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The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique to solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube- beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results. [ABSTRACT FROM AUTHOR]

Previous reports of rapid phase transformation above 18 GPa [Erskine and Nellis, Nature 349, 317 (1991)] and large elastic waves below 18 GPa [Lucas et al., J. Appl. Phys. 114, 093515 (2013)] for shock-compressed ZYB-grade highly oriented pyrolytic graphite (HOPG), but not for less oriented ZYH-grade HOPG, indicated a link between the orientational order dependence of the HOPG response above and below the phase transformation stress. To gain insight into this link and into the mechanical response of HOPG shocked to peak stresses approaching the phase transformation onset, the compressibility of ZYB- and ZYH-grade HOPG in the shocked state was examined using front surface impact experiments. Particle velocity histories and sound velocities were measured for peak stresses reaching 18 GPa. Although the locus of the measured peak stress-particle velocity states is indistinguishable for the two grades of HOPG, the measured sound velocities in the peak state reveal significant differences between the two grades. Specifically (1) the measured sound velocities are somewhat higher for ZYH-grade HOPG compared with ZYB-grade HOPG; (2) the measured sound velocities for ZYH-grade HOPG increase smoothly with compression, whereas those for ZYB-grade HOPG exhibit a significant reduction in the compression dependence from 12 GPa to 17GPa and an abrupt increase from 17GPa to 18 GPa; and (3) the longitudinal moduli, determined from the measured sound velocities, are smaller than the calculated bulk moduli for ZYB-grade HOPG shocked to peak stresses above 15 GPa, indicating the onset of an elastic instability. The present findings demonstrate that the softening of the longitudinal modulus (or elastic instability) presented here is linked to the large elastic waves and the rapid phase transformation reported previously—all observed only for shocked ZYB-grade HOPG. The elastic instability in shocked ZYB-grade HOPG is likely a precursor to the rapid phase transformation observed above 18 GPa for this HOPG grade. [ABSTRACT FROM AUTHOR]

The transformation of diamond-cubic silicon to the metallic β-Sn phase is known to be "sluggish," even when the critical pressure (∼11 GPa) for the transformation is reached. In this letter, we use nanoindentation to apply pressures to just above the critical threshold. In this regime, the sample displays purely elastic behavior at zero hold time. As the hold time at maximum load is increased up to 180 s, the percentage of indents that plastically deform also increase. Interestingly, the indents deform via one of two distinct processes: either via a phase transformation to a mixed bc8/r8-Si end phase, or by initiation of crystalline defects. Raman spectroscopy and cross-sectional transmission electron microscopy are used to show that the two deformation mechanisms are mutually exclusive under the indentation conditions presented here, and elastic modelling was utilized to propose a model for this mutually exclusive behavior. Hence, this behavior enhances the potential for application of the exotic bc8/r8-Si end phase. [ABSTRACT FROM AUTHOR]

The structural, elastic, and vibrational properties of yttrium aluminum garnet Y3Al5O12 are studied under high pressure by ab initio calculations in the framework of the density functional theory. The calculated ground state properties are in good agreement with the available experimental data. Pressure dependences of bond length and bulk moduli of the constituent polyhedra are reported. The evolution of the elastic constants and the major elastic properties, Young and shear modulus, Poisson's ratios, and Zener anisotropy ratio, are described. The mechanical stability is analyzed, on the light of "Born generalized stability criteria," showing that the garnet is mechanically unstable above 116 GPa. Symmetries, frequencies, and pressure coefficients of the Raman-active modes are discussed on the basis of the calculated total and partial phonon density of states, which reflect the dynamical contribution of each atom. The relations between the phonon modes of Y3Al5O12 and the internal and external molecular modes of the different polyhedra are discussed. Infrared-active modes, as well as the silent modes, and their pressure dependence are also investigated. No dynamical instabilities were found below 116 GPa. [ABSTRACT FROM AUTHOR]

