Reconfigurable mechanism-based metamaterials for ternary-coded elastic wave polarizers and programmable refraction control

Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are frequency-dependent and unchangeable.Here,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties.Based on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are demonstrated.Particularly,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first achieved.Then,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative refraction.Finally,the wave functions with detailed microstructures are numerically verified.

Mathematical framework of nonlinear elastic waves propagating in pre-stressed media

Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.

On Klein tunneling of low-frequency elastic waves in hexagonal topological plates

Incident particles in the Klein tunnel phenomenon in quantum mechanics can pass a very high potential barrier.Introducing the concept of tunneling into the analysis of phononic crystals can broaden the application prospects.In this study,the structure of the unit cell is designed,and the low frequency(<1 k Hz)valley locked waveguide is realized through the creation of a phononic crystal plate with a topological phase transition interface.The defect immunity of the topological waveguide is verified,that is,the wave can propagate along the original path in the cases of impurities and disorder.Then,the tunneling phenomenon is introduced into the topological valley-locked waveguide to analyze the wave propagation,and its potential applications(such as signal separators and logic gates)are further explored by designing phononic crystal plates.This research has broad application prospects in information processing and vibration control,and potential applications in other directions are also worth exploring.

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity

The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag(TPL), dual-phase-lag(DPL), Green-Naghdi-III(GNIII), Lord-Shulman(LS), and classical coupled(CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.

A NUMERICAL ANALYSIS OF THREE-DIMENSIONAL THERMOELASTIC STRESS WAVE PROPAGATION PROBLEM

This paper is concerned with the numerical technique based on the method of characteristics for three-dimensional dynamic thermoelastic problems. A numerical example for the three-dimensional stress wave propagation in a thermoelastic bar of square cross section subjected to both an impact loading and a thermal shock is presented.

Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion

In this work,we design a twisting metamaterial for longitudinal-torsional(L-T)mode conversion in pipes through exploring the theory of perfect transmodal FabryPerot interference(TFPI).Assuming that the axial and radial motions in pipes can be decoupled,we find that the metamaterial can be designed in a rectangular coordinate system,which is much more convenient than that in a cylindrical system.Numerical calculation with detailed microstructures shows that an efficient L-T mode conversion can be obtained in pipes with different radii.In addition,we fabricate mode-converting microstructures on an aluminum pipe and conduct ultrasonic experiments,and the results are in good agreement with the numerical calculations.We expect that the proposed LT mode-converting metamaterial and its design methodology can be applied in various ultrasonic devices.

Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Evaluation of soil fabric using elastic waves during load-unload

It is essential to assess the evolution of soil fabric as it has an important role in the mechanical responses of soils during complex loading conditions.This contribution carries out the physical experiments using three granular materials in the laboratory.The variations of compression and shear wave velocities(Vp and Vs)are investigated during load-unload cycles under dry and drained conditions.Supplementary discrete element method(DEM)simulations are performed to understand the evolution of soil fabric during the equivalent load-unload cycles using spherical particles.Vp and Vs are not always reversible even though the stress state regains its isotropic condition after unload,indicating that Vp and Vs are governed by not only the stress state but also the fabric change.The variations of Vp/Vs are density-and stress-dependent;a higher level of stress ratio(s01/s03)threshold is observed for denser packings to trigger a significant change in wave velocity ratio(Vp/Vs)for experimental results using spherical glass beads and simulation data using spherical particles.Considering the particle shape,a higher s01/s03 threshold is found for more angular particles than rounded particles.The DEM result reveals that Vp/Vs of spherical particles can be correlated linearly with the evolution of fabric ratio(Fver/Fhor)during loadunload in a pre-peak range under dry and drained conditions.

Experimental Study on the Wavelengths of Two-Dimensional and Three-Dimensional Freak Waves

Freak waves are commonly characterized by strong-nonlinearity, and the wave steepness, which is calculated from the wavelength, is a measure of the degree of the wave nonlinearity. Moreover, the wavelength can describe the locally spatial characteristics of freak waves. Generally, the wavelengths of freak waves are estimated from the dispersion relations of Stokes waves. This paper concerns whether this approach enables a consistent estimate of the wavelength of freak waves. The two-(unidirectional, long-crested) and three-dimensional(multidirectional, shortcrested) freak waves are simulated experimentally through the dispersive and directional focusing of component waves, and the wavelengths obtained from the surface elevations measured by the wave gauge array are compared with the results from the linear, 3rd-order and 5th-order Stokes wave theories. The comparison results suggest that the 3rd-order theory estimates the wavelengths of freak waves with higher accuracy than the linear and 5th-order theories. Furthermore, the results allow insights into the dominant factors. It is particularly noteworthy that the accuracy is likely to depend on the wave period, and that the wavelengths of longer period freak waves are overestimated but the wavelengths are underestimated for shorter period ones. In order to decrease the deviation, a modified formulation is presented to predict the wavelengths of two-and three-dimensional freak waves more accurately than the 3rd-order dispersion relation, by regression analysis. The normalized differences between the predicted and experimental results are over 50% smaller for the modified model suggested in this study compared with the 3rd-order dispersion relation.

