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A brief review on the recent development of phonon engineering and manipulation at nanoscales
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作者 Siqi Xie Hongxin Zhu +1 位作者 Xing Zhang Haidong Wang 《International Journal of Extreme Manufacturing》 SCIE EI CAS CSCD 2024年第1期177-206,共30页
Phonons are the quantum mechanical descriptions of vibrational modes that manifest themselves in many physical properties of condensed matter systems. As the size of electronic devices continues to decrease below mean... Phonons are the quantum mechanical descriptions of vibrational modes that manifest themselves in many physical properties of condensed matter systems. As the size of electronic devices continues to decrease below mean free paths of acoustic phonons, the engineering of phonon spectra at the nanoscale becomes an important topic. Phonon manipulation allows for active control and management of heat fow, enabling functions such as regulated heat transport. At the same time, phonon transmission, as a novel signal transmission method, holds great potential to revolutionize modern industry like microelectronics technology, and boasts wide-ranging applications. Unlike fermions such as electrons, polarity regulation is difficult to act on phonons as bosons, making the development of effective phonon modulation methods a daunting task.This work reviews the development of phonon engineering and strategies of phonon manipulation at different scales, reports the latest research progress of nanophononic devices such as thermal rectifiers, thermal transistors, thermal memories, and thermoelectric devices,and analyzes the phonon transport mechanisms involved. Lastly, we survey feasible perspectives and research directions of phonon engineering. Thermoelectric analogies, external field regulation, and acousto-optic co-optimization are expected to become future research hotspots. 展开更多
关键词 phonon engineering phononic device NANOSCALE
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EFFECT OF MICROSTRUCTURE ON THE HARDENING AND SOFTENING BEHAVIORS OF POLYCRYSTALLINE SHAPE MEMORY ALLOYS PART Ⅰ:MICROMECHANICS CONSTITUTIVE MODELING 被引量:5
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作者 宋固全 孙庆平 黄克智 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2000年第4期309-324,共16页
The effects of microstructure and its evolution on the macroscopic superelastic stress-strain response of polycrystalline Shape Memory Alloy(SMA)are studied by a microstructure-based constitutive model developed in th... The effects of microstructure and its evolution on the macroscopic superelastic stress-strain response of polycrystalline Shape Memory Alloy(SMA)are studied by a microstructure-based constitutive model developed in this paper.The model is established on the following basis:(1)the transformation conditions of the unconstrained single crystal SMA microdomain(to be distinguished from the bulk single crystal),which serve as the local criterion for the derivation of overall transfor- mation yield conditions of the polycrystal;(2)the micro-to macro-transition scheme by which the connection between the polycrystal aggregates and the single crystal microdomain is established and the macroscopic transformation conditions of the polycrystal SMA are derived;(3)the quantitative incorporation of three microstruc- ture factors(i.e.,nucleation,growth and orientation distribution of martensite)into the modeling.These microstructural factors are intrinsic of specific polycrystal SMA systems and the role of each factor in the macroscopic constitutive response is quan- titatively modeled.It is demonstrated that the interplay of these factors will result in different macroscopic transformation kinematics and kinetics which are responsible for the observed macroscopic stress-strain hardening or softening response,the latter will lead to the localization and propagation of transformation bands in TiNi SMA. 展开更多
关键词 phase transformation MICROSTRUCTURE hardening and softening polycrystalline material shape memory alloys
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A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes 被引量:3
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作者 Yu Wang Daining Fang +1 位作者 Ai Kah Soh Bin Liu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2007年第6期663-671,共9页
In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-... In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT's) is established to describe the nonlinear stress-strain curve of SWCNT's and to predict both the elastic properties and breaking strain of SWCNT's during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT's. 展开更多
关键词 Molecular mechanics approach Carbon nanotube Constitutive relation Young's modulus
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Fracture mechanics analysis on Smart-Cut~ technology.Part 1:Effects of stiffening wafer and defect interaction 被引量:3
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作者 Bin Gu Hongyuan Liu +2 位作者 Yiu-Wing Mai Xi Qiao Feng Shou Wen Yu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第1期73-81,共9页
