Buckling of hybrid nanocomposites with embedded graphene and carbon nanotubes

With the aid of atomistic multiscale modelling and analytical approaches, buckling strength has been determined for carbon nanofibres/epoxy composite systems. Various nanofibres configurations considered are single walled carbon nano tube (SWCNT) and single layer graphene sheet (SLGS) and SLGS/SWCNT hybrid systems. Computationally, both eigen-value and non-linear large deformation-based methods have been employed to calculate the buckling strength. The non-linear computational model generated here takes into account of complex features such as debonding between polymer and filler (delamination under compression), nonlinearity in the polymer, strain-based damage criteria for the matrix, contact between fillers and interlocking of distorted filler surfaces with polymer. The effect of bridging nanofibres with an interlinking compound on the buckling strength of nano-composites has also been presented here. Computed enhancement in buckling strength of the polymer system due to nano reinforcement is found to be in the range of experimental and molecular dynamics based results available in open literature. The findings of this work indicate that carbon based nanofillers enhance the buckling strength of host polymers through various local failure mechanisms.     

Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory

This study presents an analytical approach for buckling analysis and smart control of a single layer graphene sheet (SLGS) using a coupled polyvinylidene fluoride (PVDF) nanoplate. The SLGS and PVDF nanoplate are considered to be coupled by an enclosing elastic medium which is simulated by the Pasternak foundation. The PVDF nanoplate is subjected to an applied voltage in the thickness direction which operates in control of critical load of the SLGS. In order to satisfy the Maxwell equation, electric potential distribution is assumed as a combination of a half-cosine and linear variation. The exact analysis is performed for the case when all four ends are simply supported and free electrical boundary condition. Adopting the nonlocal Mindlin plate theory, the governing equations are derived based on the energy method and Hamilton's principle. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, stiffness of the internal elastic medium, graphene length, mode number and external electric voltage on the buckling smart control of the SLGS. The results depict that the imposed external voltage is an effective controlling parameter for buckling of the SLGS. This study might be useful for the design and smart control of nano-devices.     

Sound wave propagation in zigzag double-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory

In the present work, nonlocal Euler–Bernoulli beam theory is used to investigate the wave propagation in zigzag double-walled carbon nanotube (DWCNT) embedded in an elastic medium. Winkler-type foundation model is employed to simulate the interaction of the DWCNT with the surrounding elastic medium. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. It is noticed in the presented study that the equivalent Young’s modulus for zigzag DWCNT is derived using an energy-equivalent model. Influences of nonlocal effects, the chirality of zigzag DWCNT, Winkler modulus parameter, and aspect ratio on the frequency of DWCNT are analyzed and discussed. The new features of the vibration behavior of zigzag DWCNTs embedded in an elastic medium and some meaningful results in this paper are helpful for the application and the design of nanostructures in which zigzag DWCNTs act as basic elements.     

Surface elasticity and size effect on the vibrational behavior of silicon nanoresonators

Predominance of nano-scale effects observed in material behavior at small scales requires implementation of new simulation methods which are not merely based on classical continuum mechanic. On the other hand, although the atomistic modeling methods are capable of modeling nano-scale effects, due to the computational cost, they are not suitable for dynamic analysis of nano-structures. In this research, we aim to develop a continuum-based model for nano-beam vibrations which is capable of predicting the results of molecular dynamics (MD) simulations with considerably lower computational effort. In this classical-based modeling, the surface and core regions are taken to have different mechanical properties, where core atoms are assumed to have macroscale properties whereas surface layer is showing a different elastic modulus from the core components. By estimating physical parameters of proposed classical model using molecular dynamics results and the genetic algorithm, calibrated classical Euler–Bernoulli and Timoshenko beam models are developed. The results demonstrates that a Timoshenko beam model incorporating surface effects and having calibrated parameters, is able to provide almost the same results as molecular dynamics method which can be used to predict the vibrational behavior of nano-beams at different scales from nano to macro.     

