This study investigates the surface effects on the operation of double-ended dislocation sources in single-crystal micropillars under compression.A comprehensive theoretical framework is formulated to derive the stres...This study investigates the surface effects on the operation of double-ended dislocation sources in single-crystal micropillars under compression.A comprehensive theoretical framework is formulated to derive the stress field of the source segment and the corresponding Peach-Koehler(PK)forces acting on this segment near the free surfaces.An analytical formulation is then developed to compare the source strength with and without the influence of the surface stress.The results reveal that the surface effects on the dislocation source strength are highly sensitive to the interplay between the source length and its distance from the free surface.These surface effects can either enhance or reduce the critical stress required for the source operation by up to 50%,leading to significant fluctuations in yield strength,as commonly observed in discrete dislocation dynamics simulations and experimental studies.These findings provide different interpretations for the size-dependent and stochastic yield stress behavior in face-centered cubic(FCC)micropillars.展开更多
Magneto-active soft materials,composed of hard-magnetic particles embedded in polymeric matrices,have found widespread applications in soft robotics,active metamaterials,and shape-morphing structures across various le...Magneto-active soft materials,composed of hard-magnetic particles embedded in polymeric matrices,have found widespread applications in soft robotics,active metamaterials,and shape-morphing structures across various length scales due to their ability to undergo reversible,untethered,and rapid deformation in response to magnetic actuation.At small scales,surface effects play a crucial role in the mechanical behavior of these soft materials.In this paper,we theoretically investigate the influence of surface effects on the buckling instability and large deformation of magneto-active soft beams under a uniform magnetic field.The theoretical model is derived according to the principle of minimum potential energy and numerically solved with the finite difference method.By employing the developed theoretical model,parametric studies are performed to explore how surface effects influence the buckling instability and large deformation of magneto-active soft cantilever beams with varying geometric parameters under different uniform magnetic fields.Our results reveal that the influence of surface effects on the mechanical behavior of magneto-active soft beams depends not only on the geometric parameters but also on the magnetic field strength.Specifically,when the magnetic field strength is relatively small,surface effects reduce the deformation of magneto-active soft beams,particularly for beams with smaller thicknesses and larger length-to-thickness ratios.However,when the magnetic field strength is sufficiently large,and the beam's deformation becomes saturated,surface effects have little influence on the deformation.This work uncovers the role of surface effects in the mechanical behavior of magnetoactive soft materials,which could provide guidelines for the design and optimization of small-scale magnetic-active soft material-based applications.展开更多
Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of resi...Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of residual surface stress and surface elasticity are included.Airy stress function method and Fourier integral transform technique are used.The solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at all.Numerical results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the half-plane.Surface elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally loaded.In the remaining situations,combined effects of surface elasticity and residual surface stress should be considered.The results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface effects.The solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.展开更多
The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are derived.An electro-elastic model is developed to investigate the...The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are derived.An electro-elastic model is developed to investigate the anti-plane strain problem of Love wave propagation.By introducing three shape functions,the wave equations and electric balance equations are decoupled into three uncorrelated problems.Satisfying the boundary conditions of the top surface on the covering layer,the interlayer interface,and the matrix,a dispersive equation with the influence of multi-physical field coupling is provided.A surface PQC model is developed to investigate the surface effects on the propagation behaviors of Love waves in quasicrystal(QC)multilayered structures with nanoscale thicknesses.A novel dispersion relation for the PQC structure is derived in an explicit closed form according to the non-classical mechanical and electric boundary conditions.Numerical examples are given to reveal the effects of the boundary conditions,stacking sequence,characteristic scale,and phason fluctuation characteristics on the dispersion curves of Love waves propagating in PQC nanoplates with surface effects.展开更多
