Analytical and numerical approaches to piezoelectric bimorph

We propose an efficient and accurate approach to piezoelectric bimorph based on a refined expansion of the elastic displacement and electric potential. The field approximation of the through-the-thickness variation accounts for a shear correction and a layerwise modelling for the electric potential. A particular attention is devoted to the boundary conditions on the bottom and top faces of the plate as well as to the interface continuity conditions for the electromechanical variables. The continuity condition on the electric potential imposes some restrictions on the approximation of the electric potential. Moreover, the continuity condition on the normal component of the electric induction at the bimorph interface is ensured by a Lagrange multiplier. The equations of the piezoelectric bimorph are obtained by using variational formulation involving the appropriate boundary and continuity conditions.A selection of numerical illustrations is presented for the series and parallel piezoelectric bimorphs simply supported under cylindrical bending conditions. Two types of electromechanical load are considered (i) a surface density of force applied on the top face and (ii) an electric potential applied on the bottom and top faces of the bimorph. The results thus obtained are compared to those provided by finite element computations performed for the full 3D model and by a simplified model without shear effect. At last, the problem of piezoelectric bimorph vibration is also examined for both closed and open circuit conditions. Excellent predictions with low error estimates of the local (profile) and global responses as well as resonant frequencies are observed. The comparisons assess of the effectiveness of the present approach to piezoelectric bimorph.     

Predicting the elastic properties of single-walled carbon nanotubes

Advances in the prediction of the mechanical properties of single-walled carbon nanotubes (SWNTs) are reviewed in this paper. Based on the classical Cauchy-Born rule, a new computational method for the prediction of Young's modulus of SWNTs is investigated. Compared with the existing approaches, the developed method circumvents the difficulties of high computational efforts by taking into consideration of the microstructure of nanotube and the atomic potential of hydrocarbons. Numerical results of Young's modulus and its variation with respect to the deformation gradient tensor are given and discussed. The results obtained are in good agreement with those obtained by laboratory experiments and other numerical methods.     

Atomistic-continuum modeling for mechanical properties of single-walled carbon nanotubes

The study attempts to explore the influences of the surface effect resulting in an initial relaxed unstrained deformation and the in-layer non-bonded van der Waals (vdW) atomistic interactions on the mechanical properties of single-walled carbon nanotubes (SWCNTs) using a proposed atomistic-continuum modeling (ACM) approach. The modeling approach incorporates atomistic modeling, by virtue of molecular dynamics (MD) simulation, for simulating the initial unstrained equilibrium state, and equivalent-continuum modeling (ECM), by way of finite element approximations (FEA), for modeling the subsequent static/dynamic behaviors.SWCNTs with various radius and two different chiralities, including zigzag and armchair type, are presented. To validate the proposed technique, the present results are compared with the literature data, including numerical and experimental values. Results show that the derived elastic moduli (1.2–1.4 TPa) when considering these two nanoeffects tend to be more consistent with the published experimental data. In specific, they can increase up to 17–23% Young’s modulus, 5–15% shear modulus, 6–11% natural frequencies and 10–30% critical buckling load of the SWCNTs, implying that without considering these two effects, the material behaviors of SWCNTs would be potentially underestimated.     

单壁碳纳米管的扭转力学特性研究

利用基于高阶Cauchy-Born准则所建立的单壁碳纳米管本构模型,针对不同手性的单壁碳纳米管的扭转力学特性进行了研究.研究发现结构呈现对称性的锯齿型和扶手型单壁碳纳米管具有完全对称的扭转特性,而结构不对称的手性型单壁碳纳米管具有正反相异的扭转特性.同时,针对一系列手性不同的单壁碳纳米管的扭转力学特性展开了详细的研究.研究的部分结果与采用其他方法得到的结果进行了对比,证实了所提出方法以及预测结果的有效性和可行性.     

Facile synthesis and electrochemical properties of MnO2/carbon nanotubes

The poor electrical conductivity of MnO2 limits its use as an electrode material. To overcome this limitation, we report an easy and rapid approach to deposit nanosized MnO2 onto multi-wall carbon nanotubes functionalized with hydroxyl groups （MWCNTs-OH） by chemical reduction of KMnO4 with MnSO4 in aqueous solution under ambient conditions. Characterization with XRD and TEM reveals that the obtained MnO2/MWCNTs-OH composite is nanocrystalline and partially covered by Mn02 nanosheets with a thick- ness of 1-3 nm at a MnO2 loading of 20 wt%. Cyclic voltammetry （CV） and galvanostatic charge-discharge measurements reveal that the MnO2/MWCNTs-OH composite with a MnO2 loading of 20 wt% has a relatively high specific capacitance of 234 F/g at a scan rate of 2 mV/s and exhibits good cycling stability. Furthermore, the oxygen reduction reaction （ORR） shows that MnO2/MWCNTs-OH composite may have potential applications as a non-noble metal electrocatalyst in fuel cells and metal-air batteries.     

