Dissipative Metamaterials Research Articles

Nonlinear soliton spiral induces coupled multimode dynamics in multi-stable dissipative metamaterials

With the robust and self-trapped properties, recent advances about soliton dynamics in multi-stable mechanical metamaterials have led to many innovative techniques from signal processing to robotics. This work proposes a multi-stable mechanical metamaterial driven by nonlinear dissipative solitons, in which the coupling and decoupling of multiple locomotion modes can be achieved. Based on a cylinder network with asymmetric energy landscape, the uniform field model of Landau theory is developed. During the theoretical calculation, the analytical solutions of several dissipative solitons are derived, which allow multiple special behaviors of solitary waves, such as wave velocity gaps, directional propagation and spiral phase transition. By incorporating such effects into robotic designs, a variety of complex movements can be achieved by a single structure, including hopping, rolling, rotating, swinging, bending and translational components. In particular, as excitation positions change, the mechanical metamaterial can flexibly switch multiple locomotion modes without changing configurations, e.g., spinning and spin-less, straight and oblique as well as coupled multimode movements. This work wishes to provide some new inspirations for the applications of nonlinear elastic wave metamaterials and phase transition theory in robotics.

Origami-based bidirectional self-locking system for energy absorption

When a periodic cellular structure is subjected to high-intensity loading, lateral splashing can occur, significantly decreasing macro mechanical properties. Periodic structures with self-locking properties can overcome this inherent flaw and achieve excellent performance characteristics, including high energy absorption efficiency. In this regard, thin-walled periodic self-locking dissipative structures have been extensively studied recently. Most existing bend-dominated self-locking dissipative systems are two-dimensional and can only achieve self-locking under specific loading conditions. This paper describes a three-dimensional origami-based bidirectional self-locking system that can achieve self-locking under normal and shear loading. Furthermore, a plastic hinge model revealed the energy absorption mechanism of the origami-based cells, whose specific energy absorption (SEA) is higher than that of other existing bend-dominated self-locking cells. The bidirectional self-locking of the origami-based system was demonstrated through compression, bending and impact tests. This origami-based system has high energy absorption efficiency, and the novel bidirectional self-locking mechanism can significantly broaden the design space for periodic dissipative metamaterials.

Free propagation of resonant waves in nonlinear dissipative metamaterials

This paper deals with the free propagation problem of resonant and close-to-resonance waves in one-dimensional lattice metamaterials endowed with nonlinearly viscoelastic resonators. The resonators' constitutive and geometric nonlinearities imply a cubic coupling with the lattice. The analytical treatment of the nonlinear wave propagation equations is carried out via a perturbation approach. In particular, after a suitable reformulation of the problem in the Hamiltonian setting, the approach relies on the well-known resonant normal form techniques from Hamiltonian perturbation theory. It is shown how the constructive features of the Lie Series formalism can be exploited in the explicit computation of the approximations of the invariant manifolds. A discussion of the metamaterial dynamic stability, either in the general or in the weak dissipation case, is presented.

Vibration characteristics of linear and nonlinear dissipative elastic metamaterials rotor with geometrical nonlinearity

Theoretical researches on the vibration characteristics of a dissipative elastic metamaterials rotor with geometrical nonlinearity are presented in this work. Both linear and nonlinear damping cases are implemented in parallel to the spring of the unit. The dynamic model of the dissipative metamaterials rotor is built and discretized by the assumed mode method. Then the solutions of the nonlinear equations are obtained using the harmonic balance method, and the numerical integration method is applied to validate the solutions obtained by the analytical method. The comparisons of the dynamic behaviors for the rotor with different types of geometrical nonlinearities and dissipations are presented, and the effect of the distribution position of the absorber unit on the dynamic behaviors is investigated. The results show that the linear damping has a better capacity to reduce the amplitude compared to the nonlinear damping due to the energy dissipation near the resonance region. On the other hand, compared to the linear dissipation, the nonlinear dissipation has a better performance around the bandgap that forbids the propagation of the vibration. Moreover, these properties can be further improved by adjusting the position of the unit on the rotor. The results presented in this paper provide a theoretical basis for enhancing the properties of metamaterials rotors.