Measurement of the dependence of the elastic moduli on the strain, i.e., the characterization of nonlinear elastic properties of solid media, poses intrinsic experimental difficulties. The Dynamic AcoustoElastic Technique has been recently developed as an efficient tool for the determination of the modulus in both compression and tension. The goal of the present paper is to discuss the limitations of the experimental implementation and the interpretation of the measured quantities in terms of nonlinear parameters. For this purpose, simulation results will be presented for both classical and nonclassical nonlinear elastic media. [ABSTRACT FROM AUTHOR]

The composition-gradient electrode material is considered as one of the most promising materials for lithium-ion batteries because of its excellent electrochemical performance and thermal stability. In this work, the effects of concentration-dependent elastic modulus on Li-ions diffusion and diffusion-induce stress in the composition-gradient electrodes were studied. The coupling equations of elasticity and diffusion under both potentiostatic charging and galvanostatic charging were developed to obtain the distributions of both the Li-ions concentration and the stress. The results indicated that the effects of the concentration-dependent elastic modulus on the Li-ions diffusion and the diffusion-induce stresses are controlled by the lithiation induced stiffening factor in the composition-gradient electrodes: a low stiffening factor at the center and a high stiffening factor at the surface lead to a significant effect, whereas a high stiffening factor at the center and a low stiffening factor at the surface result in a minimal effect. The results in this work provide guidance for the selection of electrode materials. [ABSTRACT FROM AUTHOR]

A comprehensive morphological stability analysis of a nanoscale circular island during heteroepitaxial growth is presented based on continuum elasticity theory. The interplay between kinetic and thermodynamic mechanisms is revealed by including strain-related kinetic processes. In the kinetic regime, the Burton-Cabrera-Frank model is adopted to describe the growth front of the island. Together with kinetic boundary conditions, various kinetic processes including deposition flow, adatom diffusion, attachment-detachment kinetics, and the Ehrlich-Schwoebel barrier can be taken into account at the same time. In the thermodynamic regime, line tension, surface energy, and elastic energy are considered. As the strain relief in the early stages of heteroepitaxy is more complicated than commonly suggested by simple consideration of lattice mismatch, we also investigate the effects of external applied strain and elastic response due to perturbations on the island shape evolution. The analytical expressions for elastic fields induced by mismatch strain, external applied strain, and relaxation strain are presented. A systematic approach is developed to solve the system via a perturbation analysis which yields the conditions of film morphological instabilities. Consistent with previous experimental and theoretical work, parametric studies show the kinetic evolution of elastic relaxation, island morphology, and film composition under various conditions. Our present work offers an effective theoretical approach to get a comprehensive understanding of the interplay between different growth mechanisms and how to tailor the growth mode by controlling the nature of the crucial factors. [ABSTRACT FROM AUTHOR]

A modified core-shell (MC-S) model is proposed to investigate the effect of surface elasticity on the elastic properties of nanowires under bending and tension loading modes. The continuous exponential function based on bulk elasticity is applied to the surface region of nanowires to better describe the elasticity in the surface layer. Two parameters related to the surface, namely, the inhomogeneous degree constant α, and the transition region of this inhomogeneous state rs (i.e., surface layer thickness), are introduced for examining the size effects of the elastic modulus of the overall nanowires. A strong size dependence of elasticity is revealed under both bending and tension loads. Furthermore, the theoretical solution for an effective Young's modulus with relevant experiments, as well as the results of a molecular statistical thermodynamics (MST) method for zinc oxide (ZnO) nanowires, and a molecular dynamics (MD) simulation for silicon (Si) nanowires, are compared. It is shown that the theoretical curves not only agree well with the experimental data, but also fit the computational results (MST or MD) approximately below 20 nm. As a result, our model can predict the behavior of surface elasticity, with respect to the lateral size of nanostructures at a relatively small scale, no matter how stiff or soft the surface of the nanomaterials. [ABSTRACT FROM AUTHOR]

