Table of Content

01 April 2023, Volume 44 Issue 4

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Articles

Elastic twisting metamaterial for perfect longitudinal-torsional wave mode conversion

Shengjie YAO, Yijun CHAI, Xiongwei YANG, Yueming LI

2023, 44(4):  515-524.  doi:10.1007/s10483-023-2978-7

Abstract ( 898 )   HTML ( 26)   PDF (3749KB) ( 303 )  

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In this work, we design a twisting metamaterial for longitudinal-torsional (L-T) mode conversion in pipes through exploring the theory of perfect transmodal Fabry-Perot 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 L-T mode-converting metamaterial and its design methodology can be applied in various ultrasonic devices.

Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

Yanpeng YUE, Yongping WAN

2023, 44(4):  525-546.  doi:10.1007/s10483-023-2979-8

Abstract ( 878 )   HTML ( 4)   PDF (464KB) ( 102 )  

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The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem. These solutions can be reduced to the ones of an elastodynamic problem. Based on the effective medium method, these closed-form solutions can be used to establish the self-consistent equations about the frequency-dependent effective parameters, which can be numerically solved by iteration. Theoretical predictions are compared with the experimental results, and good agreement can be found. Furthermore, the analyses on the effects of microstructure and wavelength on the effective properties, resonance frequencies, and attenuation are also presented, which may provide some guidance for the microstructure design and analysis of piezoelectric composites.

A pre-strain strategy of current collectors for suppressing electrode debonding in lithium-ion batteries

Bo RUI, Bo LU, Yicheng SONG, Junqian ZHANG

2023, 44(4):  547-560.  doi:10.1007/s10483-023-2976-9

Abstract ( 819 )   HTML ( 4)   PDF (2164KB) ( 177 )  

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The interfacial debonding between the active layer and the current collector has been recognized as a critical mechanism for battery fading, and thus has attracted great efforts focused on the related analyses. However, much still remains to be studied regarding practical methods for suppressing electrode debonding, especially from the perspective of mechanics. In this paper, a pre-strain strategy of current collectors to alleviate electrode debonding is proposed. An analytical model for a symmetric electrode with a deformable and limited-thickness current collector is developed to analyze the debonding behavior involving both a pre-strain of the current collector and an eigen-strain of the active layers. The results reveal that the well-designed pre-strain can significantly delay the debonding onset (by up to 100%) and considerably reduce the debonding size. The critical values of the pre-strain are identified, and the pre-strain design principles are also provided. Based on these findings, this work sheds light on the mechanical design to suppress electrode degradation.

Multiresolution method for bending of plates with complex shapes

Jizeng WANG, Yonggu FENG, Cong XU, Xiaojing LIU, Youhe ZHOU

2023, 44(4):  561-582.  doi:10.1007/s10483-023-2972-8

Abstract ( 879 )   HTML ( 3)   PDF (789KB) ( 168 )  

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A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains. To realize this method, we design a new wavelet basis function, by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains. In the solution of differential equations, various derivatives of the unknown function are denoted as new functions. Then, the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals. Therefore, the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative. During the application of the proposed method, boundary conditions can be automatically included in the integration operations, and relevant matrices can be assured to exhibit perfect sparse patterns. As examples, we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes. By comparing the solutions obtained by the proposed method with the exact solutions, the new multiresolution method is found to have a convergence rate of fifth order. The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method (FEM) with tens of thousands of elements. In addition, because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order, we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

Antiplane shear crack in a prestressed elastic medium based on the couple stress theory

Jian CHEN, Yawei WANG, Xianfang LI

2023, 44(4):  583-602.  doi:10.1007/s10483-023-2977-6

Abstract ( 846 )   HTML ( 5)   PDF (465KB) ( 201 )  

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A prestressed elastic medium containing a mode-III crack is studied by means of the couple stress theory (CST). Based on the CST under initial stresses, a governing differential equation along with a mixed boundary value problem is established. The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method. To determine their intensity, a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial. The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor (CSIF) and the force stress intensity factor (FSIF) around the crack tips. The symmetric part of the shear stress has no singularity, and the skew-symmetric part related to the couple stress exhibits an r^-3/2 singularity, in which r is the distance from the crack tip. The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.

Dynamic coupled thermo-hydro-mechanical problem for heterogeneous deep-sea sediments under vibration of mining vehicle

Wei ZHU, Xingkai MA, Xinyu SHI, Wenbo MA

2023, 44(4):  603-622.  doi:10.1007/s10483-023-2971-7

Abstract ( 867 )   HTML ( 4)   PDF (765KB) ( 183 )  