Spatiotemporal damping of dissipative metamaterial

The concept of spatiotemporal damping is proposed to quantify the inherent wave attenuation property of dissipative metamaterials. The concept of spatiotemporal damping is more general compared to its counterparts in previous studies such as band gap and damping. Spatiotemporal damping results from the coupling effect of energy dissipation and energy scattering, and the coupling mechanism is revealed in this study. The traditional concept of damping only considers the energy dissipation effect, and the traditional concept of band gap only defines the frequency range in which wave propagation is prohibited due to the energy scattering (energy reflection) effect in metamaterials. The proposed concept of spatiotemporal damping covers both energy dissipation and energy scattering (energy reflection), which are intrinsic properties of dissipative metamaterials and are coupled with each other. Taking a two-dimensional square-lattice viscoelastic metamaterial as an example, the coupling mechanism of energy dissipation and energy scattering (energy reflection) is revealed. When the dissipative properties of the components change from low to high, the viscoelastic metamaterial strengthens the effect of energy dissipation at the sacrifice of weakening the effect of energy scattering (energy reflection), and the dominant mechanism of its spatiotemporal damping gradually switches from energy scattering (energy reflection) to energy dissipation. For the case where energy scattering (energy reflection) is dominant, the coupling effect of energy dissipation and energy scattering on spatiotemporal damping can be summarized as peak shaving and valley filling. And for the case where energy dissipation is dominant, the spatiotemporal damping increases with the enhancement of the dissipative performance of the components. The effects of main structural and material factors on the spatiotemporal damping of viscoelastic metamaterials are investigated numerically. This research has broad application prospects in the field of vibration and noise control.

The extreme mechanics of viscoelastic metamaterials

Mechanical metamaterials made of flexible building blocks can exhibit a plethora of extreme mechanical responses, such as negative elastic constants, shape-changes, programmability, and memory. To date, dissipation has largely remained overlooked for such flexible metamaterials. As a matter of fact, extensive care has often been devoted in the constitutive materials’ choice to avoid strong dissipative effects. However, in an increasing number of scenarios, where metamaterials are loaded dynamically, dissipation cannot be ignored. In this Research Update, we show that the interplay between mechanical instabilities and viscoelasticity can be crucial and that they can be harnessed to obtain new functionalities. We first show that this interplay is key to understanding the dynamical behavior of flexible dissipative metamaterials that use buckling and snapping as functional mechanisms. We further discuss the new opportunities that spatial patterning of viscoelastic properties offer for the design of mechanical metamaterials with properties that depend on the loading rate.

Nonlinear wave propagation in locally dissipative metamaterials via Hamiltonian perturbation approach

The cellular microstructure of periodic architected materials can be enriched by local intracellular mechanisms providing innovative distributed functionalities. Specifically, high-performing mechanical metamaterials can be realized by coupling the low-dissipative cellular microstructure with a periodic distribution of tunable damped oscillators, or resonators, vibrating at relatively high amplitudes. The benefit is the actual possibility of combining the design of wave-stopping bands with enhanced energy dissipation properties. This paper investigates the nonlinear dispersion properties of an archetypal mechanical metamaterial, represented by a one-dimensional lattice model characterized by a diatomic periodic cell. The intracellular interatomic interactions feature geometric and constitutive nonlinearities, which determine cubic coupling between the lattice and the resonators. The non-dissipative part of the coupling can be designed to exhibit a softening or a hardening behavior, by independently tuning the geometric and elastic stiffnesses. The nonlinear wavefrequencies and waveforms away from internal resonances are analytically determined by adopting a perturbation technique. The employed approach makes use of tools borrowed from Hamiltonian perturbation theory, together with techniques often used in the context of nearly-integrable Hamiltonian systems.The dispersion spectra are determined in closed, asymptotically approximate, form as a nonlinear function of the time-dependent decreasing amplitude decrement. The invariant manifolds defined by the harmonic periodic motions are also analytically determined. The asymptotic results are further validated numerically.

Topology optimization of dissipative metamaterials at finite strains based on nonlinear homogenization

This study presents a novel computational framework for designing optimal dissipative (damping) metamaterials under time-dependent loading conditions at finite deformations. In this framework, finite strain computational homogenization is integrated with a density-based multimaterial topology optimization. In addition, a thermodynamically consistent finite strain viscoelasticity model is incorporated together with an analytical path-dependent sensitivity analysis. Optimization formulations with and without stiffness and mass constraints are considered, and various new damping metamaterial designs are obtained that combine soft viscoelastic and stiff hyperelastic material phases. Multiscale stability analysis using the Bloch wave analysis and rank-1 convexity checks is also carried out to investigate stability of the optimized designs. Stability analyses demonstrate that the inclusion of voids or soft material phases can make a metamaterial more prone to lose micro and macro-stability. Furthermore, the concept of tunable metamaterials is explored wherein metamaterial’s response is steered towards a stable deformation path by tailoring the design with a preselected micro buckling mode.