This paper investigates the steady-state thermoelastic problem of a circular nanohole embedded in an infinitely large elastic plane subjected to a uniform far-field heat flux.A lowly conductive surface model is used t...This paper investigates the steady-state thermoelastic problem of a circular nanohole embedded in an infinitely large elastic plane subjected to a uniform far-field heat flux.A lowly conductive surface model is used to account for the effects of surface phonon scattering,while the complete Gurtin–Murdoch model is utilized to characterize the effects of surface tension and surface elasticity.The closed-form solution to the temperature and stress field surrounding the hole is derived in the context of complex variable methods.Several numerical examples are presented to analyze the influence of surface effects on thermal stress fields.It is shown that surface effects induce notable increases in normal and shear stresses around the hole.Specifically,all three stress components(hoop,normal,and shear)in the vicinity of the hole exhibit substantial augmentation with increasing surface tension and surface modulus.In particular,it is found that the presence of surface effects amplifies the variation in stress gradients and intensifies stress concentration around the hole.展开更多
Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenk...Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions： hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.展开更多
There are always severe stress concentrations around surface defects like grooves or bugles, which might induce the failure of solid materials and structures. In the present paper, we consider the elastic fields aroun...There are always severe stress concentrations around surface defects like grooves or bugles, which might induce the failure of solid materials and structures. In the present paper, we consider the elastic fields around nanosized bugles and grooves on solid surfaces. The influence of surface elasticity on the elastic deformation is addressed through a finite element method. It is found that when the size of defects shrinks to nanometer, the stress fields around such defects will be affected significantly by surface effects.展开更多
The aim of this paper is to study the free transverse vibration of a hanging nonuni- form nanoscale tube. The analysis procedure is based on nonlocal elasticity theory with surface effects. The nonlocal elasticity the...The aim of this paper is to study the free transverse vibration of a hanging nonuni- form nanoscale tube. The analysis procedure is based on nonlocal elasticity theory with surface effects. The nonlocal elasticity theory states that the stress at a point is a function of strains at all points in the continuum. This theory becomes significant for small-length scale objects such as micro- and nanostructures. The effects of nonlocality, surface energy and axial force on the natural frequencies of the nanotube are investigated. In this study, analytical solutions are formulated for a clamped-free Euler-Bernoulli beam to study the free vibration of nanoscale tubes.展开更多
The purpose of the present work is to quantify the influences of the discrete nature, the surface effects, and the large deformation on the bending resonant properties of long and ultrathin （100） silicon nanocantile...The purpose of the present work is to quantify the influences of the discrete nature, the surface effects, and the large deformation on the bending resonant properties of long and ultrathin （100） silicon nanocantilevers. We accomplish this by using an analytical semi-continuum Keating model within the framework of nonlinear, finite deformation kinematics. The semi-continuum model shows that the elastic behaviors of the silicon nanocantilevers are size-dependent and surface- dependent, which agrees well with the molecular dynamics results. It also indicates that the dominant effect on the fundamental resonant frequency shift of the silicon nanocantilever is adsorption-induced surface stress, followed by the discrete nature and surface reconstruction, whereas surface relaxation has the least effect. In particular, it is found that a large deformation tends to increase the nonlinear fundamental frequency of the silicon nanocantilever, depending not only on its size but also on the surface effects. Finally, the resonant frequency shifts due to the adsorption-induced surface stress predicted by the current model are quantitatively compared with those obtained from the experimental measurement and the other existing approach. It is noticed that the length-to-thickness ratio is the key parameter that correlates the deviations in the resonant frequencies predicted from the current model and the empirical formula.展开更多
A three-dimensional （3-D） approach based on the state space method is proposed to study size-dependent mechanical properties of ultra-thin plate-like elastic structures considering surface effects. The structure is ...A three-dimensional （3-D） approach based on the state space method is proposed to study size-dependent mechanical properties of ultra-thin plate-like elastic structures considering surface effects. The structure is modeled as a laminate composed of a bulk bounded with upper and bottom surface layers, which are allowed to have different material properties from the bulk layer. State equations, including the surface properties of the structure, can be established on the basis of 3-D fundamental elasticity to analyze the size-dependent static characteristics of the thin plate-like structure. Compared with two-dimensional plate theories based size-dependent models for thin film structures in literature, the present 3-D approach is exact, which can provide benchmark results to assess the accuracy of 2-D plate theories and various numerical approaches. To show the feasibility of the proposed approach, a 3-D analytical solution for a simply supported plate-like thin structure including surface layers is derived. An algorithm is proposed for the calculation of the state equations obtained to ensure that the numerical results can reveal the surface effects clearly even for extremely thin surface layers. Numerical examples are carried out to exhibit the surface effects and some discussions are provided based on the results obtained.展开更多