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Due to the influence of deep-sea environment, deep-sea sediments are usually heterogeneous, and their moduli of elasticity and density change as depth changes. Combined with the characteristics of deep-sea sediments, the thermo-hydro-mechanical coupling dynamic response model of heterogeneous saturated porous sediments can be established to study the influence of elastic modulus, density, frequency, and load amplitude changes on the model. Based on the Green-Lindsay generalized thermoelasticity theory and Darcy's law, the thermo-hydro-mechanical coupled dynamic response model and governing equations of heterogeneous deep-sea sediments with nonlinear elastic modulus and density are established. The analytical solutions of dimensionless vertical displacement, vertical stress, excess pore water pressure, and temperature are obtained by means of normal modal analysis, which are depicted graphically. The results show that the changes of elastic modulus and density have few effects on vertical displacement, vertical stress, and temperature, but have great effects on excess pore water pressure. When the mining machine vibrates, the heterogeneity of deep-sea sediments has great influence on vertical displacement, vertical stress, and excess pore water pressure, but has few effects on temperature. In addition, the vertical displacement, vertical stress, and excess pore water pressure of heterogeneous deep-sea sediments change more gently. The variation trends of physical quantities for heterogeneous and homogeneous deep-sea sediments with frequency and load amplitude are basically the same. The results can provide theoretical guidance for deep-sea mining engineering construction.

Model-based adaptive locomotion and clustering control of microparticles through ultrasonic topological charge modulation

H. S. LEE, H. X. CAO, D. JUNG, C. S. KIM

2023, 44(4):  623-640.  doi:10.1007/s10483-023-2973-9

Abstract ( 874 )   HTML ( 3)   PDF (14914KB) ( 272 )  

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We present a novel motion control technique for microrobot clusters to exploit the characteristics of the ultrasonic field. The method comprises two steps, i.e., introducing an ultrasonic actuation (UA) linear model for three-dimensional (3D) locomotion and controlling the topological charge (TC) in the ultrasonic vortex for microrobot clustering. Here, the TC is a controllable parameter for the expansion and contraction of the pressure null space inside the vortex. We present a TC control method to cluster sporadically distributed microrobots in a specific workspace. To validate the concept, a UA system composed of 30 ultrasonic transducers with 1 MHz frequency is fabricated, and the characteristics of the generated acoustic pressure field are analyzed through simulations. Subsequently, the performances of the adaptive controller for precise 3D locomotion and the TC control method for clustering are evaluated. Finally, the UA technology, which performs both clustering and locomotion in a complex manner, is validated with a gelatin phantom in an in-vitro environment.

Three-dimensional mixed convection stagnation-point flow past a vertical surface with second-order slip velocity

A. V. ROŞCA, N. C. ROŞCA, I. POP

2023, 44(4):  641-652.  doi:10.1007/s10483-023-2975-7

Abstract ( 920 )   HTML ( 12)   PDF (695KB) ( 194 )  

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This study is concerned with the three-dimensional (3D) stagnation-point for the mixed convection flow past a vertical surface considering the first-order and second-order velocity slips. To the authors' knowledge, this is the first study presenting this very interesting analysis. Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations (ODEs) by using appropriate similarity transformation. These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language. The effects of the governing parameters on the non-dimensional velocity profiles, temperature profiles, skin friction coefficients, and the local Nusselt number are presented in detail through a series of graphs and tables. Interestingly, it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation. The numerical computations of the present work are compared with those from other research available in specific situations, and an excellent consensus is observed. Another exciting feature for this work is the existence of dual solutions. An important remark is that the dual solutions exist for both assisting and opposing flows. A linear stability analysis is performed showing that one solution is stable and the other solution is not stable. We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics. These effects are depicted in graphs and discussed in this paper. The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow, as well as on the heat transfer characteristics.

Effect of periodic heat transfer on the transient thermal behavior of a convective-radiative fully wet porous moving trapezoidal fin

B. J. GIREESHA, M. L. KEERTHI

2023, 44(4):  653-668.  doi:10.1007/s10483-023-2974-6

Abstract ( 874 )   HTML ( 5)   PDF (409KB) ( 270 )  

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A moving trapezoidal profiled convective-radiative porous longitudinal fin wetted in a single-phase fluid is considered in the current article. The periodic variation in the fin base temperature is taken into account along with the temperature sensitive thermal conductivity and convective heat transfer coefficients. The modeled problem, which is resolved into a non-linear partial differential equation (PDE), is made dimensionless and solved by employing the finite difference method (FDM). The results are displayed through graphs and discussed. The effects of amplitude, frequency of oscillation, wet nature, Peclet number, and other relevant quantities on the distribution of temperature through the fin length and with the dimensionless time are investigated. It is deciphered that the periodic heat transfer gives rise to the wavy nature of the fin thermal profile against time. The analysis is beneficial in the design of fin structures for applications like solar collectors, space/airborne applications, and refrigeration industries.

Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows

M. HAMID, M. USMAN, Zhenfu TIAN

2023, 44(4):  669-692.  doi:10.1007/s10483-023-2970-6

Abstract ( 1947 )   HTML ( 284)   PDF (7001KB) ( 3131 )  

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The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics (MHD) flows. The time derivative is expressed by means of Caputo's fractional derivative concept, while the model is solved via the full-spectral method (FSM) and the semi-spectral scheme (SSS). The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques. The SSS is developed by discretizing the time variable, and the space domain is collocated by using equal points. A detailed comparative analysis is made through graphs for various parameters and tables with existing literature. The contour graphs are made to show the behaviors of the velocity and magnetic fields. The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows, and the concept may be extended for variable order models arising in MHD flows.