arXiv subjects

Gengkai Hu

Publications and source records attributed to Gengkai Hu.

At least 19 recordsLinked to original sources

arXiv2026

Wave Scattering at temporal interfaces with spatial-translation-symmetry mismatch

Temporal interfaces enable wave manipulation through broken time-translation symmetry, but conventional formulations generally assume that spatial-translation symmetry is preserved across the interface. Here we consider temporal interfaces between periodic media with mismatched spatial symmetries. It is discovered that the reciprocal-lattice vectors of the pre- and post-switching media enter a generalized quasi-momentum-matching condition, giving rise to reciprocal-lattice-assisted wave-vector conversion. We then develop a multichannel temporal-scattering theory and validate it in one- and two-dimensional elastic lattices. A single incident Bloch mode can thereby excite multiple post-interface Bloch modes with distinct wave vectors and frequencies, a response inaccessible at conventional temporal interfaces. These results establish symmetry mismatch as a new degree of freedom for simultaneous control of wave vector and frequency in time-modulated periodic media.

physics.class-ph↗

arXiv2026

Topological Phase Transition in Mechanical Honeycomb Lattice

Topological materials provide a new tool to direct wave energy with unprecedented precision and robustness. Three elastic topological phases, the valley Hall, Chern and spin Hall insulators, are currently studied, and they are achieved separately in rather distinct configurations. Here, we explore analytically various topological phase transitions for in-plane elastic wave in a unified mass-spring honeycomb lattice. It is demonstrated that the three elastic topological phases can be realized in this single lattice by designing mass, stiffness or introducing Coriolis' effect. In particular, the interface between valley Hall and Chern insulators is found to support topological interface mode for the first time. Perturbation method is used to derive the analytic effective continuum model in the neighbor of band degeneracy, and the physics in topological phase transitions are revealed through evaluation of topological invariants. The topologically protected interface states, their decaying profile as well as the pseudo-spin-indicating polarization specific for elastic wave are systematically analyzed, and these results are further confirmed numerically by Bloch wave analysis of domain wall strip and transient simulation of finite sized sample. This study offers a concise and unified analytical model to explore topology nature of elastic wave, and can provide intuitive guidance to design of continuum mechanical topological materials.

cond-mat.mtrl-sci↗

arXiv2026

Classification of rotational zero modes in 2D micropolar solids

Zero modes, which are deformations that cost zero energy, underlie many exotic behaviors in elastic metamaterials. While classical linear Cauchy elasticity explains many of these modes, those linked to the rotations of metamaterial inner components often lie beyond its scope. Micropolar elasticity, which incorporates translation and rotation degrees of freedom, provides a framework for capturing these rotational modes. Herein, we present the first complete symmetry-based classification of zero modes in two-dimensional micropolar solids, with an emphasis on rotation-related modes. Guided by this classification, we construct threefold rotationally symmetric micropolar metamaterials and realize typical rotational micropolar zero modes. We further show that these metamaterials exhibit wave phenomena forbidden in Cauchy continua, including the emergence of three bulk waves in the long-wavelength limit and associated triple refraction, chiral acoustic modes, as well as strong wave anisotropy. All intriguing properties are quantitatively captured by micropolar continuum descriptions, whereas the classical Cauchy continuum theory fails to predict these behaviors, even at a qualitative level. Our results establish a general framework for engineering rotation-based zero modes, opening avenues for designing metamaterials with novel wave properties.

physics.app-ph↗

arXiv2026

Resonance-induced frequency splitting and evanescent modes at temporal interfaces in elastic metamaterials

Temporal interfaces, defined by abrupt changes in material properties, break temporal translational symmetry and enable wave phenomena fundamentally different from those at spatial interfaces. Unlike spatial scattering, temporal scattering preserves momentum rather than energy, leading to instantaneous frequency shifts governed by the dispersion relations on either side of the interface. Existing studies in elastic media have mainly considered non-resonant materials, and allow only one-to-one frequency conversion across temporal interfaces. Here, we propose temporal interfaces formed by the sudden activation of local resonators in elastic metamaterials, which induces a transition from non-resonant to resonant dispersion. We demonstrate that such interfaces can induce frequency splitting among scattered waves and elucidate how the scattered-wave amplitudes are governed by the weighted modal correlation coefficients and impedances. Moreover, a novel temporal evanescent mode, characterized by spatial stationarity and temporal decay is demonstrated after the interface, which is well explained by the negative effective modulus evaluated at imaginary frequencies. These findings establish a foundational understanding of wave dynamics at temporal interfaces involving resonant materials, open new opportunities for wave manipulation in time-varying solids.

physics.app-ph↗

arXiv2026

Unimode material based low-frequency underwater acoustic isolation

Extremal materials are a specific class of Cauchy materials whose elasticity tensor has one or more zero eigenvalues. Each zero eigenvalue corresponds to a soft mode requiring zero strain energy, while non-zero eigenvalues correspond to hard modes that cost energy. According to the number, N, of zero eigenvalues, these materials can be referred to as unimode (N=1), bimode (N=2), etc. Extremal materials have enabled novel functions beyond conventional Cauchy media, e.g., phonon polarizers, Rayleigh wave isolators and underwater acoustic cloaks. These functions typically require a single extremal material. Interfaces between two extremal materials exhibit rich wave behaviors, yet have been seldom explored. Here, we proposed the concept of complementary extremal materials, i.e., the soft mode of one extremal material is a hard mode of the other. As one example, we study the interface between an isotropic unimode material and an isotropic bimode material. We show that the interface allows perfect mode conversion from longitudinal waves to transverse waves. A low-frequency underwater acoustic insulator based on complementary extremal materials is proposed. Our finding has been verified with designed metamaterials and using effective-medium modeling. This work demonstrates the potential of complementary extremal materials in controlling elastic wave polarization and waterborne sound.

physics.class-ph↗

arXiv2025

Extremal micropolar materials for elastic wave cloaking

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.

physics.app-ph↗

arXiv2024

Rayleigh surface waves of extremal elastic materials

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.

physics.class-ph↗

arXiv2023

Deformation insensitive thermal conductance of the designed Si metamaterial

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.

physics.app-ph↗

arXiv2019

An asymmetric elastic metamaterial model for elastic wave cloaking

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.

physics.class-ph↗

arXiv2018

Boundary effect on acoustic cloak with unideal pentamode material

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.

physics.class-ph↗

arXiv2018

Elastic quantum spin-Hall effect in Kagome lattices

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.

cond-mat.mes-hall↗

arXiv2018

Tunable fluid-solid metamaterials for manipulation of elastic wave propagation in broad frequency range

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.

physics.app-ph↗

arXiv2017

Longitudinal elastic wave control by pre-deforming semi-linear materials

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.

physics.class-ph↗

arXiv2017

Sound Absorption by Acoustic Microlattice with Optimized Pore Configuration

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.

cond-mat.mtrl-sci↗

arXiv2017

Broadband solid cloak for underwater acoustics

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.

physics.class-ph↗

arXiv2013

Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: membrane model

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.

cond-mat.soft↗

arXiv2013

Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: plate model

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.

cond-mat.soft↗

arXiv2012

Design Omnidirectional Wave Absorbers by Transformation Method

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.

physics.class-ph↗