Anovel functionally graded material(FGM)sandwich nanoplatemodel with surface effects is developed in thiswork.By using the Gurtin–Murdoch theory of surface elasticity,surface effects are taken into account.Governing ...Anovel functionally graded material(FGM)sandwich nanoplatemodel with surface effects is developed in thiswork.By using the Gurtin–Murdoch theory of surface elasticity,surface effects are taken into account.Governing equations for nonlinear vibrations are obtained though the balance of forces.The Galerkin method is employed to obtain the approximate solutions for nonlinear free and forced vibrations of the FGM laminates.Numerical results show that considering surface effects changes the equivalent Young’s modulus and bending stiffness of FGM sandwich nanoplates.In addition,the influences of surface effects are related to the geometric size of the nanoplate.Numerical examples are proposed to verify the effectiveness of the present results.展开更多
To effectively reduce the field concentration around a hole or crack,an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional(1D)hexagonal piezoelectric ...To effectively reduce the field concentration around a hole or crack,an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)is investigated subject to remotely mechanical and electrical loadings.The surface effect and dielectric characteristics inside the hole are considered for actuality.By utilizing the technique of conformal mapping and the complex variable method,the phonon stresses,phason stresses,and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions.Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack.Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer,the aspect ratio of the hole,and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip.The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack,which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.展开更多
In this paper,theoretical and numerical methods are combined to investigate the two-dimensional,cylindrical indentation of an elastic soft layer bonded on a rigid substrate.By incorporating the Gurtin-Murdoch’s theor...In this paper,theoretical and numerical methods are combined to investigate the two-dimensional,cylindrical indentation of an elastic soft layer bonded on a rigid substrate.By incorporating the Gurtin-Murdoch’s theory of surface elasticity into the Kerr model,we account for surface effects on the indentation behavior of a soft layer.The governing differential relation between the surface pressure and displacement of the film-substrate system is derived.For an incompressible thin layer,the explicit solutions are derived,which are simple and easy-to-use.Finite element simulations are performed using an explicit restart algorithm to study the indentation properties of the layer-substrate system and to examine the validity and accuracy of the theoretical solutions.This work holds promise for applications in mechanical characterization of soft materials,such as biological tissues and cells.展开更多
The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band st...The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.展开更多
A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia,in which the nonlocal and surface effects are consider...A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia,in which the nonlocal and surface effects are considered. Three types of boundary conditions, i.e., hinged-hinged, clamped-clamped, and clamped-hinged ends, are examined. For a hinged-hinged beam, an exact and explicit natural frequency equation is derived based on the established mathematical model. The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams. In sum, the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity, the surface elasticity, the residual surface stress, and the rotatory inertia, providing a more convenient means in comparison with numerical computations.展开更多
In this study,the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects(SEs).The nanoplates are composed o...In this study,the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects(SEs).The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers.Utilizing the modified Halpin-Tsai model,the material parameters of composite layers are obtained.The displacement field is determined by the sinusoidal shear deformation theory(SSDT).The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs.Subsequently,the nonlocal strain gradient theory(NSGT)is used to obtain the equations of motion.Next,the effects of scale parameters,graphene distribution,orthotropic viscoelastic foundation,and SEs on the propagation behavior are numerically examined.The results reveal that the wave frequency is a periodic function of the orthotropic angle.Furthermore,the wave frequency increases with the increase in the SEs.展开更多
The bending responses of functionally graded （FG） nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to an...The bending responses of functionally graded （FG） nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to analyze the influences of surface stress on bending response of FG nanobeam. The material properties are assumed to vary along the thickness of FG nanobeam in power law. The bending governing equations are derived by using the minimum total potential energy principle and explicit formulas are derived for rotation angle and deflection of nanobeams with surface effects. Illustrative examples are implemented to give the bending deformation of FG nanobeam. The influences of the aspect ratio, gradient index, and surface stress on dimensionless deflection are discussed in detail.展开更多
