Lyotropic mixture made of potassium laurate/1-undecanol/K2SO4/water presenting high birefringences and large biaxial nematic phase domain: a laser conoscopy study

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such a surface may model a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry through folding along portions of meridians. For the thinnest shells, a direct transition from the spherical conformation to the folded one can be observed. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of Poisson??s ratio. In the folded conformation, the number of folds and inner pressure are investigated, allowing us to infer shell features from mere observation and/or knowledge of external constraints.     

Buckling of spherical shells adhering onto a rigid substrate

Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization (conjugate gradient method) of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters, i.e., C_s/epsilon and C_b/epsilon where C_s and C_b are respectively the stretching and the bending constants, and epsilon is the depth of the van der Waals potential between the shell and substrate. Four different regimes of deformation are characterized as these parameters are systematically varied: (i) small deformation regime, (ii) disk formation regime, (iii) isotropic buckling regime, and (iv) anisotropic buckling regime. By measuring the various quantities of the deformed shells, we find that both discontinuous and continuous bucking transitions occur for large and small C_s/epsilon, respectively. This behavior of the buckling transition is analogous to van der Waals liquids or gels, and we have numerically determined the associated critical point. Scaling arguments are employed to explain the adhesion induced buckling transition, i.e., from the disk formation regime to the isotropic buckling regime. We show that the buckling transition takes place when the indentation length exceeds the effective shell thickness which is determined from the elastic constants. This prediction is in good agreement with our numerical results. Moreover, the ratio between the indentation length and its thickness at the transition point provides a constant number (2–3) independent of the shell size. This universal number is observed in various experimental systems ranging from nanoscale to macroscale. In particular, our results agree well with the recent compression experiment using microcapsules.     

Sound scattering from partially water-filled elastic spherical shell with an internal elastic plate

According to the equation of motion in the elastic medium and integral equation of target scattering, the sound scattering from the partially water-filled elastic spherical shells with and without an inner plate is studied using the finite element and boundary element method, and the scattering normalized form functions of the shell filled with different volume of water are computed and the mechanism of resonance scattering is analyzed. The results show that the resonance of the shell with partially water-filled and without the plate is mainly related to the volume of water, and the resonance is produced by inner water and the spherical shell. The resonance characteristics of partially water-filled elastic shell with the plate are similar to that of empty structured elastic spherical shell, and the sound field in inner water is weaker which indicates the main resonance characteristics are decided by spherical shell and the plate. In addition, the scattering characteristics of spherical shell with plate and one side full water-filled are greatly different from the partially water-filled ones.     

Buckling resistance of solid shell bubbles under ultrasound

Thin solid shell contrast agents bubbles are expected to undergo different volume oscillating behaviors when the acoustic power is increased: small oscillations when the shell remains spherical, and large oscillations when the shell buckles. Contrary to bubbles covered with thin lipidic monolayers that buckle as soon as compressed: the solid shell bubbles resist compression, making the buckling transition abrupt. Numerical simulations that explicitly incorporate a shell bending modulus give the critical buckling pressure and post-buckling shape, and show the appearance of a finite number of wrinkles. These findings are incorporated in a model based on the concept of effective surface tension. This model compares favorably to experiments when adjusting two main parameters: the buckling tension and the rupture shell tension. The buckling tension provides a direct estimation of the acoustic pressure threshold at which buckling occurs.     

Self-assembled triangular and labyrinth buckling patterns of thin films on spherical substrates

We investigated the possibility of controlling thin film buckling patterns by varying the substrate curvature and the stress induced therein upon cooling. The numerical and experimental studies are based on a spherical Ag core/SiO(2) shell system. For Ag substrates with a relatively larger curvature, the dentlike triangular buckling pattern comes out when the film nominal stress exceeds a critical value. With increasing film stress and/or substrate radius, the labyrinthlike buckling pattern takes over. Both the buckling wavelength and the critical stress increase with the substrate radius.     

