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The asymmetric transformation elasticity offers a promising method to control elastic waves. However, this method requires elastic materials that support asymmetric stresses, which is not objective within the Cauchy elasticity framework. Nevertheless, asymmetric stress tensor is a typical feature of micropolar continuum theory. Yet, possible connection between micropolar continuum theory and the asymmetric elasticity transformation has remained elusive. Here, we demonstrate that extremal micropolar media, which refer to micropolar media with easy deformation modes, can be used to design elastic cloaks following the asymmetric transformation method. A metamaterial model is proposed to achieve the required extremal micropolar parameters for cloaking. We further design a two-dimensional metamaterial cloak and verify its cloaking performance numerically. An excellent agreement between the metamaterial cloak simulation and an effective-medium calculation is obtained. This study unveils a novel strategy for controlling elastic waves through micropolar media and also sheds light on interesting properties of extremal micropolar materials., Comment: 22 pages, 7 figures

Extremal elastic materials here refer to a specific class of elastic materials whose elastic matrices exhibit one or more zero eigenvalues, resulting in soft deformation modes that, in principle, cost no energy. They can be approximated through artificially designed solid microstructures. Extremal elastic materials have exotic bulk wave properties unavailable with conventional solids due to the soft modes, offering unprecedented opportunities for manipulating bulk waves, e.g., acting as phonon polarizers for elastic waves or invisibility cloaks for underwater acoustic waves. Despite their potential, Rayleigh surface waves, crucially linked to bulk wave behaviors of such extremal elastic materials, have largely remained unexplored so far. In this paper, we theoretically investigate the propagation of Rayleigh waves in extremal elastic materials based on continuum theory and verify our findings with designed microstructure metamaterials based on pantographic structures. Dispersion relations and polarizations of Rayleigh waves in extremal elastic materials are derived, and the impact of higher order gradient effects is also investigated by using strain gradient theory. This study provides a continuum model for exploring surface waves in extremal elastic materials and may stimulate applications of extremal elastic materials for controlling surface waves., Comment: 8 figures

The thermal management have been widely focused due to broad applications. Generally, the deformation can largely tune the thermal transport. The main challenge of flexible electronics/ materials is to maintain thermal conductance under large deformation. This work investigates the thermal conductance of a nano-designed Si metamaterial constructed with curved nanobeams by molecular dynamics simulation. Interestingly, it shows that the thermal conductance of the nano-designed Si metamaterial is insensitive under a large deformation (strain~-41%). The new feature comes from the designed curved nanobeams which makes a quasi-zero stiffness. Further calculations show that, when under a large deformation, the average stress in nanobeam is ultra-small (<151 MPa) and its phonon density of states are little changed. This work provides valuable insights on multifunction, such as both stable thermal and mechanical properties, of nano-designed metamaterials.

Elastic material with its elastic tensor losing minor symmetry is considered impossible without introducing artificially body torque. Here we demonstrate the feasibility of such material by introducing rotational resonance, the amplified rotational inertia of the microstructure during dynamical loading breaks naturally the shear stress symmetry, without resorting to external body torque or any other active means. This concept is illustrated through a realistic mass-spring model together with analytical homogenization technique and band structure analysis. It is also proven that this metamaterial model can be deliberately tuned to meet the material requirement defined by transformation method for full control of elastic wave, and the relation bridging the microstructure and the desired wave functionality is explicitly given. Application of this asymmetric metamaterial to design elastic wave cloak is demonstrated and validated by numerical simulation. The study paves the way for material design used to construct the transformation media for controlling elastic wave and related devices., Comment: 22 pages, 8 figures

Pentamode materials are elastic solids with vanishing shear modulus, and can be used cloak underwater sound with solid state and broadband merits. However, pentamode materials realized with real microstructure have inevitable small shear modulus. This paper systematically studies the impact of shear rigidity and inner surface constraints on acoustic cloak with unideal pentamode material. The shear rigidity introduces a new kind of resonance in the radial direction, which is different from the traditional whispering-gallery resonance along the circumference. Totally fixed, radially fixed or free boundaries on the cloak inner surface are found to show significant difference on the cloaking function. To realize a broadband cloak with suitable boundary for practice, we propose to attach an elastic thin shell on the inner surface to virtually tune the boundary constraint. The proposed strategy is also validated with microstructure cloak simulation. This study will provide valuable guidance for the practical applications of pentamode acoustic cloak., Comment: 20 pages, 6 figures