A density-functional-theory-based finite element model to study the mechanical properties of zigzag phosphorene nanotubes

In this paper, the density functional theory calculations are used to obtain the elastic properties of zigzag phosphorene nanotubes. Besides, based on the similarity between phosphorene nanotubes and a space-frame structure, a three-dimensional finite element model is proposed in which the atomic bonds are simulated by beam elements. The results of density functional theory are employed to compute the properties of the beam elements. Finally, using the proposed finite element model, the elastic modulus of the zigzag phosphorene nanotubes is computed. It is shown that phosphorene nanotubes with larger radii have larger Young's modulus. Comparing the results of finite element model with those of density functional theory, it is concluded that the proposed model can predict the elastic modulus of phosphorene nanotubes with a good accuracy.     

Effects of surface and interface energies on the bending behavior of nanoscale multilayered beams

A modified continuum model of the nanoscale multilayered beams is established by incorporating surface and interface energies. Through the principle of minimum potential energy, the governing equations and boundary conditions are obtained. The closed-form solutions are presented and the overall Young's modulus of the beam is studied. The surface and interface energies are found to have a major influence on the bending behavior and the overall Young's modulus of the beam. The effect of surface and interface energies on the overall Young's modulus depends on the boundary condition of the beam, the values of the surface/interface elasticity constants and the initial surface/interface energy of the system. The results can be used to guide the determinations of the surface/interface elasticity properties and the initial surface/interface energies of the nanoscale multilayered materials through nanoscale beam bending experiments.     

Effect of native oxides on the elasticity of a silicon nano-scale beam

Native oxide is usually formed during the fabrication of silicon beams. A model is developed to describe the effect of native oxide on the elastic modulus of the silicon nano-beam based on the semi-continuum method. The model predicts that Young’s modulus of the nano-beam with native oxide increases as the nano-beam thickness decreases while it exhibits opposite behavior without native oxide. Native oxide dominates the beam with its scaling down to several nanometers. Young’s moduli are in the range from 123 GPa to 190 GPa when the thickness is several nanometers, and they approach the bulk value when the thickness is greater than about 500nm.     

Prediction of fish body’s passive visco-elastic properties and related muscle mechanical performance in vivo during steady swimming

For attaining the optimized locomotory performance of swimming fishes,both the passive visco-elastic properties of the fish body and the mechanical behavior of the active muscles should coordinate with the fish body’s undulatory motion pattern.However,it is difficult to directly measure the visco-elastic constitutive relation and the muscular mechanical performance in vivo.In the present paper,a new approach based on the continuous beam model for steady swimming fish is proposed to predict the fish body’s visco-elastic properties and the related muscle mechanical behavior in vivo.Given the lateral travelling-wave-like movement as the input condition,the required muscle force and the energy consumption are functions of the fish body’s visco-elastic parameters,i.e.the Young’s modulus E and the viscosity coefficient in the Kelvin model.After investigating the variations of the propagating speed of the required muscle force with the fish body’s visco-elastic parameters,we analyze the impacts of the visco-elastic properties on the energy efficiencies,including the energy utilization ratios of each element of the kinematic chain in fish swimming and the overall efficiency.Under the constraints of reasonable wave speed of muscle activation and the physiological feasibility,the optimal design of the passive visco-elastic properties can be predicted aiming at maximizing the overall efficiency.The analysis is based on the small-amplitude steady swimming of the carangiform swimmer,with typical Reynolds number varying from 2.5×104to 2.5×105,and the present results show that the non-dimensional Young’s modulus is 112±34,and the non-dimensional viscosity coefficient is 13 approximately.In the present estimated ranges,the overall efficiency of the swimming fish is insensitive to the viscosity,and its magnitude is about 0.11±0.02,in the predicted range given by previous study.     

Nonlocal plate model for nonlinear bending of single-layer graphene sheets subjected to transverse loads in thermal environments

This paper investigates the nonlinear bending behavior of a single-layer rectangular graphene sheet subjected to a transverse uniform load in thermal environments. The single-layer graphene sheet (SLGS) is modeled as a nonlocal orthotropic plate which contains small scale effect. Geometric nonlinearity in the von Kármán sense is adopted. The thermal effects are included and the material properties are assumed to be size dependent and temperature dependent, and are obtained from molecular dynamics (MD) simulations. The small scale parameter e ₀ a is estimated by matching the deflections of graphene sheets observed from the MD simulation results with the numerical results obtained from the nonlocal plate model. The numerical results show that the temperature change as well as the aspect ratio has a significant effect on the nonlinear bending behavior of SLGSs. The results reveal that the small scale parameter reduces the static large deflections of SLGSs, and the small scale effect also plays an important role in the nonlinear bending of SLGSs.     

