Multiscale Finite Element Method for Coupling Analysis of Heterogeneous Magneto-Electro-Elastic Structures in Thermal Environment

Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.

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.

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.

Publisher Correction to:Highly Elastic,Bioresorbable Polymeric Materials for Stretchable,Transient Electronic Systems

Due to typesetting mistake,Hanul Min was missed to be denoted as a corresponding author in the article.The type-setter apologizes for this.The original article has been corrected.Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,which permits use,sharing,adaptation,distribution and reproduction in any medium or format,as long as you give appropriate credit to the original author(s)and the source,provide a link to the Creative Commons licence,and indicate if changes were made.The images or other third party material in this article are included in the article’s Creative Commons licence,unless indicated otherwise in a credit line to the material.If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use,you will need to obtain permission directly from the copyright holder.

A novel relationship between elastic modulus and void ratio associated with principal stress for coral calcareous sand

Elastic moduli,e.g.shear modulus G and bulk modulus K,are important parameters of geotechnical materials,which are not only the indices for the evaluation of the deformation ability of soils but also the important basic parameters for the development of the constitutive models of geotechnical materials.In this study,a series of triaxial loading-unloading-reloading shear tests and isotropic loading-unloadingreloading tests are conducted to study several typical mechanical properties of coral calcareous sand(CCS),and the void ratio evolution during loading,unloading and reloading.The test results show that the stress-strain curves during multiple unloading processes are almost parallel,and their slopes are much greater than the deformation modulus at the initial stage of loading.The relationship between the confining pressure and the volumetric strain can be defined approximately by a hyperbolic equation under the condition of monotonic loading of confining pressure.Under the condition of confining pressure unloading,the evolution of void ratio is linear in the e-lnp0 plane,and these lines are a series of almost parallel lines if there are multiple processes of unloading.Based on the experimental results,it is found that the modified Hardin formulae for the elastic modulus estimation have a significant deviation from the tested values for CCS.Based on the experimental results,it is proposed that the elastic modulus of soils should be determined by the intersection line of two spatial surfaces in the G/K-e-p’/pa space(pa:atmosphere pressure).“Ye formulation”is further proposed for the estimation of the elastic modulus of CCS.This new estimation formulation for soil elastic modulus would provide a new method to accurately describe the mechanical behavior of granular soils.

Theoretical analysis of the elastic Kelvin-Helmholtz instability in explosive weldings

By considering the joint effects of the Kelvin-Helmholtz(KH) and Rayleigh-Taylor(RT) instabilities, this paper presents an interpretation of the wavy patterns that occur in explosive welding. It is assumed that the elasticity of the material at the interface effectively determines the wavelength, because explosive welding is basically a solid-state welding process. To this end, an analytical model of elastic hydrodynamic instabilities is proposed, and the most unstable mode is selected in the solid phase. Similar approaches have been widely used to study the interfacial behavior of solid metals in high-energy-density physics. By comparing the experimental and theoretical results, it is concluded that thermal softening,which significantly reduces the shear modulus, is necessary and sufficient for successful welding. The thermal softening is verified by theoretical analysis of the increase in temperature due to the impacting and sliding of the flyer and base plates, and some experimental observations are qualitatively validated.In summary, the combined effect of the KH and RT instabilities in solids determines the wavy morphology, and our theoretical results are in good qualitative agreement with experimental and numerical observations.

Determining the effective elastic thickness through cross-correlation between isostatic disturbances

The elastic thickness parameter was estimated using the mobile correlation technique between the observed isostatic disturbance and the gravity disturbance calculated through direct gravimetric modeling. We computed the vertical flexure value of the crust for a specific elastic thickness using a given topographic dataset. The gravity disturbance due to the topography was determined after the calculation. A grid of values for the elastic thickness parameter was generated. Then, a moving correlation was performed between the observed gravity data(representing actual surface data) and the calculated data from the forward modeling. The optimum elastic thickness of the particular point corresponded to the highest correlation coefficient. The methodology was tested on synthetic data and showed that the synthetic depth closely matched the original depth, including the elastic thickness value. To validate the results, the described procedure was applied to a real dataset from the Barreirinhas Basin, situated in the northeastern region of Brazil. The results show that the obtained crustal depth is highly correlated with the depth from known models. Additionally, we noted that the elastic thickness behaves as expected, decreasing from the continent towards the ocean. Based on the results, this method has the potential to be employed as a direct estimate of crustal depth and elastic thickness for any region.

