Negative Bulk Modulus Research Articles

An efficient multiscale method for subwavelength transient analysis of acoustic metamaterials.

A reduced-order homogenization framework is proposed, providing a macro-scale-enriched continuum model for locally resonant acoustic metamaterials operating in the subwavelength regime, for both time and frequency domain analyses. The homogenized continuum has a non-standard constitutive model, capturing a metamaterial behaviour such as negative effective bulk modulus, negative effective density and Willis coupling. A suitable reduced space is constructed based on the unit cell response in a steady-state regime and the local resonance regime. A frequency domain numerical example demonstrates the efficiency and suitability of the proposed framework.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Low-frequency noise attenuation through hybrid perforated hemispherical shells and membrane-type acoustic metamaterial

We propose a novel hybrid acoustic metamaterial that can achieve broadband sound insulation below 452 Hz and almost perfect sound absorption at 864 Hz. The metastructure was fabricated using additive manufacturing. Finite element method simulations were used to study the acoustic properties of the fabricated metamaterials. An equivalent electrical circuit was built using an electro-acoustic analogy to evaluate the sound absorption coefficient. The unique design of this meta-structure possesses two resonant frequencies. Low-frequency sound insulation is found due to the effective negative density at frequencies lower than the cutoff frequency of the elastic membrane. In contrast, a negative effective bulk modulus is the reason behind the broadband sound absorption. The theoretical and simulation results were validated through experiments. Experiments carried out showed an overall average sound transmission loss of 26.31 dB between 50 and 1600 Hz and 24.72 dB in the low-frequency zone (<400 Hz). Furthermore, over 69% of the sound intensity is absorbed in the 500–1000 Hz frequency range. The designed meta-structure exhibits broadband effective negative density below 452 Hz and effective negative bulk modulus from 864 to 1220 Hz. The design specifies a sample thickness of 3.8 cm, corresponding to a subwavelength thickness of approximately λ/10. As a result, the developed meta-structure can potentially be employed for sound insulation and absorption at low frequencies in the aerospace and automotive industries and in-room acoustic applications.

Lightweight soundproofing meta-panel for two separate broadband noises

We propose a lightweight soundproofing meta-panel, with a multi-scale lattice structure sandwiched between thin membranes, effectively suppressing two separate broadband noises. By adjusting the geometrical parameters, the meta-panel is designed to induce negative effective mass density and negative effective bulk modulus for two distinct target frequency bands: 100–500 Hz and 1000–1500 Hz, thereby achieving high transmission loss that outperforms the mass density law. A meta-panel sample is fabricated via 3D printing technology and we evaluate its sound insulation performance by measuring transmission loss and insertion loss in an impedance tube and an anechoic chamber. Experimental measurements show that the meta-panel can exhibit excellent insulation performance while being significantly lighter in weight (about 5%) compared to a steel plate, and furthermore, it effectively suppresses low-frequency road noise and high-frequency motor noise from an actual electric car.

Improved voice acquisition using acoustic metamaterials

Voice acquisition and recognition are important, because sound is the most convenient and efficient media to realize seamless and hands-free human–machine interaction. Many applications, such as smart phones, humanoid robots, smart home, autonomous vehicles, and Internet of Things, demand for high-quality voice acquisition, especially in a noisy environment. In this report, we show that the evanescent portion of human voice can be amplified by setting an acoustic metamaterial in front of a microphone; thus, the signal to noise ratio can be enhanced remarkably. Such an effect is demonstrated through a double negative acoustic metamaterial slab with simultaneous negative density and bulk modulus induced by coexisting and coupled Helmholtz and Fabry–Pérot resonances. This work provides a passive and physical means, rather than the traditional active and algorithmic method, to improve the quality of voice sound acquisition.