Nonlinear dynamics of bi-layered graphene sheet,double-walled carbon nanotube and nanotube bundle

Due to strong van der Waals (vdW) interactions, the graphene sheets and nanotubes stick to each other and form clusters of these corresponding nanostructures, viz. bi-layered graphene sheet (BLGS), double-walled carbon nanotube (DWCNT) and nanotube bundle (NB) or ropes. This research work is concerned with the study of nonlinear dynamics of BLGS, DWCNT and NB due to nonlinear interlayer vdW forces using multiscale atomistic finite element method. The energy between two adjacent carbon atoms is represented by the multibody interatomic Tersoff–Brenner potential, whereas the nonlinear interlayer vdW forces are represented by Lennard-Jones 6–12 potential function. The equivalent nonlinear material model of carbon–carbon bond is used to model it based on its force–deflection relation. Newmark’s algorithm is used to solve the nonlinear matrix equation governing the motion of the BLGS, DWCNT and NB. An impulse and harmonic excitations are used to excite these nanostructures under cantilevered, bridged and clamped boundary conditions. The frequency responses of these nanostructures are computed, and the dominant resonant frequencies are identified. Along with the forced vibration of these structures, the eigenvalue extraction problem of armchair and zigzag NB is also considered. The natural frequencies and corresponding mode shapes are extracted for the different length and boundary conditions of the nanotube bundle.     

Damping of stiffened plates by multiple layer treatments

It is shown in this paper that the modal damping and resonant frequencies of a stiffened plate structure, with a multiple layer constrained damping treatment attached to the surface, can be predicted from a knowledge of the equivalent complex modulus properties of the treatment. The equations used represent a simple extension of the classical equations of Oberst for a free layer treatment applied to an unstiffened beam or plate, with terms accounting for the effect of the stiffeners. The equivalent complex modulus properties of the treatment depend on a shear parameter, a geometrical parameter, the stiffness of the constraining layer and the loss factor of the adhesive. Experimental results are discussed.     

Material property estimates from ultrasound attenuation in fibre suspensions

An investigation of a new method for measuring fibre material properties from ultrasonic attenuation in a dilute suspension of synthetic fibres of uniform geometry is presented. The method is based on inversely solving an ultrasound scattering and absorption model of suspended fibres in water for the material properties of the fibres. Experimental results were obtained from three suspensions of nylon 66 fibres each with different fibre diameters. A forward solution to the model with reference material values is compared to experimental data to verify the model’s behaviour. Estimates of the shear and Young’s modulus, the compressional wave velocity, Poisson’s ratio and loss tangent from nylon 66 fibres are compared to data available from other sources. Experimental data confirms that the model successfully predicts that the resonance features in the frequency response of the attenuation are a function of diameter. Consistent estimated values for the compressional wave velocity and the Poisson’s ratio were found to be difficult to obtain but in combination gave values of shear modulus within previously reported values and with low sensitivity to noise. Young’s modulus was underestimated by 54% but was consistent and had low sensitivity to noise. The underestimation is believed to be caused by the assumption of isotropic material used in the model. Additional tests on isotropic fibre would confirm this. Further analysis of the model sensitivity and the reasons for the resonance features are required.     

A nonlocal Levinson beam model for free vibration analysis of zigzag single-walled carbon nanotubes including thermal effects

A nonlocal Levinson beam model is developed to study the free vibrations of a zigzag single-walled carbon nanotube (SWCNT) in thermal environments. The equivalent Young’s modulus and shear modulus for a zigzag SWCNT are derived using an energy-equivalent model. The present study illustrates that the vibration characteristics of an SWCNT are strongly dependent on the temperature change and on the chirality of a zigzag carbon nanotube. The investigation of the chirality and temperature effects on free vibration of carbon nanotubes may be used as a useful reference for the application and the design of nanoelectronic and nanodrive devices, nano-oscillators, and nanosensors, in which carbon nanotubes act as basic elements.     