Mechanics of metadamping in flexural dissipative metamaterials: Analysis and design in frequency and time domains

Locally resonant metamaterials are engineered structures with intriguing acoustic mitigation properties which stem from an interplay between incident elastic waves and a set of internal resonances. Augmented with damping, such properties are shown to vary in unique and non-trivial ways which can amplify the wave attenuation capacity in certain frequency regions, as well as curtail it at times. Wave dispersion mechanics of dissipative metamaterials in literature are typically investigated in the context of wave propagation where the wavenumber is directly involved in band structure evaluations. In this paper, we show that it is possible to conduct such investigation in the context of structural vibrations and demonstrate how modal analysis of a given finite periodic structure is sufficient to assess the accuracy of the predictions obtained from a representative unit cell. The free wave approach is known to be associated with complex frequency solutions where attenuation due to dissipation takes place only temporally and as a consequence, frequency and damping ratio band structures can be constructed. In an attempt to establish direct correlations between infinite and finite medium predictions, it is shown that a combination of frequency and damping ratio band structures (i.e. frequency and damping ratio vs. wavenumber relations) for a given unit cell leads to a new band structure directly relating the damping ratio to wave frequency, which is capable of replicating the findings obtained from the corresponding finite structure. The different phenomena encountered at the fundamental unit cell level are validated via a series of numerical simulations of metamaterial beams with a damped host medium, damped resonators, as well as combinations thereof. The results reveal that the overall damping level as well as the damping source play key roles in dictating the metadamping emergence in locally resonant metamaterials as they compare to baseline designs including phononic and homogeneous structures of equal size and shape. Finally, the notion of positive and negative metadamping is introduced and phase diagrams are constructed to guide and inform the design of such metamaterials in the presence of viscous and structural losses.

A nonlinear dissipative elastic metamaterial for broadband wave mitigation

Nonlinearity and dissipation are two important aspects in elastic metamaterials that hold the potential to provide a novel method for the control of elastic waves. Here, we present a nonlinear dissipative elastic metamaterial in a triatomic mass-spring chain to explore the interplay between nonlinearity and dissipation for broadband wave attenuation. In the study, nonlinear stiffness is considered in the spring between the primary and secondary triatomic masses, and a damper is implemented in parallel to the tertiary spring. Various numerical tests on transient wave propagations are conducted, and show that the proposed design with properly selected nonlinear and damping parameters can generate broader wave attenuation regions compared with corresponding linear dissipative metamaterials and nonlinear non-dissipative metamaterials. We quantify the effects of nonlinearity and material damping in higher harmonic wave generations and wave energy absorption using narrow band incidences and demonstrate the application of the nonlinear dissipative triatomic lattice for blast wave mitigations. This work provides a novel approach to design materials capable of suppressing blast-induced shock waves or impact generated pulses that can cause severe local damage to nearby structures.

Dissipative diatomic acoustic metamaterials for broadband asymmetric elastic-wave transmission

Much effort has been devoted to exploring asymmetric acoustic/elastic-wave transmission in various structural designs. However, the propagation unidirectionality is normally confined to a narrow frequency band. This work presents the development of a dissipative diatomic acoustic metamaterial with dual resonators to realize asymmetric elastic-wave transmission in multiple broadband ranges. We theoretically, numerically, and experimentally investigate the effect of damping on the asymmetric wave transmission. A systematic analytical discussion shows that the frequency bandwidths of asymmetric transmission regions can be significantly enlarged by the merging effect of dissipative dashpots. Numerical verifications are conducted using both mass-spring-damper lattice system and continuum models, and excellent agreements are obtained. We further observe the asymmetric elastic-wave transmission in the proposed dissipative metamaterial structure experimentally. Transient wave responses in time and frequency domains are also investigated. The enlarged asymmetric transmission bands can be analytically predicted and mathematically controlled by carefully designing and deliberately selecting the unit size parameters and material properties. This work could be potentially beneficial for applications in elastic-wave control and directional transmission devices.