In this paper, a detailed theoretical study on the dispersion of waves in carbon nanotubes (CNTs) is presented. For this purpose, CNTs are considered as nonlocal elastic thin cylindrical shells. The Eringen's nonlocal elasticity theory is used for modeling the microstructure of CNT such that the proximity of the mathematical model to the actual atomic structure of CNT is retained. The results are compared with the results that are obtained based on the second-order strain-gradient elasticity (SG) theory. It has been shown that the SG theory is the first approximation of nonlocal continuum elasticity (NC) theory, which is used in the present paper. Also, it has been shown that the bending rigidity has important effect in the dispersion of waves in CNTs. [ABSTRACT FROM AUTHOR]

The theoretical backgrounds for the depth-profiling of the optically transparent materials by picosecond ultrasonic interferometry are developed. The mathematical description of the light reflection from inhomogeneous transparent films or coatings is proposed. The inhomogeneity can be caused both by the film synthesis (intrinsic stationary inhomogeneity) and by the short acoustic transients launched in the film (time-dependent inhomogeneity). The theory indicates that the measurements of the complex optical reflectivity time evolution, caused by acoustic strain pulse propagation in such films, offer various possibilities to extract the depth profiles of intrinsic inhomogeneous distributions of mechanical/acoustical, optical, and acousto-optical parameters of the films. In particular it is proposed how the measurements of the transient complex optical reflectivity by the femtosecond optical interferometers, operating with light of different polarizations and probing the tested samples at different angles of light incidence, can be used. The spatial resolution of the method is limited by the acoustic spatial scale which, for picosecond acoustic pulses, is much shorter than optical wavelength. [ABSTRACT FROM AUTHOR]

An explicit, analytical theory for the percolation threshold, percolation saturation, and effective conductivity of a two-component system involving randomly oriented ellipsoidal inclusions is proposed. The ellipsoids may take the shape of a needle, prolate or oblate spheroid, sphere, or disk. This theory is based upon consideration of Ponte Castaneda--Willis [P. Ponte Castaneda and J. R. Willis, J. Mech. Phys. Solids 43, 1919 (1995)] microstructure in conjunction with Hashin--Shtrikman [Z. Hashin and S. Shtrikman, J. Appl. Phys. 33, 3125 (1962)] upper bound. Two critical volume concentrations, c* and c**, that represent the respective percolation threshold at which the conductive network begins to develop, and the percolation saturation, are identified. During this very short range of concentration, the electrical conductivity of the composite is found to exhibit a very sharp increase, while over the entire range, the calcutilated conductivity exhibits the widely reported sigmoidal shape. Comparison with measurement on a multi-walled carbon nanotube/alumina composite indicates that the theory could capture the major features of the experimentally observed trends sufficiently well. [ABSTRACT FROM AUTHOR]

This paper develops a model that analyzes the wave propagation in armchair single-walled carbon nanotubes (SWCNTs) under thermal environment. The effect of a small length scale is incorporated in the formulations using nonlocal Levinson beam model. Unlike Timoshenko beam theory, Levinson beam theory satisfies zero traction boundary conditions on the upper and lower surface of the structures, so there is no need to use a shear correction factor. The equivalent Young's modulus and shear modulus for armchair SWCNT are derived using an energy-equivalent model. Results indicate significant dependence of natural frequencies on the temperature change as well as the chirality of armchair carbon nanotube. These findings are important in mechanical design considerations of devices that use carbon nanotubes. [ABSTRACT FROM AUTHOR]

Graphene nanoribbons (GNRs) have been suggested as a promising material for its use as nanoelectromechanical reasonators for highly sensitive force, mass, and charge detection. Therefore the accurate determination of the size-dependent elastic properties of GNRs is desirable for the design of graphene-based nanoelectromechanical devices. In this study we determine the size-dependent Young’s modulus and carbon-carbon binding energy in a homologous series of GNRs, C4n2+6n+2H6n+4 (n=2–12), with the use of all electron first principles computations. An unexpected linearity between the binding energy and Young’s modulus is observed, making possible the prediction of the size-dependent Young’s modulus of GNRs through a single point energy calculation of the GNR ground state. A quantitative-structure-property relationship is derived, which correlates Young’s modulus to the total energy and the number of carbon atoms within the ribbon. In the limit of extended graphene sheets we determine the value of Young’s modulus to be 1.09 TPa, in excellent agreement with experimental estimates derived for graphite and suspended graphene sheets. [ABSTRACT FROM AUTHOR]