Linearized waveform inversion for vertical transversely isotropic elastic media:Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs.Seismic migration aims at obtaining structural images of subsurface geologic discontinuities.More specifically,seismic migration estimates the reflectivity function(stacked average reflectivity or pre-stack angle-dependent reflectivity)from seismic reflection data.On the other hand,seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations.Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters.Although there exist many differences,pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.Usually,seismic migration and inversion techniques assume an acoustic or isotropic elastic medium.Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property.We present a linearized waveform inversion(LWI)scheme for weakly anisotropic elastic media with vertical transversely isotropic(VTI)symmetry.It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations(ΔVp_(0)/Vp_(0)/Vs_(0)/Vs_(0)/,Δ∈,Δδ)from the long-wavelength reference model.Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration.We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method.The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images.We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters.Especially,the Thomsen parameter is the most difficult to resolve.We also analyze the multi-parameter crosstalk using scattering radiation patterns.The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Microwave-induced thermoacoustic elastic imaging:A simulation study

Microwave-induced thermoacoustic imaging(MTI)has the advantages of high resolution,high contrast,non-ionization,and non-invasive.Recently,MTI was used in the¯eld of breast cancer screening.In this paper,based on the¯nite element method(FEM)and COMSOL Multiphysics software,a three-dimensional breast cancer model suitable for exploring the MTI process is proposed to investigate the in°uence of Young's modulus(YM)of breast cancer tissue on MTI.It is found that the process of electromagnetic heating and initial pressure generation of the entire breast tissue is earlier in time than the thermal expansion process.Besides,compared with normal breast tissue,tumor tissue has a greater temperature rise,displacement,and pressure rise.In particular,YM of the tumor is related to the speed of thermal expansion.In particular,the larger the YM of the tumor is,the higher the heating and contraction frequency is,and the greater the maximum pressure is.Di®erent Young's moduli correspond to di®erent thermoacoustic signal spectra.In MTI,this study can be used to judge di®erent degrees of breast cancer based on elastic imaging.In addition,this study is helpful in exploring the possibility of microwave-induced thermoacoustic elastic imaging(MTAE).

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.

Acoustic radiation force on a cylindrical composite particle with an elastic thin shell and an internal eccentric liquid column in a plane ultrasonic wave field

A model with three-layer structure is introduced to explore the acoustic radiation force(ARF)on composite particles with an elastic thin shell.Combing acoustic scattering of cylinder and the thin-shell theorem,the ARF expression was derived,and the longitudinal and transverse components of the force and axial torque for an eccentric liquid-filled composite particle was obtained.It was found that many factors,such as medium properties,acoustic parameters,eccentricity,and radius ratio of the inner liquid column,affect the acoustic scattering field of the particle,which in turn changes the forces and torque.The acoustic response varies with the particle structures,so the resonance peaks of the force function and torque shift with the eccentricity and radii ratio of particle.The acoustic response of the particle is enhanced and exhibits higher force values due to the presence of the elastic thin shell and the coupling effect with the eccentricity of the internal liquid column.The decrease of the inner liquid density may suppress the high-order resonance peaks,and internal fluid column has less effects on the change in force on composite particle at ka>3,while limited differences exist at ka<3.The axial torque on particles due to geometric asymmetry is closely related to ka and the eccentricity.The distribution of positive and negative force and torque along the axis ka exhibits that composite particle can be manipulated or separated by ultrasound.Our theoretical analysis can provide support for the acoustic manipulation,sorting,and targeting of inhomogeneous particles.

E-Cervix imaging displaying cervical elasticity characteristics of healthy adult nulliparous women at different age groups and different menstrual cycle stages

Objective To observe the cervical elasticity of healthy adult nulliparous women at different age groups and different stages of menstrual cycle with E-Cervix imaging technology.Methods A total of 218 healthy adult nulliparous women who underwent transvaginal ultrasound examination for routine physical examination were retrospectively enrolled,including 103 in follicular phase,78 in ovulation phase and 37 in luteal phase.Cervical canal length(CL)and E-Cervix elasticity parameters were compared among different age groups and different stages of menstrual cycle,including elasticity contrast index(ECI),hardness ratio(HR),cervical internal and external orifice strain values(IOS and EOS)and IOS/EOS ratio.Results No significant difference of CL nor cervical elasticity parameters was detected among healthy adult nulliparous women at different age groups(all P>0.05).There were significant differences of ECI,HR and IOS among different menstrual cycle stages(all P<0.05),among which women in follicular phase had higher ECI and IOS but lower HR than those in luteal phase(all P<0.05).Conclusion No significant difference of cervical elasticity existed among healthy adult nulliparous women at different age groups.Meanwhile,cervical elasticity of healthy adult nulliparous women changed during menstrual cycle,in follicular phase had higher ECI and IOS but lower HR than in luteal phase.

Research on the flow stability and noise reduction characteristics of quasi-periodic elastic support skin

To enhance flow stability and reduce hydrodynamic noise caused by fluctuating pressure,a quasiperiodic elastic support skin composed of flexible walls and elastic support elements is proposed for fluid noise reduction.The arrangement of the elastic support element is determined by the equivalent periodic distance and quasi-periodic coefficient.In this paper,a dynamic model of skin in a fluid environment is established.The influence of equivalent periodic distance and quasi-periodic coefficient on flow stability is investigated.The results suggest that arranging the elastic support elements in accordance with the quasi-periodic law can effectively enhance flow stability.Meanwhile,the hydrodynamic noise calculation results demonstrate that the skin exhibits excellent noise reduction performance,with reductions of 10 dB in the streamwise direction,11 dB in the spanwise direction,and 10 dB in the normal direction.The results also demonstrate that the stability analysis method can serve as a diagnostic tool for flow fields and guide the design of noise reduction structures.