Topological phase transition measured in a dissipative metamaterial

We construct a metamaterial from radio-frequency harmonic oscillators, and find two topologically distinct phases resulting from dissipation engineered into the system. These phases are distinguished by a quantized value of bulk energy transport. The impulse response of our circuit is measured and used to reconstruct the band structure and winding number of circuit eigenfunctions around a dark mode. Our results demonstrate that dissipation can lead to topological transport in a much wider class of physical systems than considered before.

Dynamic load mitigation using dissipative elastic metamaterials with multiple Maxwell-type oscillators

Dissipative elastic metamaterials have attracted increased attention in recent times. This paper presents the development of a dissipative elastic metamaterial with multiple Maxwell-type resonators for stress wave attenuation. The mechanism of the dissipation effect on the vibration characteristics is systematically investigated by mass-spring-damper models with single and dual resonators. Based on the parameter optimization, it is revealed that a broadband wave attenuation region (stopping band) can be obtained by properly utilizing interactions from resonant motions and viscoelastic effects of the Maxwell-type oscillators. The relevant numerical verifications are conducted for various cases, and excellent agreement between the numerical and theoretical frequency response functions is shown. The design of this dissipative metamaterial system is further applied for dynamic load mitigation and blast wave attenuation. Moreover, the transient response in the continuum model is designed and analyzed for more robust design. By virtue of the bandgap merging effect induced by the Maxwell-type damper, the transient blast wave can be almost completely suppressed in the low frequency range. A significantly improved performance of the proposed dissipative metamaterials for stress wave mitigation is verified in both time and frequency domains.

Impact wave attenuation using Maxwell-type oscillators in dissipative elastic metamaterials

This work studies the development of a dissipative elastic metamaterial with single and dual-Maxwell type resonator for stress wave mitigation. Mass-spring-damper elements are used to model and analyze the mechanism of wave dissipation effect on the vibration characteristics. It is found that broadband wave attenuation region can be obtained and expanded to a wider range by properly utilizing interactions from resonant motions and viscoelastic effects of the Maxwell-type oscillators. In addition, numerical verifications are conducted for various cases, and excellent agreement between theoretical and numerical frequency response functions are obtained. The design of this dissipative metamaterial system is further applied for blast wave mitigation. By means of the bandgap merging effect that is induced by the Maxwell-type oscillator, the passing blast wave can be almost completely suppressed in the low-frequency range. A significantly improved performance of the proposed dissipative metamaterials for stress wave mitigation is verified in both time and frequency domains.

Enhancing Broadband Vibration Energy Suppression Using Local Buckling Modes in Constrained Metamaterials

Studies on dissipative metamaterials have uncovered means to suppress vibration and wave energy via resonant and bandgap phenomena through such engineered media, while global post-buckling of the infinitely periodic architectures is shown to tailor the attenuation properties and potentially magnify the effective damping effects. Yet, despite the promise suggested, the practical aspects of deploying metamaterials necessitates a focus on finite, periodic architectures, and the potential to therefore only trigger local buckling features when subjected to constraints. In addition, it is likely that metamaterials may be employed as devices within existing engineering systems, so as to motivate investigation on the usefulness of metamaterials when embedded within excited distributed or multidimensional structures. To illuminate these issues, this research undertakes complementary computational and experimental efforts. An elastomeric metamaterial, ideal for embedding into a practical engineering structure for vibration control, is introduced and studied for its relative change in broadband damping ability as constraint characteristics are modified. It is found that triggering a greater number of local buckling phenomena provides a valuable balance between stiffness reduction, corresponding to effective damping magnification, and demand for dynamic mass that may otherwise be diminished in globally post-buckled metamaterials. The concept of weakly constrained metamaterials is also shown to be uniformly more effective at broadband vibration suppression of the structure than solid elastomeric dampers of the same dimensions.

Dissipative elastic metamaterial with a low-frequency passband

We design and experimentally demonstrate a dissipative elastic metamaterial structure that functions as a bandpass filter with a low-frequency passband. The mechanism of dissipation in this structure is well described by a mass-spring-damper model that reveals that the imaginary part of the wavenumber is non-zero, even in the passband of dissipative metamaterials. This indicates that transmittance in this range can be low. A prototype for this viscoelastic metamaterial model is fabricated by 3D printing techniques using soft and hard acrylics as constituent materials. The transmittance of the printed metamaterial is measured and shows good agreement with theoretical predictions, demonstrating its potential in the design of compact waveguides, filters and other advanced devices for controlling mechanical waves.