Estimating effective acoustic properties of various configuration of perforated panels

Acoustic metamaterial attains uncommon material properties over natural material such as negative effective mass density, negative effective bulk modulus, or both. To start with, the present research demonstrates and establishes robust method to estimate and measure acoustic metamaterial properties of a Helmholtz resonator analytically using transfer matrix (TM) method and experimentally in detail. The proposed method extracts the reflection and transmission coefficients from corresponding TM to evaluate the effective acoustic metamaterial properties. For a single Helmholtz resonator, the effective bulk modulus has been observed negative; however, the effective density remains positive. In order to attain double negative material properties, the perforated panel (PP) and microperforated panel (MPP) have been introduced in parallel to resonator. The 1D electro-acoustic modeling has been carried out for all configurations to estimate effective properties analytically. Successively, the experiments have been conducted to measure the effective properties from acoustic metamaterial prospective. The analytical and experimental investigations on five different cases reveal that one can attain negative effective compressibility and effective density by cascading two PPs or MPPs with a finite duct. Moreover, by backing a Helmholtz resonator from both sides with two PPs or MPPs in parallel, one can attain double negative properties comparatively higher than earlier configuration in low-frequency zone in broadband. In total, eight different configurations have been investigated analytically and experimentally, where it has been demonstrated that the proposed compact model is more effective than a finite array of same Helmholtz resonators.

Acoustic propagation through a duct metamaterial attached with periodic multi-resonant cavities

Presently, noise pollution in ducts is considered seriously, and numerous studies concerning sound absorption in pipes are ongoing globally. Aiming at the difficulty to eliminate the low-frequency noise in pipeline, a multi-resonant cavity duct metamaterial is proposed. The acoustic properties of the metamaterial are calculated using the energy method based on the Hamilton principle and the transfer matrix methodology. The result demonstrates that the duct metamaterial, due to its band gaps and negative bulk modulus, obtains several sound absorption peaks and is advantageous to sound elimination in low frequency. The good acoustic characteristics of the duct metamaterial for sound insulation can be attributed to the plate-cavity interaction. Parametric analysis of the proposed structure is also carried out. This study demonstrates the application prospects of duct metamaterials for multi-frequency sound absorption in engineering practice.

Experimental demonstration of scalable active metamaterials with interacting cells of tunable bulk modulus

Active metamaterials can be designed to exhibit acoustic properties that are challenging to obtain using passive structures without relying on narrowband resonant behavior. Arrangements of unit cells that independently sense the local acoustic conditions and produce a coherent response, which is determined by the gain of electronics between the sensor and driver, act as a material with programmable properties. Such an active metamaterial has been previously demonstrated, but only for a single or a few non-interacting cells due to a limited understanding of how the programmed gains relate to the effective properties. Recently we developed a polarized source model to address this challenge, and based on that work we now demonstrate experimentally an active metamaterial composed of interacting cells with programmable bulk modulus. Each unit cell consists of a speaker and microphone mounted in the bottom plate of a 2D waveguide, with electronics of adjustable gain stored underneath. The field generated by a 2 × 3 arrangement of cells in response to an incident pulse was compared to the simulated scattered field of the equivalent continuous material. By tuning the gain, we accurately reproduced the behavior of a medium with negative, fractional, and large relative bulk modulus.

VELAS: An open-source toolbox for visualization and analysis of elastic anisotropy

Although elastic properties and their anisotropy play a crucial role in materials science and technology, it is not straightforward to visualize how properties such as shear modulus vary with the direction of stress/strain. Here, written in GNU Octave, we have developed an easy-to-use, flexible, and user-friendly open-source toolbox with a graphical user interface, VELAS, which automatically visualizes and analyses the elastic anisotropy of arbitrary crystal systems using second-order elastic constants. Using Voigt-Reuss-Hill averaging scheme, VELAS allows the calculation of more than ten significant mechanical properties such as modulus, hardness, anisotropy index, ductility, and bond type. It also supports the determination of the mechanical stability of crystals at atmospheric and high pressures using the Born mechanical stability criterion. VELAS provides a new easy-to-use tool for detecting and identifying unusual mechanical properties such as negative Poisson's ratio, negative linear compressibility, and negative bulk modulus. VELAS offers several alternative visualization solutions for elastic properties, such as unit spherical projection, and map projection, and supports direct output of high-quality images. Furthermore, VELAS provides users an interface to read data from the Materials Project API in both online and offline modes. After introducing the basic theory, we detail the software framework, technical route, and installation specifications of VELAS. Moreover, the reliability and versatility of VELAS are confirmed by the analysis of the cases of negative linear compressibility, negative Poisson's ratio, hardness, and fracture toughness. Program summaryProgram Title: VELASCPC Library link to program files:https://doi.org/10.17632/bj27474v6f.1Developer's repository link:https://github.com/ranzhengcode/VELASLicensing provisions: GNU General Public License 3Programming language: GNU OctaveNature of problem: To determine the mechanical stability of any crystal at atmospheric and high pressures. To automatically visualize and analyze the elastic anisotropy of arbitrary crystals and identify unusual elastic properties.Solution method: Firstly, the determination of the mechanical stability of crystals at atmospheric and high pressures using the Born mechanical stability criterion. Secondly, more than ten significant mechanical properties such as elastic moduli, ratios, hardness, and anisotropy index are analyzed using Voigt-Reuss-Hill averaging scheme. Then, the mechanical behavior of crystals in the elastic regime is derived from a comprehensive tensor analysis of the second-order elastic constants. Finally, Pugh Ratio, Hardness, and Fracture Toughness in 3D space are calculated based on our approximate treatment of elastic properties.