This work investigates the dispersion properties of Rayleigh-type surface waves propagating in a layered piezoelectric nanostructure composed of a piezoelectric nanofilm over an elastic substrate.As one of the most im...This work investigates the dispersion properties of Rayleigh-type surface waves propagating in a layered piezoelectric nanostructure composed of a piezoelectric nanofilm over an elastic substrate.As one of the most important features of nanostructures,surface effects characterized by surface stresses and surface electric displacements are taken into account through the surface piezoelectricity theory and the nonclassical mechanical and electrical boundary conditions.Concrete expressions of the dispersion equation are derived,and numerical results are provided to examine the effects of several surface-related parameters,including the surface elasticity,surface piezoelectricity,surface dielectricity,surface density,as well as surface residual stress,on the dispersion modes and phase velocity.The size-dependent dispersion behaviors occurring with surface effects are also predicted,and they may vanish once the thickness of the piezoelectric nanofilm reaches a critical value.展开更多
This paper studies surface effects on the mechanical behavior of nanoporous materials under high strains with an improved anisotropic Kelvin model. The stress-strain relations are derived by the theories of Euler-Bern...This paper studies surface effects on the mechanical behavior of nanoporous materials under high strains with an improved anisotropic Kelvin model. The stress-strain relations are derived by the theories of Euler-Bernoulli beam and surface elasticity. Mean- while, the influence of strut （or ligament） size on the mechanical properties of nanoporous materials is discussed, which becomes a key factor with consideration of the residual sur- face stress and the surface elasticity. The results show that the decrease in the strut diameter and the increase in the residual surface stress or the surface elasticity can both lead to an increase in the carrying capacity of nanoporous materials. F^lrthermore, me- chanical behaviors of anisotropic nanoporous materials in different directions （the rise direction and the transverse direction） are investigated. The results indicate that the sur- face effects in the transverse direction are more obvious than those in the rise direction for anisotropic nanoporous materials. In addition, the present results can be reduced to the cases of conventional foams as the strut size increases to micron-scale, which confirms validity of the model to a certain extent.展开更多
Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample： elastic modulus either decreases or increases with decreasing sample size. In this paper, based...Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample： elastic modulus either decreases or increases with decreasing sample size. In this paper, based on intermolecular potentials and a one dimensional model, we provide a unified understanding of the two opposite size effects. Firstly, we analyzed the microstructural variation near the surface of an fcc nanofilm based on the Lennard-Jones potential. It is found that the atomic lattice near the surface becomes looser in comparison with the bulk, indicating that atoms in the bulk are located at the balance of repulsive forces, and the elastic moduli decrease with the decreasing thickness of the film accordingly. In addition, the decrease in moduli should be attributed to both the looser surface layer and smaller coordination number of surface atoms. Furthermore, it is found that both looser and tighter lattice near the surface can appear for a general pair potential and the governing mechanism should be attributed to the surplus of the nearest force to all other long range interactions in the pair potential. Surprisingly, the surplus can be simply expressed by a sum of the long range interactions and the sum being positive or negative determines the looser or tighter lattice near surface respectively. To justify this concept, we examined ZnO in terms of Buckingham potential with long range Coulomb interactions. It is found that compared to its bulk lattice, the ZnO lattice near the surface becomes tighter, indicating the atoms in the bulk are located at the balance of attractive forces, owing to the long range Coulomb interaction. Correspondingly, the elastic modulus of one-dimensional ZnO chain increases with decreasing size. Finally, a kind of many-body potential for Cu was examined. In this case, the surface layer becomes tighter than the bulk and the modulus increases with deceasing size, owing to the long range repulsive pair interaction, as well as the cohesive many-body interaction caused by the electron redistribution.展开更多
基金supported by the Henan International Science and Technology Cooperation Program(No.242102521055)the Japan Science and Technology Agency(No.JPMJCR2092)the Japan Society for the Promotion of Science(Nos.JP24H00283,JP24K21575,and JP22K18754)。
文摘This study investigates the surface effects on the operation of double-ended dislocation sources in single-crystal micropillars under compression.A comprehensive theoretical framework is formulated to derive the stress field of the source segment and the corresponding Peach-Koehler(PK)forces acting on this segment near the free surfaces.An analytical formulation is then developed to compare the source strength with and without the influence of the surface stress.The results reveal that the surface effects on the dislocation source strength are highly sensitive to the interplay between the source length and its distance from the free surface.These surface effects can either enhance or reduce the critical stress required for the source operation by up to 50%,leading to significant fluctuations in yield strength,as commonly observed in discrete dislocation dynamics simulations and experimental studies.These findings provide different interpretations for the size-dependent and stochastic yield stress behavior in face-centered cubic(FCC)micropillars.