The thermal buckling of an armchair double-walled carbon nanotube (DWCNT), which is subjected to axial compression due to temperature rise, is derived and analyzed based on Timoshenko beam model, including transverse shear deformation and rotary inertia. According to the analysis, the effect of van der Waals force between the nanotubes on the critical buckling temperature of mode 1 of armchair DWCNT is significant, especially for smaller diameter nanotubes. The van der Waals force makes the DWCNT stiffer and increases the buckling temperature. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The critical buckling temperature ratio of a Timoshenko beam to a Euler beam for the armchair DWCNT significantly decreases with increasing the diameter and mode number. Therefore, for the higher-order modes, the Timoshenko beam model is able to predict the critical buckling temperature of larger diameter DWCNT. [ABSTRACT FROM AUTHOR]

The dynamics of microscopic bubbles in low viscosity insulating liquids has been widely investigated. It has been shown that the bubble motion (growth, collapse, and rebounds) in such liquids is governed by inertial forces. In this paper, the results of an experimental study of the dynamics of microscopic bubbles in viscous liquids (μ≥3 mPl) are presented. It is shown that, according to the conditions (injected energy, liquid viscosity, and applied pressure), the bubble motion is greatly modified. For example, no bubble rebound is observed in the higher viscosity liquids (e.g., Napvis XD110, μ=83.5 mPl) and, for a given injected energy, the ratio of the expansion time of the bubble to its implosion time drops with increasing in liquid viscosity. The bubble dynamics are then governed by liquid viscosity. Moreover, the transition of the bubble dynamics from the inertial regime to the viscous one has been experimentally observed (as far as the present authors are aware) for the first time. This transition can be explained by a refined analysis of the Rayleigh–Plesset model of bubble dynamics. The bubble dynamics regime can be deduced from a Reynolds number (ReTp) versus elasticity number (Σ) diagram, where four zones can be distinguished. Each zone corresponds to a particular regime: inertial regime with only one growth and collapse stage, inertial regime with at least one bubble rebound, viscous regime, and finally, a regime where a jet of hot liquid is produced. All experimental results are well distributed into the good part of this diagram. [ABSTRACT FROM AUTHOR]

A previous study of a single load-unload cycle of an adhesive contact between an elastic-plastic microscopic sphere and a rigid flat is extended here for several load-unload cycles. The interacting forces between the sphere and the flat obey the Lennard–Jones potential. Kinematic hardening is assumed for the sphere material to account for possible plastic shakedown, and the difference between kinematic and isotropic hardenings is discussed. The main goal of the current work is to investigate the evolution of the load-approach curves for the elastic-plastic spherical contact during its cyclic loading-unloading. These curves are presented for different physical conditions, represented by three main dimensionless parameters, which affect the behavior of the elastic-plastic adhesive contact. A transition value of the Tabor parameter is found, below which the load-approach curves are always continuous and jump-in and jump-out instabilities are not expected. [ABSTRACT FROM AUTHOR]

We report the observation of a shear direction alternatively changed crack path in a thin Fe78Si9B13 metallic glassy sheet with high strength and elasticity. This configuration of the crack path in the thin sheet under tension is discussed in the framework of the thin elastic sheet with high strength. The reason for this configuration is attributed to the interaction between the shrinkage of the thin elastic sheet with small wavelength of wrinkle and the propagating crack with high bending energy while low stretching energy. [ABSTRACT FROM AUTHOR]