The coupled effects of mechanical deformation and electronic properties in carbon nanotubes

Coupled effects of mechanical and electronic behavior in single walled carbon nanotu besare investigated by using quantum mechanics and quantum molecular dynamics. It is found that external applied electric fields can cause charge polarization and significant geometric deformation in metallic and semi-metallic carbon nanotubes. The electric induced axial tension ratio can be up to 10% in the armchair tube and 8.5% in the zigzag tube. Pure external applied load has little effect on charge distribution，but indeed influences the energy gap. Tensile load leads to a narrower energy gap and compressive load increases the gap. When the CNT is tensioned under an external electric field, the effect of mechanical load on the electronic structures of the CNT becomes significant, and the applied electric field may reduce the critical mechanical tension load remarkably. Size effects are also discussed.     

Rheological properties and percolation in suspensions of multiwalled carbon nanotubes in polycarbonate

This paper is concerned with several issues related to the rheological behavior of polycarbonate/multiwalled carbon nanotube nanocomposites. The composites were prepared by diluting a masterbatch of 15 wt.% nanotubes using melt-mixing method, and the dispersion was analyzed by SEM, TEM, and AFM techniques. To understand the percolated structure, the nanocomposites were characterized via a set of rheological, electrical, and thermal conductivity measurements. The rheological measurements revealed that the structure and properties were temperature dependent; the percolation threshold was significantly lower at higher temperature suggesting stronger nanotube interactions. The nanotube networks were also sensitive to the steady shear deformation particularly at high temperature. Following preshearing, the elastic modulus decreased markedly suggesting that the nanotubes became more rigid. These results were analyzed using simple models for suspensions of rod-like particles. Finally, the rheological, electrical, and thermal conductivity percolation thresholds were compared. As expected, the rheological threshold was smaller than the thermal and electrical threshold.     

Lithium-storage properties of SiO2 nanotubes@C using carbon nanotubes as templates

Silica-based anode material is the most concerned material at present, which has the advantages of good cycle stability, high theoretical specific capacity and abundant reserves. However, silica suffers from inherent low conductivity, severe volume expansion effect and low initial coulombic efficiency, which limits its application in lithium-ion batteries. Nanotubes structure can mitigate the volume expansion during lithiation/delithiation. In this article, silica nanotubes (SNTs) were prepared using carbon nanotubes (CNTs) as a template, and then the uniform carbon layer was coated on their surface by carbonization of citric acid. The hollow structure of nanotubes provides more sites for the insertion of Li⁺ during lithiation and additional channels for Li⁺ migration in the cycles, which improves the electrochemical performance. Conductivity can be enhanced by coating carbon layer. The specific capacity of the composite material is about 650 mAh g⁻¹ at 0.1 A g⁻¹ after 100 cycles. With a specific capacity of 400 mAh g⁻¹ even at 1 A g⁻¹ after 100 cycles. The silica-based material is a competitive anode material for lithium-ion batteries.     

Mechanical properties and deformation morphologies of covalently bridged multi-walled carbon nanotubes: Multiscale modeling

We formulate a multiscale modeling framework to investigate the deformation morphologies and energetics of covalently bridged multi-walled carbon nanotubes (MWCNTs). The formulation involves extending a previously established quasi-continuum model by incorporating the inter-wall bridging energy density function into the constitutive relations via message passing from fully atomistic simulations. Using the extended numerical model, we studied the mechanical responses of the 10-walled MWCNT with varying inter-wall bridge densities under torsion, bending, and uniaxial compression. Our simulation results show that the presence of inter-wall covalent bridges not only enhances the post-buckling rigidities of the MWCNTs, but also modifies the deformation morphologies and morphology pathways. For bending and uniaxial compression, we constructed in the space of bridge density and applied strain the deformation morphology phase diagram, where three phases, uniformly deformed phase, rippling pattern, and diamond-shaped pattern, are identified and separated by linear phase boundaries. We attribute the deformation phase transitions to the interplay of inter-wall and intra-wall interaction energies. The multiple shape transitions of MWCNTs and the elastic nature of the deformation suggest that MWCNTs can be designed as shape-memory nanodevices with tunable stabilities.     

An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes

An analytical molecular structural mechanics model for the prediction of mechanical properties of defect-free carbon nanotubes is developed by incorporating the modified Morse potential with an analytical molecular structural model. The developed model is capable of predicting Young’s moduli, Poisson’s ratios and stress–strain relationships of carbon nanotubes under tension and torsion loading conditions. Results on the mechanical properties of single-walled carbon nanotubes show that Young’s moduli of carbon nanotubes are sensitive to the tube diameter and the helicity. Young’s moduli of both armchair and zigzag carbon nanotubes increase monotonically and approach Young’s modulus of graphite when the tube diameter is increased. The nonlinear stress–strain relationships for defect-free nanotubes have been predicted, which gives a good approximation on the ultimate strength and strain to failure of nanotubes. Armchair nanotubes exhibit higher tensile strength than zigzag nanotubes but their torsion strengths are identical based on the present study. The present theoretical investigation provides a very simple approach to predict the mechanical properties of carbon nanotubes.     