Shape transformations of protein-like copolymer globules

Shapes of globules formed by amphiphilic multi-block-copolymers in a selective solvent are considered theoretically. We focus on copolymers consisting mostly of insoluble H-units forming large core surrounded by a shell of soluble P-blocks. It is shown that the globule becomes non-spherical when the effective shell tension is low enough. The resultant shape depends on the shell bending energy: it is prolate if this energy is larger than the elastic energy of the core, and oblate in the opposite case. The central result is the prediction of the formation of a surface pattern of fingers accompanying or even preempting the shape transition mentioned above. We elucidate and discuss the following finger morphologies: 1) nearly spherical knob; 2) a necklace of spherical beads extending away from the surface; 3) mostly cylindrical fingers; 4) large thorn-like fingers. The first 3 morphologies develop at equilibrium as the shell area increases (or, equivalently, the shell tension decreases). Considering the relevant kinetical aspects we show that formation of fingers is a nucleation and growth process, and that the energy of their equilibrium nucleation is likely to be high. Therefore, the finger formation may be delayed, and may actually occur in the regime where the plain spherical surface is metastable. It is the last morphology (thorn-like fingers) that characterizes the metastable regimes when the finger formation is controlled by a high activation energy. The universal features of the above predictions inviting experimental tests are discussed.     

水中分层弹性球壳高频时域回波的声学编码研究

针对水下集群目标及敌我目标识别的难题,该文提出了一种基于水中分层弹性球壳高频时域回波的声学编码原理及方法。推导了水中4层弹性球壳目标散射声压的简正级数解,并与有限元结果进行了对比验证。通过构造高频主动声呐的探测脉冲信号,与4层弹性球壳声传递函数的简正级数解做卷积运算,获得了目标的时域回波脉冲序列。研究了分层弹性球壳的厚度、各层材料属性、排布顺序等对时域回波特征的影响规律,提出了基于时域回波特征的声学编码方法。研究表明：利用水中分层弹性球壳目标高频时域回波特征能够实现声学编码,回波结构稳定,且不受限于探测方向。通过携带或安装这种分层弹性球壳结构,有望识别水下航行体/悬浮体等目标。该文的研究对水下目标的主动探测身份识别及导航等具有一定的参考价值。     

Interaction of a spherical acoustic wave with an elastic spherical shell

The interaction of a spherical acoustic wave with an elastic spherical shell is treated analytically. The solution includes the coupling between the acoustic sound field and vibration of the shell with any degree of fluid loading. The formulation for the far-field acoustic pressure is derived in terms of natural spherical wave functions, the properties of the acoustic medium, and the material constants of the shell. The far acoustic field is computed for a thin aluminum shell and several sound source locations over a large range of ka, where k is the wavenumber, and a is the shell radius. It is shown that the acoustic pressure depends significantly on whether the shell is in air or is submerged in water, particularly when the sound source is very near the surface. In air, the sound field of the shell is nearly identical to that of a rigid sphere but, in water, the shell is more compliant, which results in a damped radiation field that is characterized by vibrational resonances throughout the range of frequencies considered. As the sound sources is moved further away from the surface, however, this resonance response decreases very rapidly, and the sound field corresponds more closely to that of the shell in air.     

Acoustics of shells

We discuss the physical phenomena that arise in the scattering of acoustic waves from fluid-immersed elastic (metal) shells which may be either evacuated or filled with the same or with a different fluid. The phenomena occurring here include the formation of circumferential (peripheral, or “surface”) waves that circumnavigate the shells, propagating either as elastic waves in the shell material or as fluid-borne waves of the Scholte-Stoneley type in the external or the internal fluid. By phase matching along a closed circuit, these waves may lead to prominent resonances in the acoustic scattering amplitude, and we demonstrate how the set of observed resonance frequencies is related to the dispersive phase velocities of the surface waves, so that one can be determined from the other. In addition, we discuss how the dispersion curves (phase velocity plotted vs. frequency) of the various types of surface waves show repulsion phenomena due to their coupling through the boundary conditions. The cases of spherical and cylindrical shells are investigated here as typical examples, and as an introductory topic we additionally mention surface waves on plates where related phenomena also occur. Both the theoretical and the experimental aspects of the present subject will be considered, including the experimental visualization of the surface waves.     