A recent experiment has shown that the force required to pull off a flat circular rigid punch in adhesive contact with an array of elastic fibrils is sensitive to the thickness of the elastic backing layer to which these fibrils are attached. This result motivates us to study the effect of sample compliance on the adhesion of fibril arrays. A closed form expression for the compliance of such arrays attached to a backing layer of finite thickness is derived. Our model is based on the assumption that the adhesive strength of a fibril is deterministic. In addition, we show that the normalized pull-off force is inversely proportional to the square root of a single dimensionless parameter β. For large β, the pull-off force is low as it is governed by the stress concentration at the punch edge. For small β, this pull-off force reaches a theoretical limit that is governed by the ability of fibrils to share load equally [equal load sharing (ELS) limit]. The pull-off force predicted by our model is compared with new experimental data. Our model shows the correct trend but underestimates the pull-off force in the ELS limit. The difference between our theoretical predictions and experimental results is attributed to alignment difficulties in the experiments and the fact that the adhesive strength of fibrils is governed by local statistics. [ABSTRACT FROM AUTHOR]

By modeling the flux line as a line of centers of dilatation, it is shown that within the linear elasticity and continuum theory, the elastic interaction between a flux line and a point defect in an isotropic superconducting solid is entirely due to its surface. This surface effect, in a superconducting film with two parallel free surfaces, is considered in detail in this paper. Our analysis shows that the absolute value of the interaction energy and the interaction force between a flux line and a point defect decreases rapidly with increasing distance from the point defect to the free surface and to the flux line. The interaction between a flux line and a point defect is found to be strong only when the defect is close to the flux line and to the free surface. [ABSTRACT FROM AUTHOR]

This paper studies the vibrational characteristics of single-walled carbon nanotubes (SWNTs) with initial axial loading based on the theory of nonlocal elasticity. The consistent equations of motion for the nonlocal Euler-Bernoulli and Timoshenko beam models are provided taking into account the initial axial stress. The small scale effect on CNT wave propagation dispersion relation is explicitly revealed for different CNT wave numbers and diameters by theoretical analyses and numerical simulations. In addition, the applicability of the two beam models is explored by numerical simulations. The research work reveals the significance of the effects of small scale, transverse shear deformation and rotary inertia on wave propagation in short SWCNTs with initial axial loading. [ABSTRACT FROM AUTHOR]

Continuum mechanics modeling of carbon nanotubes has long been an attractive issue, but how to reflect exactly the physics essential of the atomic bonds still remains to be a challenging problem. To capture the distinguishing in-plane σ-σ and out-of-plane σ-π bond angle bending rigidities of C[Single_Bond]C bonds in carbon nanotubes, an equivalent beam element with rectangular section is proposed and a corresponding frame structure model for a single-walled carbon nanotube (SWNT) is developed. By using the model, the five independent elastic moduli of SWNTs with arbitrary chirality and diameter are evaluated systematically. It is found that the elastic properties of the SWNTs are transversely isotropic when the tube diameter is small. The smaller the tube diameter is, the stronger the dependence of the elastic properties on the tube size and chirality is, while when the tube diameter is large enough, the SWNTs degenerate from transversely isotropic to isotropic and the elastic moduli tend to that of a graphite sheet. The present model can be incorporated into any standard finite element software directly, providing an extremely versatile and powerful tool for the study of nanostructures that beyond the computational capability of current atomistic approaches. [ABSTRACT FROM AUTHOR]

Microcantilever-based techniques can be used to explore the autonomy and property of biomolecules (e.g., DNA and single actin filaments) which, in measurement, are adsorbed on the cantilever surface. Here, an energy method is presented to predict the cantilever deflection induced by adsorbed atoms/molecules. The cantilever is modeled as a sandwich beam containing two surface layers of a finite thickness and a bulk layer between them. The adsorptions of O atoms on Si(100) and Hg atoms on Au(100) are taken as two representative examples. We demonstrate that physisorption can induce distinctly different deformation behaviors of cantilevers, which depend not only on the adatoms but also on the substrate material. These results are consistent with relevant experimental observations. This study is helpful for optimal design of microcantilever-based measurement techniques. [ABSTRACT FROM AUTHOR]