In the present paper, continuum fracture mechanics is used to analyze the Smart-Cut process, a recently established ion cut technology which enables highly efficient fabrication of various silicon-on-insulator (SOI)... In the present paper, continuum fracture mechanics is used to analyze the Smart-Cut process, a recently established ion cut technology which enables highly efficient fabrication of various silicon-on-insulator (SOI) wafers of high uniformity in thickness. Using integral transform and Cauchy singular integral equation methods, the mode-I and mode-II stress intensity factors, energy release rate, and crack opening displacements are derived in order to examine several important fracture mechanisms involved in the Smart-Cut process. The effects of defect interaction and stiffening wafer on defect growth are investigated. The numerical results indi- cate that a stiffener/handle wafer can effectively prevent the donor wafer from blistering and exfoliation, but it slows down the defect growth by decreasing the magnitudes of SIF's. Defect interaction also plays an important role in the splitting process of SOI wafers, but its contribution depends strongly on the size, interval and internal pressure of defects. Finally, an analytical formula is derived to estimate the implantation dose required for splitting a SOI wafer. 展开更多
关键词 Smart-Cut technology Silicon-on-insulatorwafer Crack growth Fracture mechanics Stress intensityfactor
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Fracture mechanics analysis on Smart-Cut~technology.Part 2:Effect of bonding flaws 被引量:1
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作者 Bin Gu Hongyuan Liu +2 位作者 Yiu-Wing Mai Xi Qiao Feng ShouWen Yu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第2期197-203,共7页
In Part 2 of the paper on the Smart-Cut process, the effects of bonding flaws characterized by the size and internal pressure before and after splitting are studied by using fracture mechanics models. It is found that... In Part 2 of the paper on the Smart-Cut process, the effects of bonding flaws characterized by the size and internal pressure before and after splitting are studied by using fracture mechanics models. It is found that the bonding flaws with large size are prone to cause severe deviation of defect growth, leading to a non-transferred area of thin layer when splitting. In a practical Smart-Cut process where the internal pressure of bonding flaws is very small, large interfacial defects always promote defect growth in the splitting process. Meanwhile, increasing the internal pressure of the bonding flaws decreases the defect growth and its deviation before splitting. The mechanism of relaxation of stiffener constraint is proposed to clarify the effect of bonding flaws. Moreover, the progress of the splitting process is analyzed when bonding flaws are present. After splitting, those bonding flaws with large size and high internal pressure are vulnerable for the blistering of the thin film during high-temperature annealing. 展开更多
关键词 Smart-Cut technology Fracture mechanics Stress intensity factor Interfacial defect
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A MICROMECHANICS ANALYSIS FOR THE MICROSTRUCTURE DESIGN OF A TWO-PHASE PSEUDOELASTIC COMPOSITE
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作者 孙庆平 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1994年第2期162-168,共7页
A micromechanics analysis on the possibility of designing a two-phase pseudoelastic composite is made for the case where ductile transformable shape mem- ory alloy plastic particles are imbedded coherently in an elast... A micromechanics analysis on the possibility of designing a two-phase pseudoelastic composite is made for the case where ductile transformable shape mem- ory alloy plastic particles are imbedded coherently in an elastic matrix. It is demon- strated that a pseudoelastic stress-strain loop in a macroscopic loading-unloading cy- cle can be obtained by microscopically stress induced forward and reverse martensitic transformations in the SMA particles. The relation between the macroscopic stress- strain response and the material parameters of the constituents of this composite is quantified through the micromechanics calculations, which reveals that the best duc- tility and thus the greatest energy absorption capacity of this novel microstructure can be obtained by the optimum material design. 展开更多
关键词 COMPOSITE optimum material design two-phase pseudoelastic composite microstructure design
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Statistical learning prediction of fatigue crack growth via path slicing and re-weighting
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作者 Yingjie Zhao Yong Liu Zhiping Xu 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2023年第6期415-423,共9页
Predicting potential risks associated with the fatigue of key structural components is crucial in engineering design.However,fatigue often involves entangled complexities of material microstructures and service condit... Predicting potential risks associated with the fatigue of key structural components is crucial in engineering design.However,fatigue often involves entangled complexities of material microstructures and service conditions,making diagnosis and prognosis of fatigue damage challenging.We report a statistical learning framework to predict the growth of fatigue cracks and the life-to-failure of the components under loading conditions with uncertainties.Digital libraries of fatigue crack patterns and the remaining life are constructed by high-fidelity physical simulations.Dimensionality reduction and neural network architectures are then used to learn the history dependence and nonlinearity of fatigue crack growth.Path-slicing and re-weighting techniques are introduced to handle the statistical noises and rare events.The predicted fatigue crack patterns are self-updated and self-corrected by the evolving crack patterns.The end-to-end approach is validated by representative examples with fatigue cracks in plates,which showcase the digital-twin scenario in real-time structural health monitoring and fatigue life prediction for maintenance management decision-making. 展开更多