A Quantum Spin-Hall Insulator (QSHI) is implemented into a simple mass-spring Kagome lattice. The transition from the trivial state to the topological one is described by an invariant Chern number function of a contrast parameter. The band diagram and helical edge states characteristic of QSHI are obtained by a combination of numerical and analytical methods. In particular, these states are shown to be Stoneley wave solutions to a set of asymptotic continuous motion equations. Last, scatterless propagation of polarized topological edge waves around sharp corners is demonstrated and robustness is assessed through a parametric study., Comment: 9 figures

Current strategies for designing tunable locally resonant metamaterials are based on tuning the stiffness of the resonator; however, this approach presents a major shortcoming as the effective mass density is constant at high frequency. Here, this paper reports a type of tunable locally elastic metamaterial-'called tunable fluid-solid composite'-inspired by the functions of heart and vessels in animals and humans. The proposed metamaterial consists of several liquid or gas inclusions in a solid matrix, controlled through a pair of embedded pumps. Both the band gap and effective mass density at high frequency can be tuned by controlling the liquid distribution in the unit cell, as demonstrated through a combination of theoretical analysis, numerical simulation, and experimental testing. Finally, we show that the tunable fluid-solid metamaterial can be utilized to manipulate wave propagation over a broad frequency range, providing new avenues for vibration isolation and wave guiding.

An incremental wave superimposed on a pre-deformed hyper-elastic material perceives an elastic media with the instantaneous modulus of the current material. This offers a new route with a broadband feature to control elastic waves by purposely creating finite deformation field. This study proves that the governing equation of a semi-linear material under a symmetric pre-deformation condition maintains the form invariance for longitudinal wave, so the longitudinal wave control can be made by transformation method without the constraint condition on principle stretches, but this is not the case for shear waves. Therefore pre-deforming a semi-linear material provides a potential method for treating longitudinal and shear waves differently. Examples with elastic wave control and band structure shift through pre-deforming a semi-linear material are provided to illustrate this finding. Finally, a one-dimensional spring lattice is proposed to mimic a semi-linear material, and the dispersion relation for longitudinal waves in a sandwich structure with such spring lattice is shown to be invariant during elongation, confirming the result found based on a homogeneous semi-linear material. These results may stimulate researches on designing new hyper-elastic microstructures as well as designing new devices based on pre-deformed hyper-elastic materials., Comment: 7 pages, 4 figures

Sound absorption or dissipation principally involves joint interactions between sound waves, material morphology and the air medium. How these elements work most efficiently for sound absorption remains elusive to date. In this paper, we suggest a fundamental relation concisely cross-linking the three elements, which reveals that optimal sound absorption efficiency occurs when the pore size of the material is twice the thickness of the viscous boundary layer of the acoustic air medium. The study is validated by microlattice materials comprising of well-controlled regular structures that absorb sound in a tunable manner. Optimized material morphology in terms of pore size and porosity is determined to provide a robust guidance for optimizing sound absorbing materials., Comment: 14 pages, 7 figures

Application of transformation theory to underwater acoustics has been a challenging task because highly anisotropic density is unachievable in water. A possible strategy is to exploit anisotropic modulus rather than density, while has not been experimentally demonstrated. We present an annular underwater acoustic cloak designed from particular graded solid microstructures. The geometry tailored microstructures mimics meta-fluid with highly anisotropic modulus through substantially suppressed shear wave. Transient wave experiments are conducted with the cloak in a designed 2D underwater waveguide system and proved excellent cloaking performance for enclosed target over broadband frequency 9-15 kHz. This finding paves the way for controlling underwater acoustics using the structured anisotropic modulus meta-fluid., Comment: 12 pages, 4 figures

By considering the membrane's dissipation, the membrane-type acoustic metamaterial (MAM) has been demonstrated as a super absorber for low-frequency sound. In the paper, a theoretical vibroacoustic plate model is developed to reveal sound energy absorption mechanism within the MAM under a plane normal incidence. Based on the plate model in conjunction with the point matching method, the in-plane strain energy of the membrane due to the resonant and antiresonant motion of the attached masses can be accurately captured by solving the coupled vibroacoustic integrodifferential equation. Therefore, the sound absorption of the MAM is obtained and discussed, which is also in good agreement with the prediction from the finite element method. In particular, microstructure effects including eccentricity of the attached masses, the depth, thickness and loss factor of the membrane on sound absorption peak values are quantitatively investigated.