Onset of buckling in drying droplets of colloidal suspensions

Minute concentrations of suspended particles can dramatically alter the behavior of a drying droplet. After a period of isotropic shrinkage, similar to droplets of a pure liquid, these droplets suddenly buckle like an elastic shell. While linear elasticity is able to describe the morphology of the buckled droplets, it fails to predict the onset of buckling. Instead, we find that buckling is coincident with a stress-induced fluid to solid transition in a shell of particles at a droplet's surface, occurring when attractive capillary forces overcome stabilizing electrostatic forces between particles.     

On the nonlinear axisymmetric dynamic buckling behavior of clamped functionally graded spherical caps

Here, the dynamic thermal buckling behavior of functionally graded spherical caps is studied considering geometric nonlinearity based on von Karman's assumptions. The formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the material constituents. The effective material properties are evaluated using homogenization method. The governing equations obtained using finite element approach are solved employing the Newmark's integration technique coupled with a modified Newton–Raphson iteration scheme. The pressure load corresponding to a sudden jump in the maximum average displacement in the time history of the shell structure is taken as the dynamic buckling load. The present model is validated against the available isotropic case. A detailed numerical study is carried out to highlight the influences of shell geometries, power law index of functional graded material and boundary conditions on the dynamic buckling load of shallow spherical shells.     

Combined torsional buckling of double-walled carbon nanotubes with axial load in the multi-field coupled condition

The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable s...     

基于非局部弹性理论的单壁碳纳米管轴向受压屈曲研究

基于非局部弹性理论，在考虑小尺度效应影响的情况下，建立了单壁碳纳米管在均匀轴向外 部压力下的壳体模型. 得到了单壁碳纳米管的轴向受压屈曲的临界条件，验证了小尺度效应 对纳米管轴向受压屈曲的影响. 经典的壳体模型理论由于没有考虑小尺度效应影响而导致碳 纳米管轴向屈曲临界压力值偏高. 关键词： 非局部弹性理论 碳钠米管 小尺度效应 轴向受压     

Shell buckling behavior investigation of individual gallium nitride hollow nanocolumn

This paper presents research on the calculating analysis and experimental observations of shell buckling in individual gallium nitride hollow nanocolumns using nanoindentation. By using the experiment results of critical buckling strain under compression, we investigated the stiffness of hollow nanocolumns which were vertically aligned on a template by using linear elastic shell buckling theory. In addition, more studies of various possible nanomechanical behavior modes of gallium nitride hollow nanocolumns by shall model are provided. Furthermore, there was a comparison between nanocolumns by molecular dynamics simulation (one dimensional structure) and thin film by nanoindentation experiment (two dimensional structures). Finally, the buckling energy of compression for an individual gallium nitride hollow nanocolumn was also discussed. PACS 68.65.-K; 61.70.+w; 81.10.BK; 73.21.-b; 81.16.Rf     

考虑介质膨胀速率的锂离子电池管状电极中扩散诱导应力及轴向支反力分析

硅作为锂离子电池阴极材料相对于传统负极材料具有高比容量,价格低廉等优势.本文针对充电过程中锂离子电池中电极建立力学模型和扩散模型,并在扩散模型引入考虑介质膨胀速率的影响.以硅空心柱形电极为例,分析了恒流充电下介质膨胀速率对电极中扩散诱导应力分布的影响,并研究了不同内外半径比、充电速率、材料参数以及锂化诱导软化系数(lithiation induced softening factor,LISF)对轴向的支反力达到临界欧拉屈曲力所需时间的影响.结果表明,随着电极中锂浓度上升,介质膨胀速率对应力分布的影响增大,对轴向的支反力影响较小.弹性模量和应力成正比,但其与轴向的支反力达到临界欧拉屈曲力所需时间无关;扩散系数与所需时间成反比;偏摩尔体积增大时,达到临界屈曲力所需时间减少;随着LISF绝对值增大,完全锂化时轴向力降低.     

Energy of deformed and defective carbon clusters

A method is proposed for calculating the energy of deformed spherical and cylindrical carbon clusters of nanometer size. The application of the method is demonstrated by calculating the elastic energy of a spherical cluster deformed as a result of the introduction of two types of defects (disclination or dilatation center). It is proven that the energy of a defect in the cluster shell is determined by the curvature of its surface and that the spherical shape of the defect-free shell is stable.     

