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.     

Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium

In the present paper, the sinusoidal shear deformation plate theory (SDPT) is reformulated using the nonlocal differential constitutive relations of Eringen to analyze the bending and vibration of the nanoplates, such as single-layered graphene sheets, resting on two-parameter elastic foundations. The present SDPT is compared with other plate theories. The nanoplates are assumed to be subjected to mechanical and thermal loads. The equations of motion of the nonlocal model are derived including the plate foundation interaction and thermal effects. The governing equations are solved analytically for various boundary conditions. Nonlocal theory is employed to bring out the effect of the nonlocal parameter on the bending and natural frequencies of the nanoplates. The influences of nonlocal parameter, side-to-thickness ratio and elastic foundation moduli on the displacements and vibration frequencies are investigated.     

Mechanical properties of defective single-layered graphene sheets via molecular dynamics simulation

In this paper, the effects of two main types of structural defects, i.e. Stone–Wales and single vacancy, on the mechanical properties of single-layered graphene sheets (SLGSs) are investigated. To this end, molecular dynamics simulations based on the Tersoff–Brenner potential function and Nose–Hoover thermostat technique are implemented. The results obtained have revealed that the presence of defects significantly reduces the failure strain and the intrinsic strength of SLGSs, while it has a slight effect on Young’s modulus. Furthermore, the examination of loading in both armchair and zigzag directions demonstrated that SLGSs are slightly stronger in the armchair direction and defects have lower effect in this direction. Considering the fracture mechanism, the failure process of defective and perfect graphene sheets is also presented.     

Free vibration analysis of multi-layer graphene nanoribbons incorporating interlayer shear effect via molecular dynamics simulations and nonlocal elasticity

Free vibration of cantilever multi-layer graphene nanoribbons (MLGNRs) with interlayer shear effect is investigated using molecular dynamics simulations (MD) and nonlocal elasticity. Because of similarity of MLGNRs to sandwich structures, sandwich formulations are expressed in the nonlocal form. By comparing the first two frequencies of MLGNRs with various layers and lengths obtained using MD simulations with those of the nonlocal sandwich formulation; the nonlocal parameter is calibrated to match the results of two methods. The results reveal that the calibrated nonlocal parameter for predicting the second frequencies is dependent on the number of MLGNR layers, and it increases by increasing the number of layers.     

A nonlocal plate model incorporating interatomic potentials for vibrations of graphene with arbitrary edge conditions

This article presents analytical explicit frequency expressions for investigating the vibrations of single-layer graphene sheets (SLGSs). The interatomic potential is incorporated into a nonlocal continuum plate model through establishing a linkage between the strain energy density induced in the continuum and nonlocal plate constitutive relations. The model which is independent of scattered value of Young's modulus is then applied and explicit frequency formulas for the SLGSs with different edge conditions are derived using static deflection function of the nanoplate under uniformly distributed load. The reliability of the present formulation is verified by the results obtained by the molecular dynamics (MD) simulations and other research workers. The formulas are of a simple short form enabling quick and accurate evaluation of the frequency of the SLGSs and also simple calibration of scale coefficient by the use of MD simulations results.     

Stability and wrinkling of defective graphene sheets under shear deformation

The molecular dynamic simulation is performed to study the wrinkling behavior of a graphene sheet with a hole subjected to a shear loading at different temperatures. Wrinkling is inevitable under pure shear loading. Four different hole diameters of 0, 0.8, 1.6, and 3.2 nm are chosen in this simulation. The results show that the number of ridges increases with an increase of the width of the graphene sheet. The shear stress induced in the defective graphene sheet increases with increasing temperature. In addition, the shear modulus of the defective graphene sheet also increases with an increase of temperature.     

Rayleigh-Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions

Eringen's nonlocality is incorporated into the shell theory to include the small-scale effects on the axial buckling of single-walled carbon nanotubes (SWCNTs) with arbitrary boundary conditions. To this end, the Rayleigh-Ritz solution technique is implemented in conjunction with the set of beam functions as modal displacement functions. Then, molecular dynamics simulations are employed to obtain the critical buckling loads of armchair and zigzag SWCNTs, the results of which are matched with those of nonlocal shell model to extract the appropriate values of nonlocal parameter. It is found that in contrast to the chirality, boundary conditions have a considerable influence on the proper values of nonlocal parameter.     

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.     