Membrane-type Acoustic Metamaterials (MAMs) have demonstrated unusual capacity in controlling low-frequency sound transmission/reflection. In this paper, an analytical vibroacoustic membrane model is developed to study sound transmission behavior of the MAM under a normal incidence. The MAM is composed of a prestretched elastic membrane with attached rigid masses. To accurately capture finite-dimension rigid mass effects on the membrane deformation, the point matching approach is adopted by applying a set of distributed point forces along the interfacial boundary between masses and the membrane. The accuracy and capability of the theoretical model is verified through the comparison with the finite element method. In particular, microstructure effects such as weight, size and eccentricity of the attached mass, pretension and thickness of the membrane on the resulting transmission peak and dip frequencies of the MAM are quantitatively investigated. New peak and dip frequencies are found for the MAM with one and multiple eccentric attached masses. The developed model can be served as an efficient tool for design of such membrane-type metamaterials.

A general conformal mapping is proposed to design omnidirectional broadband wave absorbers by transformation method. When applied to electromagnetic (EM) and acoustic waves, the existing material parameters of the EM and acoustic omnidirectional absorbers, which are previously obtained by Hamiltonian optics and geometry acoustics, can be recovered. In addition, magnetic and mass-density-controlled omnidirectional absorbers for EM and acoustic waves can also be designed, respectively. We then apply the conformal mapping to design an omnidirectional elastic wave absorber, the corresponding material realization of such elastic absorber is also proposed and validated by numerical simulation., Comment: 12 pages, 3 figures

A transformation method based on elastic ray theory is proposed to control high frequency elastic waves. We show that ray path can be controlled in an exact manner, however energy distribution along the ray is only approximately controlled. A numerical example of an elastic rotator is provided to illustrate the method and to access the approximation. The proposed theory may be found potential applications in seismic wave protection and structure health monitoring., Comment: 13 pages, 3 figures

A metamaterial slab of anisotropic mass with one diagonal component being infinity and the other being zero is demonstrated to behave as a superlens for acoustic imaging beyond the diffraction limit. The underlying mechanism for extraordinary transmission of evanescent waves is attributed to the zero mass effect. Microstructure design for such anisotropic lens is also presented. In contrast to the anisotropic superlens based on Fabry-P\'erot resonant mechanism, the proposed lens operates without the limitation on lens thickness, thus more flexible in practical applications. Numerical modeling is performed to validate the proposed ideas., Comment: 4 figures

There are great demands to design functional devices with isotropic materials, however the transformation method usually leads to anisotropic material parameters difficult to be realized in practice. In this letter, we derive the isotropic transformed material parameters in case of elastodynamic under local conformal transformation, they are subsequently used to design a beam bender, a four-beam antenna and an approximate carpet cloak for elastic wave with isotropic materials, the simulation results validate the derived transformed material parameters. The obtained materials are isotropic and greatly simplify subsequent experimental implementation., Comment: 12 pages, 3 figures

By idealizing a general mapping as a series of local affine ones, we derive approximately transformed material parameters necessary to control solid elastic waves within classical elasticity theory. The transformed elastic moduli are symmetric, and can be used with Navier's equation to manipulate elastic waves. It is shown numerically that the method can provide a powerful tool to control elastic waves in solids in case of high frequency or small material gradient. Potential applications can be anticipated in nondestructive testing, structure impact protection, petroleum exploration and seismology., Comment: 11 pages, 1 figures

Negative mass phenomena occurring below a cut-off frequency is examined by both theoretical and experimental methods. The paper begins with the investigation on a mass-spring structure, the effective mass of which is shown to be negative below a specific frequency. Due to the decaying nature of lattice waves in the negative-mass system, the transmission drop induced by negative effective mass is demonstrated experimentally. Further investigation is conducted for a rectangular solid waveguide with clamped boundary conditions. It is shown that the lowest bandgap mode of the clamped waveguide can be attributed to negative effective mass below a cut-off frequency. Based on this observation, elastic metamaterials made of the steel grid filled by styrene butadiene rubber are designed and fabricated. Both simulation and experimental analyses demonstrate that the designed metamaterial have negative effective mass below a cut-off frequency., Comment: This paper has been withdrawn by the authors. New Journal of Physics 12 (2010) 103025