Investigation of long-wavelength elastic wave propagation through wet bentonite-filled rock joints

The saturation of the compacted bentonite buffer in the deep geological repository can cause bentonite swelling,intrusion into rock fractures,and erosion.Inevitably,erosion and subsequent bentonite mass loss due to groundwater inflow can aggravate the overall integrity of the engineered barrier system.Therefore,the coupled hydro-mechanical interaction between the buffer and rock during groundwater inflow and bentonite intrusion should be evaluated to guarantee the long-term safety of deep geological disposal.This study investigated the effect of bentonite erosion and intrusion on the elastic wave propagation characteristics in jointed rocks using a quasi-static resonant column test.Jointed rock specimens with different joint conditions(i.e.joint surface saturation and bentonite filling)were prepared using granite rock discs sampled from the Korea Underground Research Tunnel(KURT)and Gyeongju bentonite.The long-wavelength longitudinal and shear wave velocities were measured under different normal stress levels.A Hertzian-type power model was used to fit the wave velocities,and the relationship between the two fitted parameters provided the trend of joint conditions.Numerical simulations using three-dimensional distinct element code(3DEC)were conducted to better understand how the long-wavelength wave propagates through wet bentonite-filled rock joints.

The mechanism to reform dynamic performance of an elastic wave-front in a piezoelectric semiconductor by the wave-carrier interaction induced from static biasing fields

The propagation of an elastic wave(EW)in a piezoelectric semiconductor(PSC)subjected to static biasing fields is investigated.It is found that there exist two coupling waves between electric field and charge carriers.One is stimulated by the action of the polarized electric field in the EW-front on charge carriers(EFC),and the other is stimulated by the action of initial electric field in biasing fields on dynamic carriers(IEC).Obviously,the latter is a man-made and tunable wave-carrier interaction.A careful study shows that IEC can play a leading role in remaking dynamic performance of the wave-front and an inter-medium role in transferring energy from biasing fields to EW-fronts.Hence,a method is proposed to reform the EW performance by biasing-fields:reforming the dispersivity of EW-fronts by promoting competition between IEC and EFC and inverting the dissipation by the IEC to transfer energy from biasing fields to EWfronts.The corresponding tuning laws on the phase-frequency characteristics of an EW show that the wave velocity can be regulated smaller than the pure EW velocity at a lowfrequency and larger than the pure piezoelectric wave velocity at a high-frequency.As for regulating the amplitude-frequency characteristics of the EW by the IEC,analyses show that EWs can obtain amplification only for those with relatively high vibration frequencies(small wave lengths).The studies will provide guidance for theoretical analysis of waves propagating in PSCs and practical application and design of piezotronic devices.

Assessment of the Elastic-Wave Well Treatment in Oil-Bearing Clastic and Carbonate Reservoirs

A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s law.It is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free members.As the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes larger.An equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic wave.The obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.

Real-time Shear Wave Elastography Assessment of Muscle Elasticity in Patients with Renal Failure

Objective:To explore the value of real-time elastic shear wave in evaluating muscle elasticity in patients with renal failure.Methods:50 patients with chronic renal failure from January 2019 to December 2022 were randomly selected as the experimental group,and 50 healthy patients aged 21-61 during the same period were selected as the control group,and the basic information of the patients,including age,gender,body mass index,etc.,were collected.Besides,the Young's modulus of the two groups of patients were observed and analyzed.Results:The Young's modulus values of left and right gastrocnemius muscles in the experimental group were significantly lower than those in the control group(P<0.05),and there was no statistical difference between the left and right sides of the experimental group and the control group(P>0.05).Conclusion:Real-time shear wave elastography provides a non-invasive,real-time and effective tool for the assessment of muscle elasticity in patients with renal failure.Through further research and optimization,real-time shear wave elastography will play a greater role in the prevention and treatment of patients with renal failure,improving the quality of life and prognosis of patients.

Three-dimensional admittance analysis of lithospheric elastic thickness over the Louisville Ridge

Using bathymetry and altimetric gravity anomalies, a 1°×9 1° lithospheric effective elastic thickness（Te） model over the Louisville Ridge and its adjacent regions is calculated using the moving window admittance technique. For comparison, three bathymetry models are used： general bathymetric charts of the oceans, SIO V15.1,and BAT_VGG. The results show that BAT_VGG is more suitable for calculating T e than the other two models. T e along the Louisville Ridge was re-evaluated. The southeast of the ridge has a medium Te of 10–20 km, while Te increases dramatically seaward of the Tonga-Kermadec trench as a result of the collision of the Pacific and IndoAustralian plates.

MESHLESS ANALYSIS FOR THREE-DIMENSIONAL ELASTICITY WITH SINGULAR HYBRID BOUNDARY NODE METHOD

The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.

Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.

Three-Dimensional Static Analysis of Nanoplates and Graphene Sheets by Using Eringen’s Nonlocal Elasticity Theory and the Perturbation Method

A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.

Prediction of three-dimensional elastic behavior of filament-wound composites based on the bridging model

This work provides a method to predict the three-dimensional equivalent elastic properties of the filament-wound composites based on the multi-scale homogenization principle.In the meso-scale,a representative volume element(RVE)is defined and the bridging model is adopted to establish a theoretical predictive model for its three-dimensional equivalent elastic constants.The results obtained through this method for the previous experimental model are compared with the ones gained respectively by experiments and classical laminate theory to verify the reliability of this model.In addition,the effects of some winding parameters,such as winding angle,on the equivalent elastic behavior of the filament-wound composites are analyzed.The rules gained can provide a theoretical reference for the optimum design of filament-wound composites.