关键词 Fatigue crack growth Structural health monitoring Statistical noises Rare events Digital libraries
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About the special topic of mechanics and biomimetics of biomaterials and animal locomotion
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作者 Xi Qiao Feng Mao Sun 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2010年第1期3-4,共2页
Scientists have increasingly been turning their attentions to searching for inspirations from the splendid living world in order to solve various challenging problems of technologically importance. Rapid advances in o... Scientists have increasingly been turning their attentions to searching for inspirations from the splendid living world in order to solve various challenging problems of technologically importance. Rapid advances in observation techniques and computational ability will make it a reality to understand, at different time and space scales, the functions, 展开更多
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Research on fatigue evaluation method of high-speed train axle based on axle box acceleration
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作者 Wenjing Wang Yiming Zeng +1 位作者 Ruiguo Yan Yiyue Chen 《High-Speed Railway》 2023年第4期233-240,共8页
As a key safety component of the high-speed train, fatigue fracture of the axle would lead to major accidents such as derailment or overturning. The complexity of the axle dynamic stress test seriously enhances the di... As a key safety component of the high-speed train, fatigue fracture of the axle would lead to major accidents such as derailment or overturning. The complexity of the axle dynamic stress test seriously enhances the difficulty of axle fatigue damage analysis. In this paper, the dynamic stress test of the high-speed train axle was carried out,the axle box acceleration was monitored on-track during the test, and the relationship between the axle stress spectrum and acceleration was analyzed on-track. The results show that the relationships between the axle equivalent stresses and the Root Mean Square(RMS) values of the axle box vertical acceleration and lateral acceleration exhibit a strong joint probability density distribution. The concept of the virtual surface density of wheel-rail contact is also proposed to realize the purpose of using axle box acceleration to deduce axle equivalent force. The results quantify the relationship between axle box acceleration and axle equivalent force, provide a new method for predicting the axle damage using the acceleration RMS values, and open up a new approach for structural health monitoring of high-speed train axles. 展开更多
关键词 High-speed train axles Axle-box acceleration Dynamic stress of wheelset axle Fatigue damage Wheel-rail contact virtual surface density
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A comprehensive review on microchannel heat sinks for electronics cooling
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作者 Zhi-Qiang Yu Mo-Tong Li Bing-Yang Cao 《International Journal of Extreme Manufacturing》 SCIE EI CAS CSCD 2024年第2期133-162,共30页
The heat generation of electronic devices is increasing dramatically,which causes a serious bottleneck in the thermal management of electronics,and overheating will result in performance deterioration and even device ... The heat generation of electronic devices is increasing dramatically,which causes a serious bottleneck in the thermal management of electronics,and overheating will result in performance deterioration and even device damage.With the development of micro-machining technologies,the microchannel heat sink(MCHS)has become one of the best ways to remove the considerable amount of heat generated by high-power electronics.It has the advantages of large specific surface area,small size,coolant saving and high heat transfer coefficient.This paper comprehensively takes an overview of the research progress in MCHSs and generalizes the hotspots and bottlenecks of this area.The heat transfer mechanisms and performances of different channel structures,coolants,channel materials and some other influencing factors are reviewed.Additionally,this paper classifies the heat transfer enhancement technology and reviews the related studies on both the single-phase and phase-change flow and heat transfer.The comprehensive review is expected to provide a theoretical reference and technical guidance for further research and application of MCHSs in the future. 展开更多
关键词 microchannel heat sink thermal management of electronics microscale heat transfer heat transfer enhancement
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APPLICATION OF A NEW FAST MULTIPOLE BEM FOR SIMULATION OF 2D ELASTIC SOLID WITH LARGE NUMBER OF INCLUSIONS 被引量:16