Contrary to transformation optics (TO), there exist many possibilities for transformed relations of material property and field variable in case of transformation acoustics (TA). To investigate the underlining mechanism and develop a general method that can obtain the full transformed relations, an alternative interpretation to the form-invariance is explored. We consider a spatial transformation, with which a physical phenomenon described in an initial space is transformed to a deformed space, and interpret the mapping by local affine transformation point-by-point. Further, we postulate that the transformed material property and field must rebuild the same physical process, and that the energy must be conserved at each point during the transformation. These conditions impose the constraint on the transformed relation for material property and field. By establishing two local Cartesian frames defined uniquely by the spatial transformation, any physical quantity is shown to first experience a rigid rotation and then a stretch operation during the transformation. We show that the constraint conditions are not enough to determine completely the transformed relation for TA, leaving a possibility to define them differently as found in the literature. New acoustic transformations with constant density or modulus are also proposed and verified by constructing a two-dimensional acoustic cloak. Finally, we show that the transformed relation is uniquely determined for transformation optics, and discuss how this method can be extended to other transformation physics., Comment: 28 pages, 4 figures

The deformation method of transformation optics has been demonstrated to be a useful tool, especially in designing arbitrary and nonsingular transformation materials. Recently, there are emerging demands for isotropic material parameters, arising from the broadband requirement of the designed devices. In this work, the deformation method is further developed to design quasi-isotropic/isotropic transformation materials. The variational functional of the inverse Laplace's equation is investigated and found to involve the smooth and quasi-conformal nature of coordinate transformation. Together with the sliding boundary conditions, the inverse Laplace's equation can be utilized to give transformations which are conformal or quasi-conformal, depending on functionalities of interest. Examples of designing an arbitrary carpet cloak and a waveguide with arbitrary cross sections are given to validate the proposed idea. Compared with other quasi-conformal methods based on grid generation tools, the proposed method unifies the design and validation of transformation devices, and thus is much convenient., Comment: 8 pages, 4 figures

In this paper, we utilize the deformation transformation optics (DTO) method to design electromagnetic beam bender, which can change the direction of electromagnetic wave propagation as desire. According to DTO, the transformed material parameters can be expressed by deformation tensor of the spatial transformation. For a beam bender, since the three principal stretches at each point induced by the spatial transformation are independent to each other, there are many possibilities to simplify the transformed material parameters of the bender by adjusting the stretches independently. With the DTO method, we show that the reported reduced parameters of the bender obtained by equivalent dispersion relation can be derived as a special case. An isotropic bender is also proposed according to this method, and it is fabricated by stacking dielectric materials in layered form. Experiments validate the function of the designed isotropic bender for a TE wave; it is also shown that the isotropic bender has a broadband with low loss, compared with the metamaterial bender. The isotropic bender has much easier design and fabrication procedures than the metamaterial bender., Comment: 9 pages, 9 figures

A method is proposed to design arbitrary shaped two dimensional (2D) isotropic-inertia acoustic cloaks without singularity. The method is based on the deformation view of the transformation method, where the transformation tensor A is identified as the deformation gradient tensor and the transformed material parameters can be expressed by the principal stretches in the principal system of the deformation. The infinite material parameters of a perfect 2D cloak is induced by an infinite principal stretch in one direction while the other two remains finite at the inner boundary during the transformation. To circumvent this difficulty, for a 2D cloak we can choose the principal stretch perpendicular to the cloak plane to be also infinite but in the same order as the infinite principal stretch in the cloak plane during the transformation, so the transformed material parameters may keep finite. To illustrate this idea, the analytical expressions of nonsingular material parameters for a cylindrical acoustic cloak are given. For the acoustic cloaks with irregular shapes, the numerical method is proposed to evaluate the principal stretches and in turn the nonsingular material parameters. The designed 2D cloaks are validated by numerical simulation., Comment: 6 pages, 7 figures

We propose a general method to circumvent the singularity of arbitrary 2D cloaks, which arises from infinitely large values of material parameters at inner boundaries. The presented method is based on the deformation view of the transformation design method. It is shown that by adjusting the principle stretch out of the cloaking plane, 2D cloaks of arbitrary shapes without singularity can be constructed. It is also demonstrated that the method based on the equivalent dispersion relation and the design method for nonsingular 2D cloak from mirror-symmetric cross section of 3D cloak can be derived from the proposed theory. Examples of a cylindrical electromagnetic cloak and an arbitrary shaped 2D electromagnetic cloak without singularity are provided to illustrate the method., Comment: 14 pages, 4 figures