. Pentamode metamaterials only support compressional stresses at specific frequency ranges, and a band gap is a frequency range where no stresses are supported. In this paper, an elastic metamaterial with hexagonal unit cells is studied where pentamode bands or band gaps at low frequencies are obtained by varying the inner structures. The effects of structural and geometric parameters on the band width of pentamode bands or band gaps are analyzed. Simulations of materials composed of primitive cells with pentamode or band gap properties are conducted with harmonic stimulation based on the finite element method. The metamaterials can be applied as pentamode metamaterials or vibration isolation materials.

Design and optimization of three-dimensional composite multilayer cylindrical pentamode metamaterials for controlling low frequency acoustic waves

For three-dimensional pentamode metamaterials, it is of great significance to realize underwater low frequency acoustic wave control. Therefore, in order to compare with traditional double-cone pentamode metamaterials, two multilayer composite cylindrical three-dimensional pentamode metamaterials with low frequency and broad band gaps are proposed in this paper. By using pentamode metamaterials with lattice constants on the order of centimeters, the phononic band gaps below 60 Hz and the single-mode area below 30 Hz can be obtained. In addition, compared with asymmetrical double-cone locally resonant pentamode metamaterials, the lower edge frequency, relative bandwidth and figure of merit of the first phononic band gap can be reduced by up to 61.4%, 10.3% and 40.6%, respectively. It will provide reference and guidance for the engineering application of pentamode metamaterials in controlling the ultra-low frequency broadband acoustic waves, vibration and noise reduction.

Broadband Transformation Acoustic Waveguide With Anisotropic Density Based on Pentamode Metamaterials

Multiple layer anisotropic fluid medium is critical to the realization of transformation acoustic devices, such as cloak or bend waveguide. Pentamode metamaterials have attracted extensive attention as a solid artificial version with anisotropic modulus to approximate liquids. In this paper, we present an approach to realize fluid-like anisotropic density by using pentamode materials, and an underwater bend acoustic waveguide with anisotropic density is designed and fabricated to demonstrate the effectiveness of it. Simulation results indicate that, compared with anisotropic-modulus design by using pentamode materials, wider bandwidth acoustic modulation effect can be obtained. An in-depth and comprehensive analysis of the mechanisms of the broadband characteristics is provided by calculating the band structure of the pentamode metamaterials constituting the acoustic waveguides and analyzing their vibration modes. Finally, remarkable wavefront manipulation for underwater acoustics based on the acoustic waveguide with anisotropic density is experimentally verified.