Behavior Of Single-layered Graphene Sheets Research Articles

Numerical analysis of single-layered graphene sheets by a mesh-free approach

The paper presents a numerical analysis of the behavior of single-layered graphene sheet (SLGS) using a mesh-free approach based on a nonlocal continuum plate model (NCPM). The adopted NCPM constructed by incorporating the nonlocal elasticity theory into the first order shear deformation elastic plate theory is able to capture small length scale effects. Through the NCPM, the SLGS is modeled as a continuous orthotropic nanoplate. the obtained nonlocal nonlinear partial differential equations completed by boundary conditions are solved numerically by a mesh-free approach associating the asymptotic numerical method with the mesh-free collocation method based on moving least square approximation. The effects of the small-scale parameter and aspect ratio on the nonlinear bending and post-buckling behaviors of SLGS are considered. Good agreement has been established between the obtained results and those of the literature.

Comparing quantum, molecular and continuum models for graphene at large deformations

In this paper, the validity and accuracy of three interatomic potentials and the continuum shell model of Ghaffari and Sauer [1] are investigated. The mechanical behavior of single-layered graphene sheets (SLGSs) under uniaxial stretching, biaxial stretching and pure bending is studied for this comparison. The validity of the molecular and continuum models is assessed by direct comparison with density functional theory (DFT) data available in the literature. The molecular simulations are carried out employing the MM3, Tersoff and REBO + LJ potentials. The continuum formulation uses an anisotropic hyperelastic material model in the framework of the geometrically exact Kirchhoff-Love shell theory and isogeometric finite elements. Results from the continuum model are in good agreement with those from DFT. The results from the MM3 potential agree well up to the point of material instability, whereas those from the REBO + LJ and Tersoff potentials agree only for small deformations. Only the Tersoff potential is found to yield auxetic response in SLGSs under uniaxial stretch. Additionally, the transverse vibration frequencies of a pre-stretched graphene sheet and a carbon nanocone are obtained using the continuum model and molecular simulations with the MM3 potential. The variations of the frequencies from these approaches agree within an error of ≈5%.

A comparison for the non-classical plate model based on axial buckling of single-layered graphene sheets

In this study, the size effect on the axial buckling behavior of single-layered graphene sheets embedded in elastic foundation is studied. Eringen’s non-local elasticity equations are incorporated into first-order shear deformation, higher-order shear deformation, and classical plate theories. Values of Winkler and Pasternak moduli parameters, side lengths of square SLGSs, non-local parameter and mode numbers are obtained from different non-local plate theories. It is shown that the axial buckling behavior is strongly dependent on non-local parameters and moduli which are different for different numbers and side lengths. Furthermore, we find that non-locality is more influential in first-order shear deformation than other non-local plate theories, especially in certain ranges of non-local parameters. Sensitivity indices are determined based on the Sobol method in their corresponding physical ranges.

Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory

ABSTRACTIn this article, the small-scale effect on the vibration behavior of orthotropic single-layered graphene sheets is studied based on the nonlocal Reddy's plate theory embedded in elastic medium considering initial shear stress. Elastic theory of the graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. To simulate the interaction between the graphene sheet and surrounding elastic medium we used both Winkler-type and Pasternak-type foundation models. The effects of initial shear stress and surrounding elastic medium and boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets are studied considering five different boundary conditions. Numerical approach of the obtained equation is derived by differential quadrature method. Effects of shear stress, nonlocal parameter, size of the graphene sheets, stiffness of surrounding elastic medium, and boundary conditions on vibration frequency rate are investigated. The results reveal that as the stiffness of the surrounding elastic medium increases, the nonlocal effect decreases. Further, the nonlocal effect increases as the size of the graphene sheet is decreased. It is also found that the frequency ratios decrease with an increase in vibration modes.

A Structural Mechanics Approach for the Vibrational Analysis of Single-Layered Graphene Sheets

A structural mechanics approach has been employed to analyze the vibrational behavior of single-layered graphene sheets. By adopting this approach, natural frequencies and mode shapes are obtained for different chirality and imposed boundary conditions. Numerical results from the implemented modeling are examined to provide predictive equations for fundamental frequencies of cantilevered and bridged graphene sheets. With the proposed equations, the natural frequencies can be predicted and are comparable to those obtained from theoretical consideration and experimental results.