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作者 王海涛 姚振汉 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2004年第6期613-622,共10页
A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is pr... A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach.Generalized minimum residual method(GMRES)is used as an iterative solver to solve the equation system formed by BEM iteratively.The numerical results show that the scheme presented is applicable to certain large scale problems. 展开更多
关键词 boundary element fast multipole 2D elastic solid with inclusions GMRES effective property
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Direct numerical simulation of turbulent boundary layer over an anisotropic compliant wall 被引量:6
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作者 Qian-Jin Xia Wei-Xi Huang Chun-Xiao Xu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2019年第2期384-400,共17页
Direct numerical simulation of a spatially developing turbulent boundary layer over a compliant wall with anisotropic wall material properties is performed. The Reynolds number varies from 300 to approximately 860 alo... Direct numerical simulation of a spatially developing turbulent boundary layer over a compliant wall with anisotropic wall material properties is performed. The Reynolds number varies from 300 to approximately 860 along the streamwise direction, based on the external flow velocity and the momentum thickness. Eight typical cases are selected for numerical investigation under the guidance of the monoharmonic analysis. The instantaneous flow fields exhibit the traveling wavy motion of the compliant wall, and the frequency-wavenumber power spectrum of wall pressure fluctuation is computed to quantify the mutual influence of the wall compliance and the turbulent flow at different wave numbers. It is shown that the Reynolds shear stress and the pressure fluctuation are generally enhanced by the wall compliance with the parameters considered in the present study. A dynamical decomposition of the skin-friction coefficient is derived, and a new term (CW) appears due to the wall-induced Reynolds shear stress. The influence of the anisotropic compliant wall motion on the turbulent boundary layer through the wall-induced negative Reynolds shear stress is discussed. To elucidate the underlying mechanism, the budget analysis of the Reynolds stresses transportation is further carried out. The impact of the wall compliance on the turbulent flow is disclosed by examining the variations of the diffusion and velocity-pressure correlation terms. It is shown that increase of the Reynolds stresses inside the flow domain is caused by enhancement of the velocity-pressure correlation term, possibly through the long-range influence of the wall compliance on the pressure field, rather than diffusion of the wall-induced Reynolds shear stress into the fluid flow. 展开更多
关键词 Turbulent boundary layer ANISOTROPIC compliant WALL Direct numerical simulation SKIN-FRICTION coefficient REYNOLDS shear stress
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Directional Motion of Droplets in a Conical Tube or on a Conical Fibre 被引量:9
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作者 刘建林 夏热 +1 位作者 李炳蔚 冯西桥 《Chinese Physics Letters》 SCIE CAS CSCD 2007年第11期3210-3213,共4页
操作液体微滴的方向性的运动具有为一些微能流动的设备的设计和制造的意义。一个基于精力的方法被采用分析在一个圆锥形的试管或在圆锥形的纤维上扔的微滴的方向性的运动。我们执行一个实验在一个开的圆锥形的试管调查微滴的方向性的运... 操作液体微滴的方向性的运动具有为一些微能流动的设备的设计和制造的意义。一个基于精力的方法被采用分析在一个圆锥形的试管或在圆锥形的纤维上扔的微滴的方向性的运动。我们执行一个实验在一个开的圆锥形的试管调查微滴的方向性的运动。我们的理论分析和试验性的观察两个都证明那表面紧张能驱使微滴搬到圆锥形的试管。搬到圆锥形的试管的液体的批评条件被介绍。我们也在圆锥形的吸水的纤维上分析微滴,它能移动从对更厚的目的更薄。 展开更多
关键词 圆锥管 圆锥纤维管 液体 运动状态
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Aerodynamics of indirect thrust measurement by the impulse method 被引量:12
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作者 Cheng-Kang Wu Hai-Xing Wang +2 位作者 Xian Meng Xi Chen Wen-Xia Pan 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第2期152-163,共12页
The aerodynamic aspects of indirect thrust measurement by the impulse method have been studied both experimentally and numerically. The underlying basic aerodynamic principle is outlined, the phenomena in subsonic, su... The aerodynamic aspects of indirect thrust measurement by the impulse method have been studied both experimentally and numerically. The underlying basic aerodynamic principle is outlined, the phenomena in subsonic, supersonic and arc-heated jets are explored, and factors affecting the accuracy of the method are studied and discussed. Results show that the impulse method is reliable for indirect thrust measurement if certain basic requirements are met, and a simple guideline for its proper application is given. 展开更多
关键词 Thrust measurement Impulse method Aerodynamic features Cold jet Arc-heated jet
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Application of MLPG in large deformation analysis 被引量:8
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作者 Xi Zhang Zhenhan Yao Zhangfei Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第4期331-340,共10页
Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method (MLPG) is presented. A material configuration based the nonlinear MLPG formulat... Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method (MLPG) is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O(N) algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion. 展开更多