Molecular dynamics study of crystal lattice effect on mechanical properties of SiO2: A density functional tight binding investigation

In this study, molecular dynamics simulations (MD) based on quantum mechanical method in which the interactions were expressed by self-consistent charge density functional tight binding (SCC-DFTB) to investigate the mechanical properties of four different SiO2 structures. The Young's, shear and bulk modulus of systems are calculated and the results compared to experimental and other computational findings. We have observed that the hexagonal SiO2 exhibits more different mechanical behavior than other SiO2 structures because of its negative bulk modulus value. While the length of a-lattice parameters for four SiO2 crystal structures increase with the change of MD time, the length of the b and c-lattice vectors shortens. Moreover, it is analyzed the stress-strain behavior and yield points are determined from this curve of SiO2 structures. It is revealed that the plastic deformation occurs at higher stress for hexagonal SiO2 than other SiO2 structures because of its rigid solid property. These results can provide a reference for understanding the mechanical properties of various SiO2 crystal structures.

Compact acoustic metamaterial based on the 3D Mie resonance of a maze ball with an octahedral structure

Acoustic metamaterials (AMs) offer ever-expanding possibilities for manipulating sound waves. Potential applications include diagnostic medical imaging, super-absorption, acoustic sensing, and acoustic stealth. In spite of recent progress, the investigation of AMs with a three-dimensional (3D) response is lagging behind, in particular for those that exhibit an isotropic response. Here, we demonstrate a highly compact subwavelength maze-like multi-shell plastic sphere, which generates Mie resonances with isotropic monopolar and anisotropic dipole, quadrupole, and octupole modes at low frequencies for airborne sound, based on an octahedral structure. Eigenmode analysis shows that the proposed maze ball exhibits a negative bulk modulus at the monopole Mie resonance frequency in the absence of viscous losses, which is a signature of strong transmission blocking. With a diameter of 0.17λ and a volume filling factor of 13.5%, a constructed single 3D maze ball reduces the experimentally-measured transmitted acoustic energy by 67%, limited mainly by viscous losses. With optimized fabrication, the proposed 3D Mie resonator should provide a versatile approach for the manipulation of sound waves on a subwavelength scale, and lead to the realization of practical 3D metamaterial devices.

A robust three-parameter reference curve for condensed phase materials

Many isothermal equations of state lead to numerical problems under tension conditions due to negative bulk modulus. We summarize the properties of four existing models and devise a continuous non-piecewise reference curve to address this issue. The final functional form contains three fitting parameters that are directly related to the bulk modulus and its pressure derivative at the reference state and at infinite pressures. We also include bounds that guarantee the monotonicity of its pressure derivative in all volume space. To demonstrate the qualitative features of each isotherm, we conduct calibrations against experimental data for cyclotetramethylene tetranitramine, magnesium oxide, gold, and platinum. Pressure residuals and root mean square deviations show that the proposed functional form is capable of adequately fitting the data compared to other three-parameter models.

Weak-form homogenization of one-dimensional systems with hidden degrees of freedom

Acoustic metamaterials are synthetic structures that exhibit specific, often exotic, effective material properties for long-wavelength stimuli. One of the principal methods that exotic material properties, such as zero or negative mass density or bulk modulus, may be obtained is through hidden degrees of freedom. An example of a hidden degree of freedom is a resonator attached in shunt to a duct and modeling the system as just a duct with effective material properties. In this example, the resonator is “hidden” from the model by incorporating its (rather profound) effect on the system into the material properties. This paper demonstrates how hidden degrees of freedom may be incorporated into a recently developed homogenization scheme that utilizes the weak form of the dynamic system [Muhlestein, J. Acoust. Soc. Am. 147 (2020)]. Two specific examples will be considered: the shunt resonator, as described above, and a membrane inside a duct. The results are compared with other standard homogenization methods.