基金Project supported by the National Natural Science Foundation of China(Nos.12202009 and12002004)。
文摘Magneto-active soft materials,composed of hard-magnetic particles embedded in polymeric matrices,have found widespread applications in soft robotics,active metamaterials,and shape-morphing structures across various length scales due to their ability to undergo reversible,untethered,and rapid deformation in response to magnetic actuation.At small scales,surface effects play a crucial role in the mechanical behavior of these soft materials.In this paper,we theoretically investigate the influence of surface effects on the buckling instability and large deformation of magneto-active soft beams under a uniform magnetic field.The theoretical model is derived according to the principle of minimum potential energy and numerically solved with the finite difference method.By employing the developed theoretical model,parametric studies are performed to explore how surface effects influence the buckling instability and large deformation of magneto-active soft cantilever beams with varying geometric parameters under different uniform magnetic fields.Our results reveal that the influence of surface effects on the mechanical behavior of magneto-active soft beams depends not only on the geometric parameters but also on the magnetic field strength.Specifically,when the magnetic field strength is relatively small,surface effects reduce the deformation of magneto-active soft beams,particularly for beams with smaller thicknesses and larger length-to-thickness ratios.However,when the magnetic field strength is sufficiently large,and the beam's deformation becomes saturated,surface effects have little influence on the deformation.This work uncovers the role of surface effects in the mechanical behavior of magnetoactive soft materials,which could provide guidelines for the design and optimization of small-scale magnetic-active soft material-based applications.
基金supported by the National Natural Science Foundation of China(12272126,12272127)the Doctoral Fund of HPU(B2015-64).
文摘Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of residual surface stress and surface elasticity are included.Airy stress function method and Fourier integral transform technique are used.The solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at all.Numerical results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the half-plane.Surface elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally loaded.In the remaining situations,combined effects of surface elasticity and residual surface stress should be considered.The results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface effects.The solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.
基金Project supported by the National Natural Science Foundation of China(Nos.12272402 and11972365)the China Agricultural University Education Foundation(No.1101-2412001)。
文摘The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are derived.An electro-elastic model is developed to investigate the anti-plane strain problem of Love wave propagation.By introducing three shape functions,the wave equations and electric balance equations are decoupled into three uncorrelated problems.Satisfying the boundary conditions of the top surface on the covering layer,the interlayer interface,and the matrix,a dispersive equation with the influence of multi-physical field coupling is provided.A surface PQC model is developed to investigate the surface effects on the propagation behaviors of Love waves in quasicrystal(QC)multilayered structures with nanoscale thicknesses.A novel dispersion relation for the PQC structure is derived in an explicit closed form according to the non-classical mechanical and electric boundary conditions.Numerical examples are given to reveal the effects of the boundary conditions,stacking sequence,characteristic scale,and phason fluctuation characteristics on the dispersion curves of Love waves propagating in PQC nanoplates with surface effects.
基金supported by the National Natural Science Foundation of China(Grant No.11902116)the Natural Science Foundation of Guangdong Province(Grant No.2022A1515011773)the Natural Science Foundation of Guangzhou City(Grant No.202201010317).