Elastic instability of bilayer graphene using atomistic finite element

In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.     

LiNbO_3:Fe晶体中光写入平面光波导的导光特性研究

从光折变效应的单中心模型和载流子的光伏迁移机理出发给出了高斯片光在LiNbO3:Fe晶体中导致的折射率变化分布的解析表达式 .利用片光以“三明治”辐照方式在LiNbO3:Fe晶体中写入了平面光波导结构 .用切片干涉法测量了波导区的折射率分布 ,并对波导进行了简单的导光测试 .根据射线方程以及波导的折射率分布对光写入波导的导光特性进行了模拟计算分析 .研究结果表明 ,在LiNbO3:Fe晶体中光写入光波导是可行的     

Structural and anisotropic elastic properties of hexagonal MP (M = Ti,Zr, Hf) monophosphides determined by first-principles calculations

First-principles calculations were performed to investigate the structural properties, phase stabilities, elastic properties and thermal conductivities of MP (M = Ti, Zr, Hf) monophosphides. These monophosphides are thermodynamically and mechanically stable. Values for the bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by Voigt–Reuss–Hill approximation. The mechanical anisotropy was discussed via several anisotropy indices and three-dimensional (3D) surface constructions. The order of elastic anisotropy is ZrP > HfP > TiP. The minimum thermal conductivities of these monophosphides were investigated using Clarke’s model and Cahill’s model. The results revealed that these monophosphides are suitable for use as thermal insulating materials and that their minimum thermal conductivities are anisotropic.     

带状注速调管多间隙扩展互作用输出腔等效电路的研究

带状注扩展互作用速调管(SBEIK)结合了带状注速调管与扩展互作用速调管的优势,在微波和毫米波真空电子器件中具有显著的技术潜力.本文提出了应用于SBEIK的五间隙哑铃型扩展互作用耦合腔输出回路的等效电路模型,获得了建立复杂多间隙扩展互作用腔的等效电路理论的方法.通过推导出的理论,快速确定了五间隙扩展互作用耦合腔的工作模式、谐振频率及间隙阻抗矩阵,由间隙阻抗的频率特性曲线快速估算出各模式对应的带宽,分析研究了耦合系数k以及Q e对于多间隙腔模式频率间隔及带宽的影响.此外,利用三维PIC仿真软件对相应的SBEIK五间隙输出腔高频特性进行了粒子模拟,结果表明,三维仿真获得的工作模式带宽特性与等效电路法计算结果基本一致,证明了本文所建立的等效电路方法的准确性和有效性.     

Anisotropic elastic properties of MB (M = Cr,Mo, W) monoborides: a first-principles investigation

First principles calculations were performed to systematically investigate structure properties, phase stability and mechanical properties of MB (M = Cr, Mo, W) monoborides in orthorhombic and tetragonal structures. The results of equilibrium structures are in good agreement with other available theoretical and experimental data. The elastic properties, including bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by the Voigt-Reuss-Hill approximation. All considered monoborides are mechanically stable. The results of elastic anisotropies show that elastic anisotropy of orthorhombic structure is larger than that of tetragonal structure. Moreover, the minimum thermal conductivities were also estimated using the Cahill’s model, and the results indicate that the minimum thermal conductivities show a dependence on directions.     

Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets

In this article, an atomistic model is developed to study the buckling and vibration characteristics of single-layered graphene sheets (SLGSs). By treating SLGSs as space-frame structures, in which the discrete nature of graphene sheets is preserved, they are modeled using three-dimensional elastic beam elements for the bonds. The elastic moduli of the beam elements are determined via a linkage between molecular mechanics and structural mechanics. Based on this model, the critical compressive forces and fundamental natural frequencies of single-layered graphene sheets with different boundary conditions and geometries are obtained and then compared. It is indicated that the compressive buckling force decreases when the graphene sheet aspect ratio increases. At low aspect ratios, the increase of aspect ratios will result in a significant decrease in the critical buckling load. It is also indicated that increasing aspect ratio at a given side length results in the convergence of buckling envelops associated with armchair and zigzag graphene sheets. The influence of boundary conditions will be studied for different geometries. It will be shown that the influence of boundary conditions is not significant for sufficiently large SLGSs.