Dissipative elastic metamaterials for broadband wave mitigation at subwavelength scale

In this paper, an elastic metamaterial with multiple dissipative resonators is presented for broadband wave mitigation by properly utilizing interactions from resonant motions and viscoelastic effects of the constitutive material. The working mechanism of the metamaterial to suppress broadband waves is clearly revealed in a dissipative mass-in-mass lattice system through both negative effective mass density and effective metadamping coefficient. Based on the novel metadamping mechanism, a microstructure design of the dissipative metamaterial made of multi-layered viscoelastic continuum media is first proposed for efficient attenuation of a transient blast wave. It is found that the extremely broadband waves can be almost completely mitigated with metamaterials at subwavelength scale. The results of the study could be used in developing new multifunctional composite materials to suppress the shock or blast waves which may cause severe local damage to engineering structures.

Attenuation of short stress pulses in strongly nonlinear dissipative metamaterial

Attenuation of short stress pulses under different levels of precompression was investigated in a one-dimensional strongly nonlinear discrete metamaterial assembled using alternating steel disks and toroidal Nitrile O-rings. The results were compared with the numerical modeling. A double power-law is used to describe the nonlinear interaction between the disks due to the compression of rubber O-rings. The dispersion behavior caused by the periodic arrangement of elements is contributing to the attenuation of pulse, but could not explain the experimental observations. It was explained by taking into account the nonlinear viscous behavior of O-rings. The numerical simulations were able to predict the dependence of the signal speed on the precompression force, a significant decrease of the pulse width with the precompression and the attenuation of the leading positive pulse, the latter of major significance in the protection against impact. This strongly nonlinear dissipative metamaterial has a potential for attenuation of dynamic loading and allows an enhanced tunability of signal speed and degree of attenuation.

Microstructural design studies for locally dissipative acoustic metamaterials

Stress wave attenuation performance of locally dissipative acoustic metamaterials with various damped oscillator microstructures is studied using mechanical lattice models. The presence of damping is represented by a complex effective mass. Analytical solutions and numerical verifications of transmissibility are obtained for Kelvin-Voigt-type (KVO), Maxwell-type, and Zener-type (ZO) oscillators with viscous damping. Although peak attenuation at resonance is diminished, dissipative microstructures can provide broad spectrum attenuation without increasing mass ratio, obviating the bandgap width limitation of locally resonant microstructures. KVO gives the best broad spectrum performance akin to a low-pass filter for excitation frequencies above a cut-off value for a prescribed transmissibility criterion. For ZO, by tailoring the damping and stiffness, the frequency range of appreciable attenuation can at least span the bandgap widths of two limiting locally resonant cases. Static and frequency-dependent measures of optimal damping that maximize the attenuation characteristics are proposed. A transitional value for the excitation frequency is identified within the locally resonant bandgap, above which there always exists an optimal amount of damping that renders the attenuation for the dissipative metamaterial greater than that for the locally resonant case. Further microstructures with hysteretic damping depict a frequency-independent scaling in the effective mass and attenuation factor, but the bandgap width remains nearly the same as that for the corresponding viscously damped microstructures. This study demonstrates that dissipative microstructures, which are to some extent unavoidable in practical designs, when tuned, provide a means to substantially enhance the attenuation bandwidth of locally resonant acoustic metamaterials while also enabling the removal of the energy sequestered by the oscillators from the system.

Three-dimensional point spread function of multilayered flat lenses and its application to extreme subwavelength resolution

The three-dimensional (3D) point spread function (PSF) of multilayered flat lenses was proposed in order to characterize the diffractive behavior of these subwavelength image formers. We computed the polarization-dependent scalar 3D PSF for a wide range of slab widths and for different dissipative metamaterials. In terms similar to the Rayleigh criterion we determined unambiguously the limit of resolution featuring this type of image-forming device. We investigated the significant reduction of the limit of resolution by increasing the number of layers, which may drop nearly 1 order of magnitude. However, this super-resolving effect is obtained in detriment of reducing the depth of field. Limitations exist on the formation of 3D images.