文摘This paper investigates the steady-state thermoelastic problem of a circular nanohole embedded in an infinitely large elastic plane subjected to a uniform far-field heat flux.A lowly conductive surface model is used to account for the effects of surface phonon scattering,while the complete Gurtin–Murdoch model is utilized to characterize the effects of surface tension and surface elasticity.The closed-form solution to the temperature and stress field surrounding the hole is derived in the context of complex variable methods.Several numerical examples are presented to analyze the influence of surface effects on thermal stress fields.It is shown that surface effects induce notable increases in normal and shear stresses around the hole.Specifically,all three stress components(hoop,normal,and shear)in the vicinity of the hole exhibit substantial augmentation with increasing surface tension and surface modulus.In particular,it is found that the presence of surface effects amplifies the variation in stress gradients and intensifies stress concentration around the hole.
基金the School of Civil and Environmental Engineering at Nanyang Technological University, Singapore for kindly supporting this research topic
文摘Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions： hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.
基金supported by the National Natural Science Foundation of China(No.10602042)the NCET Program of the Ministry of Education.
文摘There are always severe stress concentrations around surface defects like grooves or bugles, which might induce the failure of solid materials and structures. In the present paper, we consider the elastic fields around nanosized bugles and grooves on solid surfaces. The influence of surface elasticity on the elastic deformation is addressed through a finite element method. It is found that when the size of defects shrinks to nanometer, the stress fields around such defects will be affected significantly by surface effects.
文摘The aim of this paper is to study the free transverse vibration of a hanging nonuni- form nanoscale tube. The analysis procedure is based on nonlocal elasticity theory with surface effects. The nonlocal elasticity theory states that the stress at a point is a function of strains at all points in the continuum. This theory becomes significant for small-length scale objects such as micro- and nanostructures. The effects of nonlocality, surface energy and axial force on the natural frequencies of the nanotube are investigated. In this study, analytical solutions are formulated for a clamped-free Euler-Bernoulli beam to study the free vibration of nanoscale tubes.
基金Project supported by the National Natural Science Foundation of China(Grant No.41075026)the Open Research Fund of Key Laboratory of MEMS of Ministry of Education,Southeast University,China(Grant Nos.2009-03 and 2010-02)+2 种基金the SpecialFund for Meteorology Research in the Public Interest,China(Grant No.GYHY200906037)the Priority Academic ProgramDevelopment of Sensor NetworksModern Meteorological Equipment of Jiangsu Higher Education Institutions,China
文摘The purpose of the present work is to quantify the influences of the discrete nature, the surface effects, and the large deformation on the bending resonant properties of long and ultrathin （100） silicon nanocantilevers. We accomplish this by using an analytical semi-continuum Keating model within the framework of nonlinear, finite deformation kinematics. The semi-continuum model shows that the elastic behaviors of the silicon nanocantilevers are size-dependent and surface- dependent, which agrees well with the molecular dynamics results. It also indicates that the dominant effect on the fundamental resonant frequency shift of the silicon nanocantilever is adsorption-induced surface stress, followed by the discrete nature and surface reconstruction, whereas surface relaxation has the least effect. In particular, it is found that a large deformation tends to increase the nonlinear fundamental frequency of the silicon nanocantilever, depending not only on its size but also on the surface effects. Finally, the resonant frequency shifts due to the adsorption-induced surface stress predicted by the current model are quantitatively compared with those obtained from the experimental measurement and the other existing approach. It is noticed that the length-to-thickness ratio is the key parameter that correlates the deviations in the resonant frequencies predicted from the current model and the empirical formula.
基金supported by the Natural Science Foundation of Anhui Province(No.070414190).
文摘A three-dimensional （3-D） approach based on the state space method is proposed to study size-dependent mechanical properties of ultra-thin plate-like elastic structures considering surface effects. The structure is modeled as a laminate composed of a bulk bounded with upper and bottom surface layers, which are allowed to have different material properties from the bulk layer. State equations, including the surface properties of the structure, can be established on the basis of 3-D fundamental elasticity to analyze the size-dependent static characteristics of the thin plate-like structure. Compared with two-dimensional plate theories based size-dependent models for thin film structures in literature, the present 3-D approach is exact, which can provide benchmark results to assess the accuracy of 2-D plate theories and various numerical approaches. To show the feasibility of the proposed approach, a 3-D analytical solution for a simply supported plate-like thin structure including surface layers is derived. An algorithm is proposed for the calculation of the state equations obtained to ensure that the numerical results can reveal the surface effects clearly even for extremely thin surface layers. Numerical examples are carried out to exhibit the surface effects and some discussions are provided based on the results obtained.
