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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]