CHAOTIC BEHAVIOR RESULTING IN TRANSIENT AND STEADY STATE INSTABILITIES OF PRESSURE-LOADED SHALLOW SPHERICAL SHELLS

In this paper, the axisymmetric dynamic behavior and snap-through buckling of thin elastic shallow spherical shells under harmonic excitation is investigated. Based on Marguerre kinematical assumptions, the governing partial differential equations of motion for a pre-loaded cap are presented in the form of a compatibility equation and a transverse motion equation. The continuous model is reduced to a finite degree of freedom system using the Galerkin method and a Fourier-Bessel approach. Results show that pre-loaded shells may exhibit co-existing stable equilibrium states and that with the application of sufficiently large dynamic loads the structure escapes from the well corresponding to pre-buckling configurations to another. This escape load may be much lower than the corresponding quasi-static buckling load. Indeed, complex resonances can occur until the system snaps-through, often signalling the loss of stability. As parameters are slowly varied, steady state instabilities may occur; these can include jumps to resonance, subharmonic period-doubling bifurcations, cascades to chaos, etc. Moreover a sudden pulse of excitation may lead to a transient failure of the system. In this paper, we examine how spherical caps under harmonic loading may be assessed in an engineering context, with a view to design against steady state instabilities as well as the various modes of transient failure. Steady state and transient stability boundaries are presented in which special attention is devoted to the determination of the critical load conditions. From this theoretical analysis, dynamic buckling criteria can be properly established which may constitute a consistent and rational basis for design of these shell structures under harmonic loading.     

Sound scattering from underwater elastic spherical shell covered with multilayered medium approximated acoustic cloak

The anechoic performance and mechanism of underwater elastic spherical shell covered with coating are studied at low frequencies.The acoustic cloak is anisotropic material,which can be designed with homogeneous isotropic materials on the basis of effective medium approximation theory.The analytic expression of scattering acoustic field from the shell covered with multilayered medium is formulated and the scattering form function,resonance mode,acoustic field distribution are computed,the scattering characteristics and mechanism of transmission are analyzed.The results show that the direction of sound transmission inside the multilayered medium is changed,the acoustic field is deflected gradually,and the acoustic energy flux is guided around the target,which reduces the scattering intensity at low frequencies,the acoustic intensity of target＇s surface is very weak.Excepting the first resonance peak in spectrum produced by the zero order partial wave,the other resonance modes of elastic spherical shell are not excitated and the multilayered medium can suppress the resonance of the spherical shell effectively.     

Interaction of a plane progressive sound wave with a functionally graded spherical shell

An exact analysis is carried out to study interaction of a time-harmonic plane progressive sound field with a radially inhomogeneous thick-walled elastic isotropic spherical shell suspended in and filled with compressible ideal fluid mediums. Using the laminated approximation method, a modal state equation with variable coefficients is set up in terms of appropriate displacement and stress functions and their spherical harmonics. Taylor’s expansion theorem is then employed to obtain the solution to the modal state equation ultimately leading to calculation of a global transfer matrix. Numerical example is given for a water-submerged/air-filled Aluminum/Zirconia elastic spherical sandwich shell containing a functionally graded interlayer and subjected to an incident progressive plane sound wave. The mechanical properties of the interlayer are assumed to vary smoothly and continuously across the thickness with the change of volume concentration of its constituents. The effect of incident wave frequency, thickness and compositional gradient of the interlayer on the form function amplitude and the average radiation force acting on the composite shell are examined. Limiting cases are considered and fair agreements with well-known solutions are established.     

Analysis of elastic properties of a spherical shell using a semiconductor laser autodyne

The possibility of using a semiconductor laser autodyne for estimating the elastic properties of a spherical shell simulating the eyeball is investigated. Estimation is based on the determination of the parameters of motion of a segment of a spherical shell under the action of a pneumatic pulse. The results lead to the conclusion that the ratio of the deflection to the acceleration of the shell is a constant quantity weakly depending on the pressure of pneumatic pulses and on the distance between their source and the shell.