基金supported by the Natural Science Foundation of Hebei Province(A2022203025)the Science and Technology Project of Hebei Education Department(ZD2021104).
文摘Anovel functionally graded material(FGM)sandwich nanoplatemodel with surface effects is developed in thiswork.By using the Gurtin–Murdoch theory of surface elasticity,surface effects are taken into account.Governing equations for nonlinear vibrations are obtained though the balance of forces.The Galerkin method is employed to obtain the approximate solutions for nonlinear free and forced vibrations of the FGM laminates.Numerical results show that considering surface effects changes the equivalent Young’s modulus and bending stiffness of FGM sandwich nanoplates.In addition,the influences of surface effects are related to the geometric size of the nanoplate.Numerical examples are proposed to verify the effectiveness of the present results.
基金supported by the National Natural Science Foundation of China(Nos.12072166,11862021)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(No.NJYT-19-A06)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(No.2020MS01006)。
文摘To effectively reduce the field concentration around a hole or crack,an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)is investigated subject to remotely mechanical and electrical loadings.The surface effect and dielectric characteristics inside the hole are considered for actuality.By utilizing the technique of conformal mapping and the complex variable method,the phonon stresses,phason stresses,and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions.Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack.Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer,the aspect ratio of the hole,and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip.The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack,which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.
文摘In this paper,theoretical and numerical methods are combined to investigate the two-dimensional,cylindrical indentation of an elastic soft layer bonded on a rigid substrate.By incorporating the Gurtin-Murdoch’s theory of surface elasticity into the Kerr model,we account for surface effects on the indentation behavior of a soft layer.The governing differential relation between the surface pressure and displacement of the film-substrate system is derived.For an incompressible thin layer,the explicit solutions are derived,which are simple and easy-to-use.Finite element simulations are performed using an explicit restart algorithm to study the indentation properties of the layer-substrate system and to examine the validity and accuracy of the theoretical solutions.This work holds promise for applications in mechanical characterization of soft materials,such as biological tissues and cells.
基金the National Natural Science Foundation of China(No.11847009)the Natural Science Foundation of Suzhou University of Science and Technology(No.XKQ2018007)。
文摘The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.
基金School of Civil and Environmental Engineering at Nanyang Technological University, Singapore for kindly supporting this research topic.
文摘A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia,in which the nonlocal and surface effects are considered. Three types of boundary conditions, i.e., hinged-hinged, clamped-clamped, and clamped-hinged ends, are examined. For a hinged-hinged beam, an exact and explicit natural frequency equation is derived based on the established mathematical model. The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams. In sum, the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity, the surface elasticity, the residual surface stress, and the rotatory inertia, providing a more convenient means in comparison with numerical computations.
基金supported by the National Natural Science Foundation of China(Nos.11502218,11672252,11602204,and 12102373)the Fundamental Research Funds for the Central Universities of China(No.2682020ZT106)。
文摘In this study,the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects(SEs).The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers.Utilizing the modified Halpin-Tsai model,the material parameters of composite layers are obtained.The displacement field is determined by the sinusoidal shear deformation theory(SSDT).The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs.Subsequently,the nonlocal strain gradient theory(NSGT)is used to obtain the equations of motion.Next,the effects of scale parameters,graphene distribution,orthotropic viscoelastic foundation,and SEs on the propagation behavior are numerically examined.The results reveal that the wave frequency is a periodic function of the orthotropic angle.Furthermore,the wave frequency increases with the increase in the SEs.