Multi-material topology optimisation of micro-composites with reduced stress concentration for optimal functional performance

This study develops a new multi-material topology optimisation framework for design of periodic micro-composites with optimal functional performance and reduced stress concentration. First, multi-material topology optimisation is developed based on the alternating active phase algorithm and inverse homogenisation method with the sensitivity analysis derived for specific property objective i.e., negative Poisson's ratio (NPR) or maximum effective bulk modulus (EBM) and (p-norm macroscopic) stress objective. Then, the effects of initial material distribution and weight ratio (w1, w2 assigned to the property and stress objectives, respectively) are investigated, and the evaluation indices are also developed to obtain the optimal solution. Further, two cases related to the design of micro-composites for maximised either NPR or EBM with reduced maximum stress are performed. The results show that when designing the multi-material NPR micro-composites, the decrease of w1/w2 contributes to a general decease of both NPR and maximum stress. While in designing the maximum EBM, decreasing w1/w2 leads to the reduced maximum stress and simultaneously reduced EBM; hereby, a decision-making method as well as the proposed evaluation index are both applied and compared for acquiring the optimal result. This study provides new methods and solutions to multi-material micro-composites design for future industrial applications.

Experimental and numerical investigations of ventilated acoustic metamaterial based in-parallel arrangement of Helmholtz resonator for façade screen

Understanding urban noise as a serious environmental problem in urban centers, the development and application of noise control strategies have demanded a recent effort by several researches. In this case, the development of acoustic metamaterial artificially designed to manipulate the wave phenomena has become a recent topic, aiming at optimized responses, and enables the development of subwavelength devices with potential application in passive ventilation and noise mitigation, providing better environmental conditions in buildings. The present paper intends to contribute to the knowledge in this field by investigating the concept of an acoustic metamaterial with negative bulk modulus based in a parallel arrangement of Helmholtz Resonators. Experimental and numerical investigations are carried out to determine the acoustic potential of the proposed meta structure in terms of sound absorption and sound transmission loss. The developed concept exhibits significant benefits in the properties of sound transmission loss, and seems a potential application for noise control at specific frequency bands (mainly at low to middle frequency) in building façades.

Intuitive understandings of negative bulk modulus of metamaterials composed of Helmholtz resonators

We present theoretical and experimental results to obtain an intuitive understanding of bulk modulus of metamaterials composed of Helmholtz resonators (HR). Using transmission line theory, we introduce an intuitive method to determine the frequency domain in which the negative bulk modulus appears. The results obtained by simulations and experiments are consistent with theoretical results found using transmission line theory. The results suggest that wider negative (BNG) areas of bulk modulus can be obtained using two HRs than one HR of the same total cavity volume.

Negative-stiffness composite systems and their coupled-field properties

Composite materials consisting of negative-stiffness inclusions in positive-stiffness matrix may exhibit anomalous effective coupled-field properties through the interactions of the positive and negative phases, giving rise to extremely large or small effective properties. In this work, effective viscoelastic properties of a continuum composite system under the effects of negative inclusion Young’s modulus ratio $$\lambda _E = E_{\text {inc}}/E_{\text {matrix}}$$ are studied with the finite element method. Furthermore, effective coupled-field properties, such as thermal expansion coefficient, dielectric constants and piezeoelectric constants, are numerically calculated under the effects of negative inclusion bulk modulus ratio $$\lambda _K=K_{\text {inc}}/K_{\text {matrix}}$$ . Stability boundaries are determined by applying small dynamic perturbation to the systems through boundary surfaces, and the system is unstable if its field variables become divergent in time. For viscoelastic composite systems containing small volume fractions, less than $$V_i = 1.5 \%$$ , the systems can be stable up to $$\lambda _E \approx -0.3$$ in 0.3 s under 10 Hz driving frequency. For $$V_i = 5.1 \%$$ case, its stability boundary is around $$\lambda _E \approx 0$$ . Larger inclusion volume fraction reduces allowable negative stiffness in the viscoelastic system. All anomalous peaks found in the coupled-field properties are in the unstable regime, except for the piezoelectric and thermal-expansion anomalies in the composite system with electrically insulated inclusions and large inclusion volume fraction $$V_i = 26.81 \%$$ . Insulated inclusions may cause charge accumulation at the inclusion–matrix interface and boundary surface effects may serve as stabilizing agents to the composite system. Since it is known that negative-stiffness composite is unstable in the purely elastic system in statics, stability enhancement found here in the negative-stiffness systems with viscoelastic and coupled-field effects may be considered as multiphysics-induced stabilization.