Buckling analysis of graphene sheets embedded in an elastic medium based on the kp-Ritz method and non-local elasticity theory

Graphene finds application in nanoscale electronic devices, nano sensors and nanocomposites in which graphene sheets usually rest on an elastic medium. Buckling of graphene sheets can occur in such structures, which significantly influences its performance. Therefore, it is essential to investigate the buckling behavior of graphene for better engineering design and manufacture. The present work provides an element-free kp-Ritz framework to analyze the buckling behavior of graphene. The element-free kp-Ritz method is first implemented to investigate the buckling behavior of single-layered graphene sheets (SLGSs) embedded in elastic foundations, based on the classical plate theory (CLP), incorporating the non-local elasticity theory, which takes small effects into account when dealing with nanostructures. A Winkler-type model is adopted to simulate the functioning of the elastic medium. Numerical solutions for critical buckling loads of SLGSs are obtained by solving the governing differential equations derived from the principle of minimum potential energy using the element-free kp-Ritz method. The concepts of non-local parameter effects and non-local effects are distinguished. The influence of non-local parameters for both side length and aspect ratio on critical buckling loads of SLGSs is analyzed. Additionally, the effects of non-local parameters and the Winkler modulus parameter on the buckling patterns are discussed.

Impact behavior of single-layered graphene sheets based on analytical model and molecular dynamics simulation

A dynamic analysis of impact of striker on single-layered graphene sheets (SLGSs) is investigated by using analytical spring-mass model and the molecular dynamics (MD) and finite element simulations.An analytical model is conducted to obtain the maximum dynamic deflections of a square and rectangular SLGSs with various values of side-length and striker parameter. The accuracy and stability of the present methods are verified by MD simulations and explicit finite element analysis.Effect of (i) chirality, (ii) graphene side-length, (iii) striker mass and (iv) striker velocity on the maximum dynamic deflections of graphene are investigated.The results show that chirality does not have a significant effect in impact behavior of SLGSs.It is found that the present spring-mass model have an excellent capability to predict the maximum dynamic deflections of SLGSs due to impact loading before fracture is occurred.

Nonlocal mass-nanosensor model based on the damped vibration of single-layer graphene sheet influenced by in-plane magnetic field

Nano-materials such as graphene sheets have a great opportunity to be applied in development of a new generation of nanomechanical sensors and devices due to their unique physical properties. Based on the nonlocal continuum theory and vibration analysis, the single-layered graphene sheet with attached nanoparticles affected by in-plane magnetic field is proposed as a new type of the mass-nanosensor. The nonlocal Kirchhoff-Love plate theory is adopted to describe mechanical behavior of single-layered graphene sheet as an orthotropic nanoplate. The equation of motion of a simply supported orthotropic nanoplate is derived, where the influence of Lorentz magnetic force is introduced through classical Maxwell׳s equations. Complex natural frequencies, damped frequency shifts and relative shift of damping ratio for nanoplate with attached nanoparticles are obtained in the explicit form. The influences of the nonlocal and magnetic field parameter, different mass weights and positions of attached nanoparticles and damping coefficients on the relative damped frequency shift and relative shift of damping ratio are examined. The presented results can be useful in the analysis and design of nanosensors applied in the presence of strong magnetic field. Our results show that magnetic field could be successfully used to improve sensibility performances of nanomechanical sensors.

Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into the different types of plate theory namely as classical plate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT). An exact solution is conducted to obtain the critical biaxial buckling loads of simply-supported square and rectangular SLGSs with various values of side-length and nonlocal parameter corresponding to each type of nonlocal plate model. Then, molecular dynamics (MD) simulations are performed for a series of armchair and zigzag SLGSs with different side-lengths, the results of which are matched with those obtained by the nonlocal plate models to extract the appropriate values of nonlocal parameter relevant to each type of nonlocal elastic plate model and chirality. It is found that the present nonlocal plate models with their proposed proper values of nonlocal parameter have an excellent capability to predict the biaxial buckling response of SLGSs.

Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory

Nonlocal elasticity theory is implemented to investigate the buckling behavior of single-layered graphene sheet (SLGS) embedded in an elastic medium. Nonlocal elasticity theory accounts for the small-size effects when dealing with nanostructures such as graphene sheets. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction between the graphene sheet and the surrounding elastic medium. Based on principle of virtual work, governing differential equations for the aforementioned problem are derived. Differential quadrature method is being employed and numerical solutions for the buckling loads of SLGS are obtained. Numerical results show that the buckling loads of SLGS are strongly dependent on the small scale coefficients and the stiffness of the surrounding elastic medium. With elastic medium modeled as Winkler-type foundation, the nonlocal effects are found to have decrease–increase–decrease pattern with increase in stiffness of elastic medium.

Vibrational analysis of single-layered graphene sheets

A molecular structural mechanics method has been implemented to investigate thevibrational behavior of single-layered graphene sheets. By adopting this approach, modeshapes and natural frequencies are obtained. Vibrational analysis is performed withdifferent chirality and boundary conditions. Numerical results from the atomistic modelingare employed to develop predictive equations via a statistical nonlinear regression model.With the proposed equations, fundamental frequencies of single-layered graphene sheetswith considered boundary conditions can be predicted within 3% difference with respect tothe atomistic simulation.