导电石墨烯孔道内双电层结构的研究

为有效开发和利用新能源,人们迫切需要高性能的超级电容器提供能量的存储和转换.在超级电容器中双电层结构扮演着关键性的角色.本文利用分子动力学方法通过建立开放的石墨烯纳米孔道(1～2 nm),研究了KCl溶液在纳米孔道内的双电层结构,同时也比较了恒电量模拟(Q)和恒电势模拟法(U)下双电层结构的异同.结果表明在恒电势模拟法考虑了导电石墨烯壁的镜像作用使结果更符合实验中的材料系统.而石墨烯壁的镜像作用能额外吸附离子从而增强孔道内部的阴阳离子,这可能有助于电极电容的提升.通过对不同孔道高度的研究,本文发现水分子作为介电材料在水基超级电容器中发挥着决定性的作用.它能在很大程度上抵消不同离子和不同孔道高度下双电层的变化,从而在不同情况下获得了相似的电容.     

A hybrid continuum and molecular mechanics model for the axial buckling of chiral single-walled carbon nanotubes

The purpose of this study is to describe the axial buckling behavior of chiral single-walled carbon nanotubes (SWCNTs) using a combined continuum-atomistic approach. To this end, the nonlocal Flugge shell theory is implemented into which the nonlocal elasticity of Eringen incorporated. Molecular mechanics is used in conjunction with density functional theory (DFT) to precisely extract the effective in-plane and bending stiffnesses and Poisson's ratio used in the developed nonlocal Flugge shell model. The Rayleigh-Ritz procedure is employed to analytically solve the problem in the context of calculus of variation. The results generated from the present hybrid model are compared with those from molecular dynamics simulations as a benchmark of good accuracy and excellent agreement is achieved. The influences of small scale factor, commonly used boundary conditions and chirality on the critical buckling load are fully explored. It is indicated that the importance of the small length scale is affected by the type of boundary conditions considered.     

Sonochemical synthesis and fabrication of perovskite type calcium titanate interfacial nanostructure supported on graphene oxide sheets as a highly efficient electrocatalyst for electrochemical detection of chemotherapeutic drug

In green approaches for electrocatalyst synthesis, sonochemical methods play a powerful role in delivering the abundant surface areas and nano-crystalline properties that are advantageous to electrocatalytic detection. In this article, we proposed the sphere-like and perovskite type of bimetal oxides which are synthesized through an uncomplicated sonochemical procedure. As a yield, the novel calcium titanate (orthorhombic nature) nanoparticles (CaTiO₃ NPs) decorated graphene oxide sheets (GOS) were obtained through simple ultrasonic irradiation by a high-intensity ultrasonic probe (Titanium horn; 50 kHz and 60 W). The GOS/CaTiO₃ NC were characterized morphologically and chemically through the analytical methods (SEM, XRD, and EDS). Besides, as-prepared nanocomposites were modified on a GCE (glassy carbon electrode) and applied towards electrocatalytic and electrochemical sensing of chemotherapeutic drug flutamide (FD). Notably, FD is a crucial anticancer drug and also a non-steroidal anti-androgen chemical. Mainly, the designed and modified sensor has shown a wide linear range (0.015–1184 µM). A limit of detection was calculated as nanomolar level (5.7 nM) and sensitivity of the electrode is 1.073 μA μM⁻¹ cm⁻². The GOS/CaTiO₃ modified electrodes have been tested in human blood and urine samples towards anticancer drug detection.     

A general finite element model for numerical simulation of structure dynamics

A finite element model used to simulate the dynamics with continuum and discontinuum is presented. This new approach is conducted by constructing the general contact model. The conventional discrete element is treated as a standard finite element with one node in this new method. The one-node element has the same features as other finite elements, such as element stress and strain. Thus, a general finite element model that is consistent with the existed finite element model is set up. This new model is simple in mathematical concept and is straightforward to be combined into the existing standard finite element code. Numerical example demonstrates that this new approach is more effective to perform the dynamic process analysis in which the interactions among a large number of discrete bodies and continuum objects are included.     

用FS多体势模型模拟金属铜的冷却过程

采用常温、常压分子动力学模拟方法模拟了在周期性边界条件下由500个原子构成的液态Cu模型系统的凝固过程,考察了不同降温速率下液态Cu的凝固行为.模拟结果很好地重现了实验值.模拟中原子间作用势采用FS势,结构分析采用双体分布函数、对分析技术、内能、均方位移等方法,得到了原子体系微观结构组态变化的重要信息,并利用能量分析的方法对体系微观结构的变化进行了说明.