基金supported by the National Natural Science Foundation of China(11302055)Heilongjiang Post-doctoral Scientific Research Start-up Funding(LBH-Q14046)
文摘The bending responses of functionally graded （FG） nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to analyze the influences of surface stress on bending response of FG nanobeam. The material properties are assumed to vary along the thickness of FG nanobeam in power law. The bending governing equations are derived by using the minimum total potential energy principle and explicit formulas are derived for rotation angle and deflection of nanobeams with surface effects. Illustrative examples are implemented to give the bending deformation of FG nanobeam. The influences of the aspect ratio, gradient index, and surface stress on dimensionless deflection are discussed in detail.
基金Project supported by the National Natural Science Foundation of China(Nos.11802185 and 11872041)the Natural Science Foundation of Hebei Province of China(No.A2019210203)the Youth Fund Project of Hebei Education Department of China(No.QN2018037)
文摘This work investigates the dispersion properties of Rayleigh-type surface waves propagating in a layered piezoelectric nanostructure composed of a piezoelectric nanofilm over an elastic substrate.As one of the most important features of nanostructures,surface effects characterized by surface stresses and surface electric displacements are taken into account through the surface piezoelectricity theory and the nonclassical mechanical and electrical boundary conditions.Concrete expressions of the dispersion equation are derived,and numerical results are provided to examine the effects of several surface-related parameters,including the surface elasticity,surface piezoelectricity,surface dielectricity,surface density,as well as surface residual stress,on the dispersion modes and phase velocity.The size-dependent dispersion behaviors occurring with surface effects are also predicted,and they may vanish once the thickness of the piezoelectric nanofilm reaches a critical value.
基金supported by the National Natural Science Foundation of China(Nos.11472025,10932001,and 11272030)
文摘This paper studies surface effects on the mechanical behavior of nanoporous materials under high strains with an improved anisotropic Kelvin model. The stress-strain relations are derived by the theories of Euler-Bernoulli beam and surface elasticity. Mean- while, the influence of strut （or ligament） size on the mechanical properties of nanoporous materials is discussed, which becomes a key factor with consideration of the residual sur- face stress and the surface elasticity. The results show that the decrease in the strut diameter and the increase in the residual surface stress or the surface elasticity can both lead to an increase in the carrying capacity of nanoporous materials. F^lrthermore, me- chanical behaviors of anisotropic nanoporous materials in different directions （the rise direction and the transverse direction） are investigated. The results indicate that the sur- face effects in the transverse direction are more obvious than those in the rise direction for anisotropic nanoporous materials. In addition, the present results can be reduced to the cases of conventional foams as the strut size increases to micron-scale, which confirms validity of the model to a certain extent.
基金supported by the National Natural Science Foundation of China (Nos10721202,10432050,10772012 and10732090)the CAS innovation program (KJCX2-YW-M04)
文摘Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample： elastic modulus either decreases or increases with decreasing sample size. In this paper, based on intermolecular potentials and a one dimensional model, we provide a unified understanding of the two opposite size effects. Firstly, we analyzed the microstructural variation near the surface of an fcc nanofilm based on the Lennard-Jones potential. It is found that the atomic lattice near the surface becomes looser in comparison with the bulk, indicating that atoms in the bulk are located at the balance of repulsive forces, and the elastic moduli decrease with the decreasing thickness of the film accordingly. In addition, the decrease in moduli should be attributed to both the looser surface layer and smaller coordination number of surface atoms. Furthermore, it is found that both looser and tighter lattice near the surface can appear for a general pair potential and the governing mechanism should be attributed to the surplus of the nearest force to all other long range interactions in the pair potential. Surprisingly, the surplus can be simply expressed by a sum of the long range interactions and the sum being positive or negative determines the looser or tighter lattice near surface respectively. To justify this concept, we examined ZnO in terms of Buckingham potential with long range Coulomb interactions. It is found that compared to its bulk lattice, the ZnO lattice near the surface becomes tighter, indicating the atoms in the bulk are located at the balance of attractive forces, owing to the long range Coulomb interaction. Correspondingly, the elastic modulus of one-dimensional ZnO chain increases with decreasing size. Finally, a kind of many-body potential for Cu was examined. In this case, the surface layer becomes tighter than the bulk and the modulus increases with deceasing size, owing to the long range repulsive pair interaction, as well as the cohesive many-body interaction caused by the electron redistribution.