Using first-principles calculations within the generalized gradient approximation, we predicted the lattice parameters, elastic constants, vibrational properties, and electronic structure of cementite (Fe3C). Its nine single-crystal elastic constants were obtained by computing total energies or stresses as a function of applied strain. Furthermore, six of them were determined from the initial slopes of the calculated longitudinal and transverse acoustic phonon branches along the [100], [010], and [001] directions. The three methods agree well with each other; the calculated polycrystalline elastic moduli are also in good overall agreement with experiments. Our calculations indicate that Fe3C is mechanically stable. The experimentally observed high elastic anisotropy of Fe3C is also confirmed by our study. Based on electronic density of states and charge density distribution, the chemical bonding in Fe3C was analyzed and was found to exhibit a complex mixture of metallic, covalent, and ionic characters. [ABSTRACT FROM AUTHOR]

This article presents a complete and asymptotic representation of the one-dimensional nanobeam model with nonlocal stress via an exact variational principle approach. An asymptotic governing differential equation of infinite-order strain gradient model and the corresponding infinite number of boundary conditions are derived and discussed. For practical applications, it explores and presents a reduced higher-order solution to the asymptotic nonlocal model. It is also identified here and explained at length that most publications on this subject have inaccurately employed an excessively simplified lower-order model which furnishes intriguing solutions under certain loading and boundary conditions where the results become identical to the classical solution, i.e., without the small-scale effect at all. Various nanobeam examples are solved to demonstrate the difference between using the simplified lower-order nonlocal model and the asymptotic higher-order strain gradient nonlocal stress model. An important conclusion is the discovery of significant over- or underestimation of stress levels using the lower-order model, particularly at the vicinity of the clamped end of a cantilevered nanobeam under a tip point load. The consequence is that the design of a nanobeam based on the lower-order strain gradient model could be flawed in predicting the nonlocal stress at the clamped end where it could, depending on the magnitude of the small-scale parameter, significantly over- or underestimate the failure criteria of a nanobeam which are governed by the level of stress. [ABSTRACT FROM AUTHOR]

A strain k·p model is used to investigate lattice temperature dependence of the piezoresistivity of p-doped silicon nanobeams in the range of 100–600 K, based on the self-consistent solution to the coupled Schrödinger–Poisson equations. According to quasiharmonic approximation, an analytical semicontinuum atomistic lattice model is presented to describe the effect of size and temperature on elastic constants of the silicon nanobeam by using the anharmonic Keating model. The result presented here indicates the piezoresistive coefficient of the silicon nanobeam, which is dependent on quantum confinement effects, has a negative and nonlinear temperature coefficient. A quantitative comparison of the piezoresistive coefficients calculated with and without considering the elastic constant correction shows that it is crucial to incorporate the size-dependent elastic constant correction in order to quantify the piezoresistivity. [ABSTRACT FROM AUTHOR]

Crack propagation in a wrinkled thin film of gold deposited on polydimethylsiloxane (PDMS) was affected by the presence of folding defects—the ripple dislocations. The ripple pattern, ripple dislocations, and the crack were simultaneously formed after the tensile load applied on the PDMS substrate was removed. The crack, however, was unstable and propagated forward. The propagation rate increased when the crack passed by the ripple dislocations, but less significantly when it advanced near a ripple dislocation dipole. Such crack dislocation interaction implies that the ripple dislocation has an internal stress field. The measured data of the rate process were analyzed based on the theory of fracture mechanics, and an empirical relationship between the crack velocity and the crack extension force was presented. [ABSTRACT FROM AUTHOR]

The article presents comments on the paper "Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory." It states that there are inconsistencies in applied forces and the handling of the governing equations. It presents mathematical models showing the governing differential equation of motion for free vibration of fluid-conveying tubes to examine transverse deflection and shear force on the cross section.