关键词 Meshless method MLPG. Large deformation HYPERELASTICITY Hyperelasto-plasticity
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AN EQUIVALENT CONTINUUM METHOD OF LATTICE STRUCTURES 被引量:8
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作者 Fan Hualin Yang Wei 《Acta Mechanica Solida Sinica》 SCIE EI 2006年第2期103-113,共11页
An equivalent continuum method is developed to analyze the effective stiffness of three-dimensional stretching dominated lattice materials. The strength and three-dimensional plastic yield surfaces are calculated for ... An equivalent continuum method is developed to analyze the effective stiffness of three-dimensional stretching dominated lattice materials. The strength and three-dimensional plastic yield surfaces are calculated for the equivalent continuum. A yielding model is formulated and compared with the results of other models. The bedding-in effect is considered to include the compliance of the lattice joints. The predicted stiffness and strength are in good agreement with the experimental data, validating the present model in the prediction of the mechanical properties of stretching dominated lattice structures. 展开更多
关键词 stretching dominated lattice materials equivalent continuum method effective stiffness yield surface bedding-in effect
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Base force element method of complementary energy principle for large rotation problems 被引量:8
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作者 Yijiang Peng Yinghua Liu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第4期507-515,共9页
Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacemen... Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM. 展开更多
关键词 Base force element method (BFEM) Complementary energy principle Lagrange multiplier method Geometrically nonlinear Large rotation
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Morphology of liquid drops and thin films on a solid surface with sinusoidal microstructures 被引量:6
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作者 Jian Lin Liu Xi Qiao Feng Shou Wen Yu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第4期315-322,共8页
Surface microstructures of solid materials play a significant role in various wetting and dewetting phenomena. In the present paper, the effect of micro- and nano-structures of a substrate surface on the morphology an... Surface microstructures of solid materials play a significant role in various wetting and dewetting phenomena. In the present paper, the effect of micro- and nano-structures of a substrate surface on the morphology and evolution of liquid droplets and thin films is examined. The governing equations satisfied by droplets and films on a sinusoidal surface are derived by considering van der Waals force, surface tension, gravity and hydrostatic pressure. The morphologies of both liquid droplets and thin films are numerically simulated under various characteristic sizes of roughness. It is found that the droplet shapes show a significant dependence upon the characteristic sizes of substrate microstructures. A thin liquid film on a hydrophilic substrate may have a horizontal surface or replicate the substrate morphology, depending on the wavelength of roughness. 展开更多
关键词 Microstructure ROUGHNESS Wetting Thin film DROPLET
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Capillary Adhesion of Microbeams: Finite Deformation Analysis 被引量:8
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作者 刘建林 冯西桥 《Chinese Physics Letters》 SCIE CAS CSCD 2007年第8期2349-2352,共4页
Capillary force may cause adhesion of devices at micro- and nano-scales. Considering the fact that large deformation is often involved in adhesion of microbeams, we analysed the capillary adhesion of two beams using f... Capillary force may cause adhesion of devices at micro- and nano-scales. Considering the fact that large deformation is often involved in adhesion of microbeams, we analysed the capillary adhesion of two beams using finite deformation elasticity theory. The critical adhesion condition can be obtained from the present method as a function of the bending stiffness, Young's contact angle, the spacing of the two beams as well as the surface tensions of the solid and liquid phases. The solution for the capillary adhesion of a beam with a rigid substrate is also given. The results from the finite deformation analysis are compared with that of infinitesimal deformation method in order to show the necessity of accounting for the nonlinear effect associated with large deflection. The method adopted in this study can also be used to solve other adhesion problems associated with van der Waals force or electrostatic force. 展开更多
关键词 SURFACE MECHANICS FORCES
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RIGID FINITE ELEMENT AND ITS APPLICATIONS IN ENGINEERING 被引量:7
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作者 钱令希 张雄 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1995年第1期44-50,共7页
Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summari... Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summarized in this paper. Based on the theory of RFEM, the Elastic Body-Seams Model (EBSM) is proposed to take the deformation and damage of rock masses into account. 展开更多
关键词 ROCK AND SOIL ENGINEERING RIGID FINITE ELEMENT SLOPE STABILITY LIMIT ANALYSIS
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