Nonlocal plate model for nonlinear bending of bilayer graphene sheets subjected to transverse loads in thermal environments (original) (raw)
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Computer Methods in Applied Mechanics and Engineering, 2013
Nonlinear transverse vibration response is investigated for bilayer graphene sheets (BLGSs) in thermal environments by using molecular dynamics simulation and nonlocal elasticity. The BLGS is modeled as a nonlocal double-layered plate which contains small scale effect and van der Waals interaction forces. The 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 simulations. The small scale parameter e 0 a is estimated by matching the natural frequencies of graphene sheets observed from the molecular dynamics simulation results with the numerical results obtained from the nonlocal plate model. The results show that the stacking sequence has a small effect, while the aspect ratio has a moderate effect on the nonlinear vibration response of BLGSs. In contrast, the temperature change has a significant effect on the nonlinear vibration response of BLGSs. The results reveal that the small scale effect also plays an important role in the nonlinear vibration of BLGSs.
2017
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 classical plate theory (CLPT). A Generalized Differential Quadrature Method (GDQM) approach is utilized and numerical solutions for the critical buckling loads are obtained. Then, molecular dynamics (MD) simulations are performed for a series of zigzag SLGSs with different side-lengths and with various boundary conditions, the results of which are matched with those obtained by the nonlocal plate model to numerical the appropriate values of nonlocal parameter relevant to each type of boundary conditions.
Applied Mathematical Modelling, 2014
Graphene-polymer nano-composites are one of the most applicable engineering nanostructures with superior mechanical properties. In the present study, a finite element (FE) approach based on the size dependent nonlocal elasticity theory is developed for buckling analysis of nanoscaled multi-layered graphene sheets (MLGSs) embedded in polymer matrix. The van der Waals (vdW) interactions between the graphene layers and graphene-polymer are simulated as a set of linear springs using the Lennard-Jones potential model. The governing stability equations for nonlocal classical orthotropic plates together with the weighted residual formulation are employed to explicitly obtain stiffness and buckling matrices for a multi-layered super element of MLGS. The accuracy of the current finite element analysis (FEA) is approved through a comparison with molecular dynamics (MD) and analytical solutions available in the literature. Effects of nonlocal parameter, dimensions, vdW interactions, elastic foundation, mode numbers and boundary conditions on critical in-plane loads are investigated for different types of MLGS. It is found that buckling loads of MLGS are generally of two types namely In-Phase (INPH) and Out-of-Phase (OPH) loads. The INPH loads are independent of interlayer vdW interactions while the OPH loads depend on vdW interactions. It is seen that the decreasing effect of nonlocal parameter on the OPH buckling loads dwindles as the interlayer vdW interactions become
Temperature-dependent elastic properties of single layer graphene sheets
Materials & Design, 2010
Elastic properties of single layer graphene sheets (SLGSs) with different values of aspect ratio are presented by using molecular dynamics simulation. SLGSs subjected to uniaxial tension, shear load and transverse uniform pressure are simulated under temperature varying from 300K to 700K. Based on the classical plate theory, an individual orthotropic plate model is adopted for SLGSs. By direct measuring the
The bending of single layer graphene sheets: the lattice versus continuum approach
Nanotechnology, 2010
The out-of-plane bending behaviour of single layer graphene sheets (SLGSs) is investigated using a special equivalent atomistic-continuum model, where the C-C bonds are represented by deep shear bending and axial stretching beams and the graphene properties by a homogenization approach. SLGS models represented by circular and rectangular plates are subjected to linear and nonlinear geometric point loading, similar to what is induced by an atomic force microscope (AFM) tip. The graphene models are developed using both a lattice Q.1 and a continuum finite element discretization of the partial differential equations describing the mechanics of the graphene. The minimization of the potential energy allows us to identify the thickness, elastic parameters and force/displacement histories of the plates, in good agreement with other molecular dynamic (MD) and experimental results. We note a substantial equivalence of the linear elastic mechanical properties exhibited by circular and rectangular sheets, while some differences in the nonlinear geometric elastic regime for the two geometrical configurations are observed. Enhanced flexibility of SLGSs is observed by comparing the nondimensional force versus displacement relations derived in this work and the analogous ones related to equivalent plates with conventional isotropic materials.
Mechanical properties of double-layered graphene sheets
Computational Materials Science, 2013
In this paper, the molecular structural mechanics method is employed to calculate the mechanical properties of a double-layered carbon graphene sheet more accurately. For this purpose, covalent bonds are modeled using nonlinear beam elements and van der Waals interactions are replaced by nonlinear truss elements. Morse potential and Lennard-Jones potential equations are used to simulate the covalent bonds and van der Waals interactions, respectively. For each atom, van der Waals forces are considered with respect to all the other atoms located in its cutoff radius. In addition to in-plane mechanical properties of single and double-layered graphene sheets some out-of-plane properties like the thickness-wise stiffness and shear modulus are studied. The results indicate that Young's modulus of a double-layered carbon graphene sheet decreases linearly with strain while Poisson's ratio is independent from it. Also it is noted that the thickness-wise stiffness significantly increases while the distance between the two layers declines however the shear modulus is independent from shear strain.
Physics Letters a, 2009
Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. The developed equations of motion have been applied to study buckling characteristics of nanoplates such as graphene sheets. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for critical buckling loads of the graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the small scale effect on the critical buckling load of graphene sheets. Effects of (i) nonlocal parameter, (ii) length, (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the critical buckling load have been investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the stability analysis of nanoplates and nanoshells.
Anisotropic Thermal and Mechanical Characteristics of Graphene: A Molecular Dynamics Study
Journal of Experimental and Theoretical Physics, 2019
In the present work, molecular dynamics simulation has been performed to characterize the thermal and mechanical behavior of graphene sheet. For this purpose, graphene sheet is subjected to dynamic heating process and its melting point has been predicted. Structural and thermal properties have been analyzed using radial distribution function and energy per atom. To analyze factors affecting melting temperature, four graphene sheets with different dimensions have been chosen for the dynamic heating process. The melting temperature of graphene decreases with increase in the sheet dimension, hence graphene sheet having smaller dimensions show relatively better thermal stability. To analyze the mechanical behavior, graphene sheet has been subjected to uniaxial tensile loading along zigzag and armchair directions respectively. It is observed that zigzag-oriented graphene sheet shows high fracture strength and stability as compared to armchair direction. Multilayer graphene sheets have been selected to investigate the effect of multilayers on the mechanical strength. It can be revealed from results that fracture strength decreases with increase in layers, however, brittleness of the sample relatively decreases with increase in a number of graphene layers.