Dynamic characteristics of multi-span spinning beams with elastic constraints under an axial compressive force

A theoretical model for the multi-span spinning beams with elastic constraints under an axial compressive force is proposed.The displacement and bending angle functions are represented through an improved Fourier series,which ensures the continuity of the derivative at the boundary and enhances the convergence.The exact characteristic equations of the multi-span spinning beams with elastic constraints under an axial compressive force are derived by the Lagrange equation.The efficiency and accuracy of the present method are validated in comparison with the finite element method(FEM)and other methods.The effects of the boundary spring stiffness,the number of spans,the spinning velocity,and the axial compressive force on the dynamic characteristics of the multi-span spinning beams are studied.The results show that the present method can freely simulate any boundary constraints without modifying the solution process.The elastic range of linear springs is larger than that of torsion springs,and it is not affected by the number of spans.With an increase in the axial compressive force,the attenuation rate of the natural frequency of a spinning beam with a large number of spans becomes larger,while the attenuation rate with an elastic boundary is lower than that under a classic simply supported boundary.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Helmholtz decomposition with a scalar Poisson equation in elastic anisotropic media

P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation can also be used to better understand and distinguish wave types in complex media.At present,the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering,low-rank approximation,and vector Poisson equation.Most of these methods require multiple Fourier transforms or the calculation of large matrices,which require high computational costs for problems with large scale.In this paper,an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain.For 2D problems,the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation.Therefore,compared with existing methods based on pseudoHelmholtz decomposition operators,this method can significantly reduce the computational cost.Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.

Design and fabrication of compound varifocal lens driven by polydimethylsiloxane film elastic deformation

A compound varifocal lens based on electromagnetic drive technology is designed and fabricated, where the polydimethylsiloxane(PDMS) film acts as a driving component, while the PDMS biconvex lens and the plane-concave lens form a coaxial compound lens system. The plane-concave lens equipped with driving coils is installed directly above the PDMS lens surrounded by the annular magnet. When different currents are applied, the annular magnet moves up and down, driving the PDMS film to undergo elastic deformation, and then resulting in longitudinal movement of the PDMS lens. The position change of the PDMS lens changes the focal length of the compound lens system. To verify the feasibility and practicability of this design, a prototype of our compound lens system is fabricated in experiment. Our proposed compound lens shows that its zoom ability reaches 9.28 mm when the current ranges from -0.20 A to 0.21 A.

Comparative study of nudged elastic band and molecular dynamics methods for diffusion kinetics in solid-state electrolytes

Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynamics(MD)methods,provide powerful tools for the design of solid-state electrolytes.The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures.However,it relies on simulations at temperatures much higher than working temperature.This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark.We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV.The calculated diffusion barrier is 0.31 eV from both methods.The diffusion coefficients at room temperature are 4.3×10^(-9) cm^(2)⋅s^(−1) and 2.2×10^(-9) cm^(2)⋅s^(−1),respectively,from the NEB and MD methods.Our results justify the reliability of the MD method,even though high temperature simulations have to be employed to overcome the limitation on simulation time.

Impacts of artificial dams on terrestrial water storage changes and the Earth's elastic load response during 1950-2016: A case study of medium and large reservoirs in Chinese mainland

The construction of dams for intercepting and storing water has altered surface water distributions, landsea water exchanges, and the load response of the solid Earth. The lack of accurate estimation of reservoir properties through the land surface and hydrological models can lead to water storage simulation and extraction errors. This impact is particularly evident in many artificial reservoirs in China. The study aims to comprehensively assess the spatiotemporal distribution and trends of water storage in medium and large reservoirs(MLRs) in Chinese mainland during 1950-2016, and to investigate the gravity,displacement, and strain effects induced by the reservoir mass concentration using the load elasticity theory. In addition, the impoundment contributions of MLRs to the relative sea level changes were assessed using a sea-level equation. The results show impoundment increases in the MLRs during1950-2016, particularly in the Yangtze River(Changjiang) and southern basins, causing significant elastic load effects in the surrounding areas of the reservoirs and increasing the relative sea level in China's offshore. However, long-term groundwater estimation trends are overestimated and underestimated in the Yangtze River and southwestern basins, respectively, due to the neglect of the MLRs impacts or the uncertainty of the hydrological model's output(e.g., soil moisture, etc.). The construction of MLRs may reduce the water mass input from land to the ocean, thus slowing global sea level rise. The results of the impact of human activities on the regional water cycle provide important references and data support for improving the integration of hydrological models, evaluating Earth's viscoelastic responses under longterm reservoir storage, enhancing in-situ and satellite geodetic measurements, and identifying the main factors driving sea level changes.