On numerical techniques in CFD

Numerical techniques play an important role in CFD. Some of them are reviewed in this paper. The necessity of using high order difference scheme is demonstrated for the study of high Reynolds number viscous flow. Physical guide lines are provided for the construction of these high order schemes. To avoid unduly ad hoc tremtment in the boundary region the use of compact scheme is recommended because it has a small stencil size compared with the traditional finite difference scheme. Besides preliminary Fourier analysis shows the compact scheme can also yield better space resolution which makes it more suitable to study flow with multiscales e.g. turbulence. Other approaches such as perturbation method and finite spectral method are also emphasized. Typical numerical simulations were carried out. The first deals with Euler equations to show its capabilities to capture flow discontinuity. The second deals with Navier-Stokes equations studying the evolution of a mixing layer, the pertinent structures at different times are shown. Asymmetric break down occurs and also the appearance of small vortices. The project supported by the National Natural Science Foundation of China (No.19393100) The Lecture in Memory of Prof. Pei-Yuan Chou, Presented at the Eighth Asian Congress of Fluid Mechanics, Shenzhen, China, December 6–10, 1999     

The effects of chirality and boundary conditions on the mechanical properties of single-walled carbon nanotubes

The effects of chirality and boundary conditions on the elastic properties and buckling behavior of single-walled carbon nanotubes are investigated using atomistic simulations. The influences of the tube length and diameter are also included. It is found that the elastic properties of carbon nanotubes at small deformations are insensitive to the tube chirality and boundary conditions during compression. However, for large deformations occurred upon both compression and bending, the tube buckling behavior is shown to be very sensitive to both tube chirality and boundary conditions. Therefore, while the popular continuum thin shell model can be successfully applied to describe nanotube elastic properties at small deformation such as the Young’s modulus, it cannot correctly account for the buckling behavior. These results may allow better evaluation of nanotube mechanical properties via appropriate atomistic simulations.     

Analytical and numerical solutions of the Local Inertial Equations

Neglecting the convective terms in the Saint-Venant Equations (SVE) in flood hydrodynamic modelling can be done without a loss in accuracy of the simulation results. In this case the Local Inertial Equations (LInE) are obtained. Herein we present two analytical solutions for the Local Inertial Equations. The first is the classical instantaneous Dam-Break Problem and the second a steady state solution over a bump. These solutions are compared with two numerical schemes, namely the first order Roe scheme and the second order MacCormack scheme. Comparison between analytical and numerical results shows that the numerical schemes and the analytical solution converge to a unique solution. Furthermore, by neglecting the convective terms the original numerical schemes remain stable without the need for adding entropy correction, artificial viscosity or special initial conditions, as in the case of the full SVE.     

The influence of mechanical deformation on the electrical properties of single wall carbon nanotubes

Recent experimental studies and atomistic simulations have shown that carbon nanotubes (CNTs) display strong interplay between the mechanical deformation and electrical properties. We have developed a simple and accurate method to determine atom positions in a uniformly deformed CNT via a continuum analysis based on the interatomic potential. A shift vector is introduced to ensure the equilibrium of atoms. Such an approach, involving only three variables for the entire CNT, agrees very well with the molecular mechanics calculations. We then study the effect of mechanical deformation on the band gap change of single wall CNTs under tension, torsion, and combined tension/torsion via the k-space tight-binding method. Prior studies without this shift vector lead to significant overestimation of the band gap change. It is established that the conducting CNTs may easily become semi-conducting ones subject to mechanical deformation, but the semi-conducting CNTs never become conducting ones upon deformation.     

Analytical and numerical solutions for axisymmetric flow of nanofluid due to non-linearly stretching sheet

This article reports the laminar axisymmetric flow of nanofluid over a non-linearly stretching sheet. The model used for nanofluid contains the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The recently proposed boundary condition is considered which requires the mass flux of nanoparticles at the wall to be zero. Analytic solutions of the arising boundary value problem are obtained by optimal homotopy analysis method. Moreover the numerical solutions are computed by Keller–Box method. Both the solutions are found in excellent agreement. The behavior of Brownian motion on the fluid temperature and wall heat transfer rate is insignificant. Further the nanoparticle volume fraction distribution is found to be negative near the vicinity of the stretching sheet.     

Coarse-grained potentials of single-walled carbon nanotubes

We develop the coarse-grained (CG) potentials of single-walled carbon nanotubes (SWCNTs) in CNT bundles and buckypaper for the study of the static and dynamic behaviors. The explicit expressions of the CG stretching, bending and torsion potentials for the nanotubes are obtained by the stick-spiral and the beam models, respectively. The non-bonded CG potentials between two different CG beads are derived from analytical results based on the cohesive energy between two parallel and crossing SWCNTs from the van der Waals interactions. We show that the CG model is applicable to large deformations of complex CNT systems by combining the bonded potentials with non-bonded potentials. Checking against full atom molecular dynamics calculations and our analytical results shows that the present CG potentials have high accuracy. The established CG potentials are used to study the mechanical properties of the CNT bundles and buckypaper efficiently at minor computational cost, which shows great potential for the design of micro- and nanomechanical devices and systems.