Analytical modeling of one-dimensional resonant asymmetric and reciprocal acoustic structures as Willis materials

As building blocks of acoustic metamaterials, resonant scatterers have demonstrated their ability to modulate the effective fluid parameters, which subsequently possess extreme properties such as negative bulk modulus or negative mass density. Promising applications have been shown such as extraordinary absorption, focusing, and abnormal refraction for instance. However, acoustic waves can be further controlled in Willis materials by harnessing the coupling parameters. In this work, we derive the closed forms of the effective parameters from the transfer matrix in three asymmetric and reciprocal one-dimensional resonant configurations and exhibit the differences in terms of coupling coefficients. The way in which Willis coupling occurs in spatially asymmetric unit cells is highlighted. In addition, the analysis shows the absence of odd Willis coupling for reciprocal configurations. These effective parameters are validated against experimental and numerical results in the three configurations. This article paves the way of a novel physical understanding and engineering use of Willis acoustic materials.

Molecular Dynamics Study of Anti-Wear Erosion and Corrosion Protection of PTFE/Al2O3 (010) Coating Composite in Water Hydraulic Valves

Cavitation erosion and corrosion commonly occur on the surface of fluid dynamic system components, mostly water hydraulic valves, causing the failure of metal parts. Coating of polytetrafluoroethylene (PTFE) on Al2O3 (010) was created by varying the chain length of polytetrafluoroethylene. Calculations were conducted by molecular dynamic (MD) simulations. This study shows that the K10 and K20 chain lengths’ mechanical properties possess negative elastic, shear, and bulk modulus values. We have found that the K10 chain length composition shows the high results of binding energy and negative bulk modulus of 6267.16 kJ/mol and −3709.54 GPa, respectively. The K10 chain length was observed to possess a higher cohesive energy density (CED) and solubility parameter of (6.885 ± 0.00076) × 109 J/m3 and (82.974 ± 0.005) (J/cm3)0.5, respectively. It was also found that increasing the chain length contributes to decreasing the binding energy and solubility parameter of PTFE/Al2O3 (010) composition. These results are vital for overcoming the repetitive regime of high compressive strength of water microjets on the valves’ material surface. Improved values of the cohesive energy density and solubility parameters imply the water’s superior hydrophobic effect.

Solidity without inhomogeneity: perfectly homogeneous, weakly coupled, UV-complete solids

Solid-like behavior at low energies and long distances is usually associated with the spontaneous breaking of spatial translations at microscopic scales, as in the case of a lattice of atoms. We exhibit three quantum field theories that are renormalizable, Poincaré invariant, and weakly coupled, and that admit states that on the one hand are perfectly homogeneous down to arbitrarily short scales, and on the other hand have the same infrared dynamics as isotropic solids. All three examples presented here lead to the same peculiar solid at low energies, featuring very constrained interactions and transverse phonons that always propagate at the speed of light. In particular, they violate the well known {c}_L^2>frac{4}{3}{c}_T^2 bound, thus showing that it is possible to have a healthy renormalizable theory that at low energies exhibits a negative bulk modulus (we discuss how the associated instabilities are absent in the presence of suitable boundary conditions). We do not know whether such peculiarities are unavoidable features of large scale solid-like behavior in the absence of short scale inhomogeneities, or whether they simply reflect the limits of our imagination.

Effective metamaterial properties for non-local active acoustic media

Acoustic metamaterials are generally composed of complex arrays of subwavelength unit cells that can be cumbersome to analyze and simulate. Consequently, it is common practice to approximate metamaterials as homogeneous media with unique material properties, most commonly negative or near-zero density, negative or near-zero bulk modulus, or both negative or near-zero density and bulk modulus. In addition to easing the computational burden associated with complex metamaterial structures, effective material properties can provide deeper understanding of system behavior, providing additional insight and tools in the development of acoustic metamaterials. Here, we present a method for determining effective material properties for a non-local, active acoustic metamaterial. We contrast these properties with those typically associated with acoustic metamaterials and discuss how such properties are characteristic of a new class of acoustic metamaterials.